source: vis_dev/glu-2.3/src/cuBdd/doc/cudd.ps @ 106

%!PS-Adobe-2.0
%%Creator: dvipsk 5.86 p1.5d Copyright 1996-2001 ASCII Corp.(www-ptex@ascii.co.jp)
%%based on dvipsk 5.86 Copyright 1999 Radical Eye Software (www.radicaleye.com)
%%Title: cudd.dvi
%%Pages: 48
%%PageOrder: Ascend
%%BoundingBox: 0 0 612 792
%%DocumentFonts: Times-Roman CMMI12 Times-Bold Times-Italic CMSY10 CMR10
%%+ CMMI10 CMMI8 Courier CMSY8 CMR8 Times-BoldItalic
%%EndComments
%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: dvips -Ppdf -o cudd.ps cudd
%DVIPSParameters: dpi=8000, compressed
%DVIPSSource:  TeX output 2005.05.17:2315
%%BeginProcSet: tex.pro
%!
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S
/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy
setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask
restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3
def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90
rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0
N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop
false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A
length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}
forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{
BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat
{BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch
round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0
rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B
/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}
B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p
-3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{
0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: alt-rule.pro
%!
% Patch by TVZ
% Makes dvips files draw rules with stroke rather than fill.
% Makes narrow rules more predictable at low resolutions
% after distilling to PDF.
% May have unknown consequences for very thick rules.
% Tested only with dvips 5.85(k).
TeXDict begin
/QV {
  gsave newpath /ruleY X /ruleX X
  Rx Ry gt
  { ruleX ruleY Ry 2 div sub moveto Rx 0 rlineto Ry }
  { ruleX Rx 2 div add ruleY moveto 0 Ry neg rlineto Rx }
  ifelse
  setlinewidth 0 setlinecap stroke grestore
} bind def
end

%%EndProcSet
%%BeginProcSet: texc.pro
%!
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3
def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90
rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0
N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop
false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A
length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}
forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{
BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat
{BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch
round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0
rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B
/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}
B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p
-3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{
0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: 8r.enc
% @@psencodingfile@{
%   author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry",
%   version = "0.6",
%   date = "1 July 1998",
%   filename = "8r.enc",
%   email = "tex-fonts@@tug.org",
%   docstring = "Encoding for TrueType or Type 1 fonts
%                to be used with TeX."
% @}
% 
% Idea is to have all the characters normally included in Type 1 fonts
% available for typesetting. This is effectively the characters in Adobe
% Standard Encoding + ISO Latin 1 + extra characters from Lucida.
% 
% Character code assignments were made as follows:
% 
% (1) the Windows ANSI characters are almost all in their Windows ANSI
% positions, because some Windows users cannot easily reencode the
% fonts, and it makes no difference on other systems. The only Windows
% ANSI characters not available are those that make no sense for
% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
% (173). quotesingle and grave are moved just because it's such an
% irritation not having them in TeX positions.
% 
% (2) Remaining characters are assigned arbitrarily to the lower part
% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
% 
% (3) Y&Y Lucida Bright includes some extra text characters; in the
% hopes that other PostScript fonts, perhaps created for public
% consumption, will include them, they are included starting at 0x12.
% 
% (4) Remaining positions left undefined are for use in (hopefully)
% upward-compatible revisions, if someday more characters are generally
% available.
% 
% (5) hyphen appears twice for compatibility with both 
% ASCII and Windows.
% 
/TeXBase1Encoding [
% 0x00 (encoded characters from Adobe Standard not in Windows 3.1)
  /.notdef /dotaccent /fi /fl
  /fraction /hungarumlaut /Lslash /lslash
  /ogonek /ring /.notdef
  /breve /minus /.notdef 
% These are the only two remaining unencoded characters, so may as
% well include them.
  /Zcaron /zcaron 
% 0x10
 /caron /dotlessi 
% (unusual TeX characters available in, e.g., Lucida Bright)
 /dotlessj /ff /ffi /ffl 
 /.notdef /.notdef /.notdef /.notdef
 /.notdef /.notdef /.notdef /.notdef
 % very contentious; it's so painful not having quoteleft and quoteright
 % at 96 and 145 that we move the things normally found there to here.
 /grave /quotesingle 
% 0x20 (ASCII begins)
 /space /exclam /quotedbl /numbersign
 /dollar /percent /ampersand /quoteright
 /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash
% 0x30
 /zero /one /two /three /four /five /six /seven
 /eight /nine /colon /semicolon /less /equal /greater /question
% 0x40
 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O
% 0x50
 /P /Q /R /S /T /U /V /W
 /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
% 0x60
 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o
% 0x70
 /p /q /r /s /t /u /v /w
 /x /y /z /braceleft /bar /braceright /asciitilde
 /.notdef % rubout; ASCII ends
% 0x80
 /.notdef /.notdef /quotesinglbase /florin
 /quotedblbase /ellipsis /dagger /daggerdbl
 /circumflex /perthousand /Scaron /guilsinglleft
 /OE /.notdef /.notdef /.notdef
% 0x90
 /.notdef /.notdef /.notdef /quotedblleft
 /quotedblright /bullet /endash /emdash
 /tilde /trademark /scaron /guilsinglright
 /oe /.notdef /.notdef /Ydieresis
% 0xA0
 /.notdef % nobreakspace
 /exclamdown /cent /sterling
 /currency /yen /brokenbar /section
 /dieresis /copyright /ordfeminine /guillemotleft
 /logicalnot
 /hyphen % Y&Y (also at 45); Windows' softhyphen
 /registered
 /macron
% 0xD0
 /degree /plusminus /twosuperior /threesuperior
 /acute /mu /paragraph /periodcentered
 /cedilla /onesuperior /ordmasculine /guillemotright
 /onequarter /onehalf /threequarters /questiondown
% 0xC0
 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
 /Egrave /Eacute /Ecircumflex /Edieresis
 /Igrave /Iacute /Icircumflex /Idieresis
% 0xD0
 /Eth /Ntilde /Ograve /Oacute
 /Ocircumflex /Otilde /Odieresis /multiply
 /Oslash /Ugrave /Uacute /Ucircumflex
 /Udieresis /Yacute /Thorn /germandbls
% 0xE0
 /agrave /aacute /acircumflex /atilde
 /adieresis /aring /ae /ccedilla
 /egrave /eacute /ecircumflex /edieresis
 /igrave /iacute /icircumflex /idieresis
% 0xF0
 /eth /ntilde /ograve /oacute
 /ocircumflex /otilde /odieresis /divide
 /oslash /ugrave /uacute /ucircumflex
 /udieresis /yacute /thorn /ydieresis
] def

%%EndProcSet
%%BeginProcSet: texps.pro
%!
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics
exch def dict begin 0 1 255{exch dup type/integertype ne{pop pop 1 sub
dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}
ifelse}for Metrics/Metrics currentdict end def[2 index currentdict end
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
end

%%EndProcSet
%%BeginProcSet: special.pro
%!
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
{userdict/md get type/dicttype eq{userdict begin md length 10 add md
maxlength ge{/md md dup length 20 add dict copy def}if end md begin
/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
save N userdict maxlength dict begin/magscale true def normalscale
currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{
psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2
roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath
moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict
begin/SpecialSave save N gsave normalscale currentpoint TR
@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{
CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto
closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx
sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR
}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse
CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury
lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N
/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end}
repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N
/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX
currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY
moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X
/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0
1 startangle endangle arc savematrix setmatrix}N end

%%EndProcSet
%%BeginProcSet: color.pro
%!
TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll
}repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def
/TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{
setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{
/currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch
known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC
/Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC
/Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0
setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0
setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61
0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC
/Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0
setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87
0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{
0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{
0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC
/Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0
setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0
setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90
0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC
/Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0
setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0
0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{
0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{
0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC
/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0
setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC
/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0
0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1
0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11
0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0
setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0
0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC
/Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0
setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0
0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0
1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC
/PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0
setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{
0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor}
DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70
setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0
setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1
setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end

%%EndProcSet
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueXX 5000791 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark

%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /minus put
dup 48 /prime put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueXX 5000818 def
currentdict end
currentfile eexec
9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352
05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23
b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a
f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145
d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a
5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8
7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345
191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc
430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474
5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5
08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d
98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b
b910bf03a69374e341e8036ff92c949f3dc6e86aaa7a2b795f6c8778f24792ad
3b0ad9c6860c74a28bd5d91131bfe67fa38e497a42cd07709200689bb41b5c9b
11035da5e0b62a2d3ce23c89aeefe2c24c73b0e3509fac65f9888b3892730acd
cbd2905eea435d89352ce710dd91bbe1c02d70578dea44c27b1a77e560211c8a
9dd7eae7a4a514a9a630cc563baff981603245ef41c66627cb4b7e32d3417dd9
2d48ea931d10c3731f8ea8f3918436b98bdc7b41a875605470d05b52cb5b0b25
be5ac20901f8b1ee2906ee7a3f4d1bf87dc869074fcbe5e96f88f86f87b1c62c
092d4d4aa3b4e81f49a97f49e01880050eda7d42d407798e9e4cbe668a22c7b8
c389a657838d0cdb143e20abbdde05d412eda26bcffc97f3cf9345582010ddb9
1a0463c27463fee0c760dd4b13bcf87775585912
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark

%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 110 /n put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueXX 5087383 def
currentdict end
currentfile eexec
80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98
74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730
48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f
15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff
da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427
bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3
038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225
dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c
db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03
6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0
d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68
7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0
09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe
6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058
86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d
5c9bed0dce7b63810f906b33ea4955531ca1ed1fc120cc56dc1e277a33222cc6
c3a97552607b865783faf0895cbeccd0df54f57bd162a88494768435eda71a39
69718c0c5912d3167bb0971546d733e735aa9bcd89f5aa154656031ab3f6fe41
94ec225ad03ab8b67a9da43ab365c4df17c23e79f685c3b6fd5b654e4a6f2603
6cec3a8641b0b57f93eb95f9e238832aeac2061f3153e0f375513c974f1c38f7
b59edcc94716f2862cf71c9a2be8430985da1cd813b1e1c1b9310564a2eb1aff
52c190f50fc981dccb64bb2c1f7a62c216f211c162c2ed1c554ef49fbaf12b31
aa3b2a80fee259dc0a2a4242869ddec7c29e2941792b28bba7f2c6f77ef69638
12b07d6843f33b51e01c8626b26edc34e1e0fffadede5fb468e8cd5de7e5a64c
366967578f415484d122834de4a647541d66989f7d8b25d1712d8d16729bd9a6
472c2338069b3c63f83a878e9d80592eb2f12293bb88d6202356c5a85c592db2
52a1e43015cc0490af29d8f1662e1ae0030e6bf9879975297b9c2e8f694126ec
882c698ccfc49d77b61dc7c2707163f0251f66666b71c4e4bede3645adde9a3c
a65f9d16b6753ed17612fa23896f0b45f3bdd8954b9ba679fe9ab54c4e162993
7e9b331bc08eb21fa64b36e6e0ddfb9aa275347b04d1f9eb036814290e751edc
98cab068a89b96ecaf655c7cd14a99d04e6a41bc4540dcf6a20d6252877fa203
08311a1383e00bec8313de63cbcefadff87a875031518dc2cefe94f12e18eaac
69d90c156b223c7ff539dc2f041d73295f54a4053d2056a9b070950b05a27e3d
bb13e903b715616c60d83a3414b8efbf5ec118f6d235293385fb43146f5c1bbd
7f80c9e447d606040c1fb658bfcd131d5031ce74005b9ad40e49c057fbea10ac
bec893532381ce15349ad2aff869c4372d2c9b2ea926234c1e004f3e4b3c8fbb
8806f089570dfcd2f82d693fc2231cbaadbc1399c6754d1165644e019f2705d0
de80f963dd28e73b0b2bc23661e1ae719472606a99849cbed827729c2959bf62
36b3569677329d8a98d3fcb1828d6715483d2f5e7238210c2c937820f7b35d86
ea3e3db65ab534f58feb033732bd686fa8ee6c25031bd3d0b8e9a10dab6603b4
041136448317e952eb979367c74df298de2369daf71ba92179b00afb417201a7
b6ae88690beead74630a89003cc55242295c5749531ea29d12edb18344f5fe60
773851b68367de9ab6b22e01412dccfedc8f766aadfba53f2bff0f37aaa317e2
720430b2e5d1abfac869588c788fac0f925647
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark

%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 59 /comma put
dup 76 /L put
dup 85 /U put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 110 /n put
dup 120 /x put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueXX 5087385 def
currentdict end
currentfile eexec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%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 53 /five put
dup 61 /equal put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueXX 5000793 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark

%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /minus put
dup 162 /periodcentered put
dup 178 /bullet put
dup 102 /braceleft put
dup 103 /braceright put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueXX 5000820 def
currentdict end
currentfile eexec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%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 178 /epsilon1 put
dup 60 /less put
dup 62 /greater put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueXX 5087386 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark

%%EndFont 
TeXDict begin 40258431 52099146 1000 8000 8000 (cudd.dvi)
@start /Fa 137[ 538 674 1[ 472 472 8[ 337 2[ 404 538
606 538 16[ 808 13[ 875 808 67[{ TeXBase1Encoding ReEncodeFont} 12
1212.12 /Times-BoldItalic rf /Fb 136[ 665 7[ 498 2[ 277
108[{ TeXBase1Encoding ReEncodeFont} 3 996.264 /Times-Italic
rf /Fc 204[ 470 470 470 470 48[{ } 4 885.568 /CMR8 rf
/Fd 207[ 255 47[ 732{ } 2 885.568 /CMSY8 rf /Fe 133[ 442
498 498 719 498 498 277 388 332 1[ 498 498 498 775 277
498 1[ 277 498 498 332 442 498 442 498 442 9[ 940 719
719 609 11[ 719 2[ 609 719 665 7[ 277 277 10[ 277 249
332 249 41[ 554 2[{ TeXBase1Encoding ReEncodeFont} 39
996.264 /Times-Roman rf /Ff 201[ 332 332 332 332 332
332 49[{ TeXBase1Encoding ReEncodeFont} 6 664.176 /Times-Roman
rf /Fg 201[ 443 443 443 443 443 443 49[{ TeXBase1Encoding ReEncodeFont}
6 885.568 /Times-Roman rf /Fh 130[ 727 727 727 727 727
727 727 727 727 727 727 727 727 727 727 727 727 727 727
727 727 727 727 727 727 727 727 727 727 1[ 727 1[ 727
727 727 727 1[ 727 1[ 727 727 727 727 727 727 727 727
727 727 727 2[ 727 727 727 727 727 727 727 727 727 727
727 727 727 727 727 727 727 727 727 727 727 727 727 727
727 727 727 727 727 727 727 727 727 727 2[ 727 1[ 727
727 727 33[{ TeXBase1Encoding ReEncodeFont} 84 1212.12
/Courier rf /Fi 133[ 590 664 1[ 959 664 739 442 517 590
739 739 664 739 1107 369 739 1[ 369 739 664 442 590 739
590 739 664 6[ 886 2[ 1328 959 959 886 739 959 1[ 812
1033 1[ 1254 886 1033 1[ 517 1033 1033 812 1[ 959 959
886 959 7[ 664 664 664 664 664 664 664 664 664 664 369
332 46[{ TeXBase1Encoding ReEncodeFont} 56 1328.35 /Times-Bold
rf /Fj 145[ 571 110[{ } 1 885.568 /CMMI8 rf /Fk 135[ 693
9[ 728 4[ 418 698 578 593 16[ 828 8[ 825 16[ 337 59[{ } 9
1212.12 /CMMI10 rf /Fl 194[ 943 7[ 606 2[ 606 606 606
4[ 943 1[ 471 471 40[{ } 8 1212.12 /CMR10 rf /Fm 152[ 606
606 86[ 606 13[ 337 1[{ } 4 1212.12 /CMSY10 rf /Fn 133[ 472
538 538 808 538 606 337 472 472 606 606 606 606 875 337
538 337 337 606 606 337 538 606 538 606 606 6[ 674 1[ 741
1010 741 875 674 606 741 875 741 875 808 1010 674 808
538 404 875 875 741 741 875 808 741 741 7[ 606 1[ 606
3[ 606 606 606 2[ 303 404 3[ 404 404 404 35[ 606 606
2[{ TeXBase1Encoding ReEncodeFont} 63 1212.12 /Times-Italic
rf /Fo 87[ 404 16[ 1212 606 1[ 538 538 24[ 538 606 606
875 606 606 337 472 404 606 606 606 606 943 337 606 337
337 606 606 404 538 606 538 606 538 3[ 404 1[ 404 741
875 875 1144 875 875 741 674 808 875 674 875 875 1078
741 875 472 404 875 875 674 741 875 808 808 875 5[ 337
337 606 606 606 606 606 606 606 606 606 606 337 303 404
303 684 1[ 404 404 404 1[ 1010 33[ 674 674 2[{
TeXBase1Encoding ReEncodeFont} 82 1212.12 /Times-Roman
rf /Fp 105[ 606 27[ 538 606 606 875 606 674 404 472 538
1[ 674 606 674 1010 337 674 1[ 337 674 606 404 538 674
538 674 606 6[ 808 875 875 1212 875 875 808 674 875 1[ 741
943 875 1144 808 2[ 472 943 943 741 808 875 875 808 875
5[ 404 404 1[ 606 606 606 606 606 606 606 606 606 1[ 303
1[ 303 691 3[ 404 36[ 674 2[{ TeXBase1Encoding ReEncodeFont} 64
1212.12 /Times-Bold rf /Fq 135[ 797 1151 1[ 886 531 620
708 2[ 797 886 1328 443 886 1[ 443 886 797 531 708 886
708 1[ 797 11[ 1151 1063 1[ 1151 1[ 974 2[ 1505 3[ 620
1240 1240 2[ 1151 1151 1[ 1151 10[ 797 797 797 797 797
797 5[ 909 3[ 531 39[{ TeXBase1Encoding ReEncodeFont} 38
1594.02 /Times-Bold rf /Fr 193[ 1012 1[ 1012 60[{ } 2
1328.35 /CMMI12 rf /Fs 133[ 590 664 2[ 664 664 369 517
442 1[ 664 664 664 1033 369 2[ 369 1[ 664 442 590 664
590 664 590 11[ 959 1[ 739 5[ 1181 6[ 739 812 959 886
886 1[ 1223 8[ 664 1[ 664 2[ 664 664 664 1[ 332 1[ 332
44[{ TeXBase1Encoding ReEncodeFont} 36 1328.35 /Times-Roman
rf /Ft 140[ 744 637 2[ 956 956 1488 532 956 1[ 532 1[ 956
1[ 849 1[ 849 1[ 849 11[ 1381 2[ 1276 1[ 1064 11[ 1381
1276 8[ 532 5[ 956 1[ 956 956 2[ 478 46[{ TeXBase1Encoding ReEncodeFont}
22 1912.83 /Times-Roman rf end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 8000dpi
TeXDict begin

%%EndSetup
%%Page: 1 1
1 0 bop Black Black Black Black Ft 10724 12498 a(CUDD:) 478
b(CU) g(Decision) h(Diagram) g(P) -29 b(ackag) r(e) 20777
14933 y(Release) 479 b(2.4.1) p Fs 21909 18301 a(F) -20
b(abio) 332 b(Somenzi) 11977 19851 y(Department) h(of) f(Electrical) h
(and) f(Computer) h(Engineering) 16816 21400 y(Uni) -33
b(v) -20 b(ersity) 334 b(of) e(Colorado) h(at) f(Boulder) p
Fr 18774 22950 a(<) p Fs(F) -20 b(abio@Colorado.EDU) p
Fr(>) p Fs 22195 25644 a(May) 332 b(17,) g(2005) p Fq
5978 30874 a(Contents) p Fp 5978 33634 a(1) 1212 b(Intr) -22
b(oduction) 30847 b(4) 5978 36351 y(2) 1212 b(Ho) -12
b(w) 303 b(to) g(Get) f(CUDD) 27711 b(5) p Fo 7796 37857
a(2.1) 1273 b(The) 303 b(CUDD) g(P) -18 b(ackage) 1207
b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 2275 w(5) p Black 7796 39362 a(2.2) 1273 b(CUDD) 304
b(Friends) 1050 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h
(.) f(.) g(.) p Black 2275 w(5) p Black Fp 5978 42080
a(3) 1212 b(User') -45 b(s) 302 b(Manual) 29829 b(5) p
Fo 7796 43585 a(3.1) 1273 b(Compiling) 303 b(and) h(Linking) 678
b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black
2275 w(6) p Black 7796 45091 a(3.2) 1273 b(Basic) 303
b(Data) g(Structures) 648 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) h
(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f
(.) g(.) p Black 2275 w(6) p Black 10584 46596 a(3.2.1) 1454
b(Nodes) 540 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.)
g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h
(.) f(.) g(.) p Black 2275 w(6) p Black 10584 48102 a(3.2.2) 1454
b(The) 303 b(Manager) 777 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) h
(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f
(.) g(.) p Black 2275 w(7) p Black 10584 49607 a(3.2.3) 1454
b(Cache) 609 b(.) d(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h
(.) f(.) g(.) p Black 2275 w(8) p Black 7796 51113 a(3.3) 1273
b(Initializing) 303 b(and) g(Shutting) g(Do) -30 b(wn) 303
b(a) g(DdManager) 1016 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.)
f(.) g(.) p Black 2275 w(8) p Black 7796 52618 a(3.4) 1273
b(Setting) 303 b(P) -18 b(arameters) 1136 b(.) 606 b(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) h(.) f(.) g(.) p Black 2275 w(9) p Black
7796 54124 a(3.5) 1273 b(Constant) 303 b(Functions) 847
b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 2275 w(9) p Black 10584 55629 a(3.5.1) 1454 b(One,) 304
b(Logic) f(Zero,) f(and) i(Arithmetic) f(Zero) 542 b(.) 606
b(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black
2275 w(9) p Black 10584 57134 a(3.5.2) 1454 b(Prede\002ned) 304
b(Constants) 639 b(.) 606 b(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black
1669 w(10) p Black 10584 58640 a(3.5.3) 1454 b(Background) 440
b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(10) p Black 10584 60145 a(3.5.4) 1454 b(Ne) -30
b(w) 304 b(Constants) 838 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) h(.) f
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g
(.) p Black 1669 w(11) p Black 7796 61651 a(3.6) 1273
b(Creating) 303 b(V) -135 b(ariables) 346 b(.) 606 b(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(11) p
Black 10584 63156 a(3.6.1) 1454 b(Ne) -30 b(w) 304 b(BDD) f(and) h(ADD)
f(V) -135 b(ariables) 540 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(11) p
Black 10584 64662 a(3.6.2) 1454 b(Ne) -30 b(w) 304 b(ZDD) f(V) -135
b(ariables) 1043 b(.) 606 b(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black
1669 w(12) p Black 7796 66167 a(3.7) 1273 b(Basic) 303
b(BDD) h(Manipulation) 579 b(.) 606 b(.) g(.) g(.) g(.) g(.) h(.) f(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(12) p Black Black 25600 69672 a(1) p Black
90 rotate dyy eop
%%Page: 2 2
2 1 bop Black Black Fo 7796 7638 a(3.8) 1273 b(Basic) 303
b(ADD) g(Manipulation) 513 b(.) 606 b(.) g(.) g(.) g(.) g(.) h(.) f(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(13) p Black 7796 9143 a(3.9) 1273 b(Basic) 303
b(ZDD) g(Manipulation) 647 b(.) 606 b(.) g(.) g(.) g(.) g(.) h(.) f(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(14) p Black 7796 10649 a(3.10) 667 b(Con) -48
b(v) -18 b(erting) 303 b(ADDs) f(to) i(BDDs) f(and) g(V) -73
b(ice) 304 b(V) -135 b(ersa) 1126 b(.) 606 b(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(15) p Black
7796 12154 a(3.11) 667 b(Con) -48 b(v) -18 b(erting) 303
b(BDDs) g(to) g(ZDDs) f(and) i(V) -73 b(ice) 303 b(V) -135
b(ersa) 352 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f
(.) g(.) p Black 1669 w(15) p Black 7796 13660 a(3.12) 667
b(V) -135 b(ariable) 303 b(Reordering) h(for) e(BDDs) h(and) h(ADDs) 853
b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(16) p Black 7796 15165 a(3.13) 667 b(Grouping) 303
b(V) -135 b(ariables) 783 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h
(.) f(.) g(.) p Black 1669 w(19) p Black 7796 16671 a(3.14) 667
b(V) -135 b(ariable) 303 b(Reordering) h(for) e(ZDDs) 919
b(.) 606 b(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(20) p Black
7796 18176 a(3.15) 667 b(K) -30 b(eeping) 303 b(Consistent) g(V) -135
b(ariable) 303 b(Orders) g(for) f(BDDs) h(and) h(ZDDs) 613
b(.) 606 b(.) h(.) f(.) g(.) p Black 1669 w(21) p Black
7796 19682 a(3.16) 667 b(Hooks) 713 b(.) 606 b(.) g(.) h(.) f(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(21) p Black 7796 21187 a(3.17) 667 b(The) 303
b(SIS/VIS) f(Interf) -12 b(ace) 324 b(.) 606 b(.) g(.) g(.) g(.) g(.) g
(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) h(.) f(.) g(.) p Black 1669 w(22) p Black 10584 22693
a(3.17.1) 848 b(Using) 303 b(the) g(CUDD) h(P) -18 b(ackage) 304
b(in) f(SIS) 322 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) h(.) f(.) g(.) p Black 1669 w(22) p Black 7796 24198
a(3.18) 667 b(Writing) 303 b(Decision) g(Diagrams) f(to) h(a) h(File)
749 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) h(.) f(.) g(.) p Black 1669 w(23) p Black 7796 25704
a(3.19) 667 b(Sa) -24 b(ving) 303 b(and) g(Restoring) g(BDDs) 1041
b(.) 606 b(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(25) p
Black Fp 5978 28421 a(4) 1212 b(Pr) -22 b(ogrammer') -45
b(s) 302 b(Manual) 24937 b(25) p Fo 7796 29927 a(4.1) 1273
b(Compiling) 303 b(and) h(Linking) 678 b(.) 606 b(.) g(.) g(.) g(.) g
(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) h(.) f(.) g(.) p Black 1669 w(25) p Black 7796 31432
a(4.2) 1273 b(Reference) 303 b(Counts) 683 b(.) 606 b(.) g(.) g(.) g(.)
g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(25) p
Black 10584 32938 a(4.2.1) 1454 b(NULL) 303 b(Return) g(V) -135
b(alues) 541 b(.) 606 b(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.)
g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black
1669 w(26) p Black 10584 34443 a(4.2.2) p Fn 1454 w(Cudd) p
17161 34443 364 45 v 437 w(Recur) -12 b(siveDer) -45
b(ef) p Fo 480 w(vs.) p Fn 302 w(Cudd) p 29870 34443
V 437 w(Der) g(ef) p Fo 604 w(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.)
h(.) f(.) g(.) p Black 1669 w(27) p Black 10584 35949
a(4.2.3) 1454 b(When) 304 b(Increasing) e(the) i(Reference) f(Count) h
(is) e(Unnecessary) 1153 b(.) 606 b(.) p Black 1669 w(27) p
Black 10584 37454 a(4.2.4) 1454 b(Saturating) 303 b(Increments) g(and) g
(Decrements) 1183 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.)
p Black 1669 w(27) p Black 7796 38959 a(4.3) 1273 b(Complement) 304
b(Arcs) 478 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g
(.) p Black 1669 w(28) p Black 7796 40465 a(4.4) 1273
b(The) 303 b(Cache) 480 b(.) 607 b(.) f(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(28) p
Black 10584 41970 a(4.4.1) 1454 b(Cache) 305 b(Sizing) 842
b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(29) p Black 10584 43476 a(4.4.2) 1454 b(Local) 303
b(Caches) 710 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(30) p Black 7796 44981 a(4.5) 1273 b(The) 303
b(Unique) g(T) -97 b(able) 611 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) h(.) f(.) g(.) p Black 1669 w(30) p Black 7796
46487 a(4.6) 1273 b(Allo) -30 b(wing) 303 b(Asynchronous) f(Reordering)
814 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) h(.) f(.) g(.) p Black 1669 w(32) p Black 7796 47992
a(4.7) 1273 b(Deb) -24 b(ugging) 334 b(.) 607 b(.) f(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black
1669 w(33) p Black 7796 49498 a(4.8) 1273 b(Gathering) 303
b(and) g(Interpreting) g(Statistics) 816 b(.) 606 b(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(33) p Black 10584 51003 a(4.8.1) 1454 b(Non) 304
b(Modi\002able) f(P) -18 b(arameters) 1164 b(.) 606 b(.) g(.) g(.) g(.)
g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(34) p Black 10584 52509 a(4.8.2) 1454 b(Modi\002able) 303
b(P) -18 b(arameters) 827 b(.) 606 b(.) g(.) h(.) f(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
Black 1669 w(37) p Black 10584 54014 a(4.8.3) 1454 b(Extended) 304
b(Statistics) e(and) h(Reporting) 809 b(.) 606 b(.) g(.) g(.) g(.) g(.)
g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(39) p
Black 7796 55520 a(4.9) 1273 b(Guidelines) 303 b(for) f(Documentation)
952 b(.) 606 b(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(39) p
Black Fp 5978 58237 a(5) 1212 b(The) 303 b(C++) g(Interface) 27225
b(40) p Fo 7796 59743 a(5.1) 1273 b(Compiling) 303 b(and) h(Linking) 678
b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g
(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black
1669 w(40) p Black 7796 61248 a(5.2) 1273 b(Basic) 303
b(Manipulation) 714 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h
(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f
(.) g(.) p Black 1669 w(40) p Black Fp 5978 63966 a(6) 1212
b(Ackno) -12 b(wledgments) 27337 b(41) p Black Fo 25600
69672 a(2) p Black 90 rotate dyy eop
%%Page: 3 3
3 2 bop Black Black Fp 7796 7638 a(Refer) -22 b(ences) 31189
b(41) 7796 10356 y(Index) 33856 b(43) p Black Fo 25600
69672 a(3) p Black 90 rotate dyy eop
%%Page: 4 4
4 3 bop Black Black Fq 5978 7638 a(1) 1594 b(Intr) -29
b(oduction) p Fo 5978 10398 a(The) 360 b(CUDD) h(package) g(pro) -18
b(vides) 360 b(functions) f(to) i(manipulate) g(Binary) f(Decision) g
(Diagrams) 5978 11904 y(\(BDDs\)) 458 b([5) o(,) h(3],) 497
b(Algebraic) 459 b(Decision) g(Diagrams) f(\(ADDs\)) g([1) o(],) 497
b(and) 459 b(Zero-suppres) n(sed) 5978 13409 y(Binary) 428
b(Decision) h(Diagrams) f(\(ZDDs\)) e([12].) 751 b(BDDs) 429
b(are) f(used) g(to) h(represent) e(switching) 5978 14914
y(functions;) 456 b(ADDs) 406 b(are) g(used) g(to) g(represent) f
(function) h(from) p Fm 405 w(f) p Fl(0) p Fk(;) p Fl
202 w(1) p Fm(g) p Fj 35668 14475 a(n) p Fo 36700 14914
a(to) g(an) g(arbitrary) f(set.) 5978 16420 y(ZDDs) 268
b(represent) g(switching) h(functions) f(lik) -12 b(e) 269
b(BDDs;) 281 b(ho) -30 b(we) g(v) -18 b(er) -48 b(,) 274
b(the) -18 b(y) 269 b(are) g(much) g(more) g(ef) -30
b(\002-) 5978 17925 y(cient) 330 b(than) g(BDDs) h(when) f(the) h
(functions) e(to) i(be) f(represented) g(are) g(characteristic) g
(functions) 5978 19431 y(of) 395 b(cube) i(sets,) 418
b(or) 396 b(in) g(general,) 420 b(when) 396 b(the) h(ON-set) e(of) h
(the) h(function) f(to) g(be) g(represented) g(is) 5978
20936 y(v) -18 b(ery) 302 b(sparse.) 375 b(The) -18 b(y) 303
b(are) g(inferior) f(to) h(BDDs) g(in) g(other) g(cases.) 7859
22442 y(The) 384 b(package) h(pro) -18 b(vides) 384 b(a) g(lar) -22
b(ge) 385 b(set) e(of) h(operations) g(on) g(BDDs,) 405
b(ADDs,) f(and) 385 b(ZDDs,) 5978 23947 y(functions) 307
b(to) g(con) -48 b(v) -18 b(ert) 308 b(BDDs) g(into) f(ADDs) h(or) f
(ZDDs) h(and) g(vice) g(v) -18 b(ersa,) 308 b(and) g(a) g(lar) -22
b(ge) 308 b(assort-) 5978 25453 y(ment) 303 b(of) g(v) -30
b(ariable) 302 b(reordering) h(methods.) 7859 26958 y(The) g(CUDD) h
(package) g(can) g(be) f(used) g(in) g(three) g(w) -12
b(ays:) p Black Fm 7796 29202 a(\262) p Black Fo 606
w(As) 232 b(a) h(black) g(box.) 352 b(In) 232 b(this) g(case,) 247
b(the) 233 b(application) g(program) f(that) h(needs) f(to) h
(manipulate) 9008 30707 y(decision) 297 b(diagrams) g(only) g(uses) f
(the) h(e) -18 b(xported) 297 b(functions) g(of) g(the) g(package.) 374
b(The) 297 b(rich) 9008 32213 y(set) 303 b(of) g(functions) g(included)
h(in) g(the) f(CUDD) i(package) f(allo) -30 b(ws) 303
b(man) -18 b(y) 304 b(applications) f(to) 9008 33718
y(be) 280 b(written) h(in) f(this) g(w) -12 b(ay) -79
b(.) 369 b(Section) 280 b(3) h(describes) e(ho) -30 b(w) 280
b(to) h(use) f(the) g(e) -18 b(xported) 281 b(functions) 9008
35223 y(of) 315 b(the) h(package.) 413 b(An) 316 b(application) g
(written) f(in) h(terms) e(of) i(the) f(e) -18 b(xported) 316
b(functions) e(of) 9008 36729 y(the) 342 b(package) h(needs) f(not) g
(concern) h(itself) e(with) h(the) g(details) g(of) g(v) -30
b(ariable) 342 b(reordering,) 9008 38234 y(which) 303
b(may) h(tak) -12 b(e) 303 b(place) g(behind) h(the) f(scenes.) p
Black Fm 7796 40633 a(\262) p Black Fo 606 w(As) 333
b(a) g(clear) g(box.) 466 b(When) 334 b(writing) e(a) i(sophisticated) e
(application) i(based) f(on) g(decision) 9008 42138 y(diagrams,) 444
b(ef) -30 b(\002cienc) -18 b(y) 417 b(often) f(dictates) h(that) f
(some) h(functions) f(be) g(implemented) h(as) 9008 43644
y(direct) 448 b(recursi) -30 b(v) -18 b(e) 447 b(manipulation) i(of) e
(the) i(diagrams,) 484 b(instead) 448 b(of) g(being) g(written) g(in)
9008 45149 y(terms) 431 b(of) h(e) -18 b(xisting) 431
b(primiti) -30 b(v) -18 b(e) 432 b(functions.) 762 b(Section) 432
b(4) g(e) -18 b(xplains) 432 b(ho) -30 b(w) 432 b(to) g(add) g(ne) -30
b(w) 9008 46655 y(functions) 459 b(to) g(the) g(CUDD) h(package.) 846
b(It) 458 b(also) h(details) g(ho) -30 b(w) 460 b(to) f(write) g(a) g
(recursi) -30 b(v) -18 b(e) 9008 48160 y(function) 303
b(that) g(can) g(be) h(interrupted) f(by) g(dynamic) g(v) -30
b(ariable) 303 b(reordering.) p Black Fm 7796 50559 a(\262) p
Black Fo 606 w(Through) 255 b(an) h(interf) -12 b(ace.) 359
b(Object-oriented) 256 b(languages) g(lik) -12 b(e) 255
b(C++) h(and) f(Perl5) h(can) g(free) 9008 52064 y(the) 323
b(programmer) g(from) f(the) h(b) -24 b(urden) 323 b(of) g(memory) g
(management.) 436 b(A) 324 b(C++) e(interf) -12 b(ace) 9008
53570 y(is) 365 b(included) h(in) f(the) h(distrib) -24
b(ution) 364 b(of) h(CUDD.) i(It) e(automatically) h(frees) e(decision)
h(di-) 9008 55075 y(agrams) 379 b(that) g(are) g(no) g(longer) h(used) e
(by) i(the) f(application) h(and) f(o) -18 b(v) g(erloads) 379
b(operators.) 9008 56580 y(Almost) 440 b(all) g(the) g(functionality) g
(pro) -18 b(vided) 440 b(by) h(the) f(CUDD) h(e) -18
b(xported) 440 b(functions) g(is) 9008 58086 y(a) -24
b(v) -30 b(ailable) 402 b(through) g(the) g(C++) g(interf) -12
b(ace,) 426 b(which) 403 b(is) e(especially) h(recommended) h(for) 9008
59591 y(f) -12 b(ast) 406 b(prototyping.) 689 b(Section) 407
b(5) h(e) -18 b(xplains) 407 b(ho) -30 b(w) 407 b(to) g(use) g(the) h
(interf) -12 b(ace.) 688 b(A) 407 b(Perl5) g(in-) 9008
61097 y(terf) -12 b(ace) 482 b(also) f(e) -18 b(xists) 481
b(and) h(is) g(ditrib) -24 b(uted) 481 b(separately) -79
b(.) 913 b(\(See) 482 b(Section) g(2.2.\)) 912 b(Some) 9008
62602 y(applications) 303 b(de\002ne) g(their) g(o) -30
b(wn) 303 b(interf) -12 b(aces.) 375 b(See) 304 b(for) e(e) -18
b(xample) 303 b(Section) h(3.17.) 5978 64846 y(In) 378
b(the) h(follo) -30 b(wing,) 397 b(the) 379 b(reader) f(is) g(supposed)
h(to) f(be) h(f) -12 b(amiliar) 378 b(with) h(the) g(basic) f(ideas) h
(about) 5978 66351 y(decision) 303 b(diagrams,) f(as) h(found,) g(for) f
(instance,) h(in) g([3].) p Black 25600 69672 a(4) p
Black 90 rotate dyy eop
%%Page: 5 5
5 4 bop Black Black Fq 5978 7638 a(2) 1594 b(Ho) -16
b(w) 398 b(to) h(Get) f(CUDD) p Fi 5978 10442 a(2.1) 1328
b(The) 332 b(CUDD) g(P) -13 b(ackage) p Fo 5978 12766
a(The) 474 b(CUDD) h(package) h(is) e(a) -24 b(v) -30
b(ailable) 475 b(via) g(anon) -18 b(ymous) 474 b(FTP) g(from) g
(vlsi.Colorado.EDU.) 5978 14271 y(A) 385 b(compressed) g(tar) h(\002le)
g(named) p Fh 386 w(cudd-2.) r(4.1.tar) r(.gz) p Fo 386
w(can) g(be) g(found) g(in) f(directory) p Fh 5978 15777
a(pub) p Fo(.) 376 b(Once) 304 b(you) f(ha) -24 b(v) -18
b(e) 303 b(this) g(\002le,) p Black Black Fh 9008 18279
a(gzip) 728 b(-dc) g(cudd-) r(2.4.1.t) r(ar.gz) g(|) g(tar) g(xvf) g(-)
p Fo 5978 20780 a(will) 344 b(create) h(directory) p
Fh 345 w(cudd-2) r(.4.1) p Fo 346 w(and) g(its) f(subdirectories.) 500
b(These) 344 b(directories) g(con-) 5978 22286 y(tain) 397
b(the) h(decision) f(diagram) h(package,) 422 b(a) 398
b(fe) -30 b(w) 397 b(support) f(libraries,) 421 b(and) 397
b(a) h(to) -12 b(y) 398 b(application) 5978 23791 y(based) 281
b(on) g(the) g(decision) g(diagram) g(package.) 369 b(There) 281
b(is) f(a) i(README) e(\002le) h(with) g(instructions) 5978
25297 y(on) 426 b(con\002guration) g(and) g(installation) g(in) p
Fh 426 w(cudd-2) r(.4.1) p Fo(.) 745 b(Y) -133 b(ou) 426
b(can) h(use) f(a) g(compiler) g(for) 5978 26802 y(either) 303
b(ANSI) f(C) i(or) f(C++.) 7859 28308 y(Once) h(you) f(ha) -24
b(v) -18 b(e) 303 b(made) h(the) f(libraries) f(and) h(program,) g(you)
g(can) h(type:) p Black Black Fh 9008 30809 a(cd) 728
b(nanotra) r(v) 9008 32315 y(nanotr) r(av) f(-p) h(1) g(-autody) r(n) f
(-reor) r(dering) h(sifti) r(ng) g(-trav) 9008 33820
y(mult32) r(a.blif) p Fo 5978 36322 a(This) 236 b(will) h(run) f(a) h
(simple-minded) g(FSM) f(tra) -24 b(v) -18 b(ersal) 236
b(program.) 353 b(\(On) 237 b(a) g(200) h(MHz) e(PentiumPro) 5978
37828 y(\(TM) n(\),) 354 b(it) h(tak) -12 b(es) 354 b(about) h(6) f
(sec.\)) 529 b(The) 355 b(output) f(produced) h(by) f(the) h(program) f
(can) h(be) f(check) -12 b(ed) 5978 39333 y(ag) -6 b(ainst) 263
b(the) h(contents) g(of) p Fh 264 w(cudd-2) r(.4.1/nan) r(otrav/m) r
(ult32a.) r(out) p Fo(.) 363 b(More) 263 b(infor) -24
b(-) 5978 40838 y(mation) 230 b(on) h(the) p Fh 230 w(nanotr) r(av) p
Fo 231 w(program) e(can) i(be) g(found) f(in) p Fh 230
w(cudd-) r(2.4.1/na) r(notrav/) r(README) p Fo(.) 7859
42344 y(If) 336 b(you) h(w) -12 b(ant) 337 b(to) g(be) f(noti\002ed) h
(of) g(ne) -30 b(w) 336 b(releases) g(of) g(the) h(CUDD) h(package,) 346
b(send) 336 b(a) h(mes-) 5978 43849 y(sage) 303 b(to) p
Fh 303 w(Fabio@Co) r(lorado.) r(EDU) p Fo(.) p Fi 5978
47172 a(2.2) 1328 b(CUDD) 333 b(Friend) n(s) p Fo 5978
49496 a(T) -97 b(w) -12 b(o) 249 b(CUDD) h(e) -18 b(xtensions) 248
b(are) i(a) -24 b(v) -30 b(ailable) 249 b(via) h(anon) -18
b(ymous) 249 b(FTP) g(from) f(vlsi.Colorado.EDU.) p Black
Fm 7796 51997 a(\262) p Black Fn 606 w(P) -97 b(erlDD) p
Fo 372 w(is) 373 b(an) g(object-oriented) g(Perl5) f(interf) -12
b(ace) 373 b(to) g(CUDD.) g(It) g(is) f(or) -22 b(g) -6
b(anized) 373 b(as) g(a) 9008 53503 y(standard) 342 b(Perl) h(e) -18
b(xtension) 343 b(module.) 496 b(The) 342 b(Perl) h(interf) -12
b(ace) 343 b(is) f(at) h(a) g(some) -30 b(what) 343 b(higher) 9008
55008 y(le) -30 b(v) -18 b(el) 303 b(than) g(the) g(C++) g(interf) -12
b(ace,) 303 b(b) -24 b(ut) 303 b(it) g(is) f(not) h(as) g(complete.) p
Black Fm 7796 57510 a(\262) p Black Fn 606 w(DDcal) p
Fo 311 w(is) 308 b(a) i(graphic) f(BDD) h(calculator) f(based) g(on) h
(CUDD,) g(Perl-Tk,) g(and) f(dot.) 394 b(\(See) 9008
59015 y(Section) 303 b(3.18) g(for) g(information) f(on) p
Fn 304 w(dot) p Fo(.\)) p Fq 5978 62917 a(3) 1594 b(User') -59
b(s) 397 b(Manual) p Fo 5978 65677 a(This) 302 b(section) h(describes) f
(the) h(use) g(of) g(the) g(CUDD) h(package) g(as) e(a) i(black) f
(box.) p Black 25600 69672 a(5) p Black 90 rotate dyy
eop
%%Page: 6 6
6 5 bop Black Black Fi 5978 7638 a(3.1) 1328 b(Compiling) 332
b(and) g(Linking) p Fo 5978 9962 a(T) -97 b(o) 302 b(b) -24
b(uild) 303 b(an) g(application) h(that) f(uses) g(the) g(CUDD) h
(package,) g(you) f(should) g(add) p Black Black Fh 5978
12463 a(#include) 729 b("util.) r(h") 5978 13969 y(#include) g("cudd.) r
(h") p Fo 5978 16471 a(to) 410 b(your) h(source) f(\002les,) 438
b(and) 411 b(should) f(link) p Fh 411 w(libcud) r(d.a) p
Fo(,) p Fh 438 w(libmt) r(r.a) p Fo(,) p Fh 438 w(libst) r(.a) p
Fo(,) 438 b(and) p Fh 5978 17976 a(libutil.) r(a) p Fo
360 w(to) 360 b(your) g(e) -18 b(x) g(ecutable.) 547
b(\(All) 360 b(these) g(libraries) f(are) h(part) g(of) f(the) i
(distrib) -24 b(u) n(tion.\)) 5978 19482 y(Some) 254
b(platforms) g(require) g(speci\002c) h(compiler) f(and) h(link) -12
b(er) 255 b(\003ags.) 359 b(Refer) 255 b(to) f(the) p
Fh 255 w(Makefi) r(le) p Fo 5978 20987 a(in) 303 b(the) g(top) g(le) -30
b(v) -18 b(el) 303 b(directory) g(of) f(the) i(distrib) -24
b(u) n(tion.) 7859 22492 y(K) -30 b(eep) 257 b(in) f(mind) g(that) g
(whate) -30 b(v) -18 b(er) 255 b(\003ags) h(af) -30 b(fect) 255
b(the) h(size) g(of) g(data) g(structures\227f) n(or) g(instance) 5978
23998 y(the) g(\003ags) g(used) g(to) h(use) f(64-bit) g(pointers) g
(where) g(a) -24 b(v) -30 b(ailable\227must) 256 b(be) h(speci\002ed) f
(when) h(com-) 5978 25503 y(piling) 303 b(both) g(CUDD) h(and) f(the) g
(\002les) g(that) g(include) h(its) e(header) h(\002les.) p
Fi 5978 28826 a(3.2) 1328 b(Basic) 332 b(Data) h(Structur) -24
b(es) p Fp 5978 31150 a(3.2.1) 1212 b(Nodes) p Fo 5978
33473 a(BDDs,) 335 b(ADDs,) h(and) 329 b(ZDDs) f(are) h(made) g(of) g
(DdNode') -67 b(s.) 453 b(A) 329 b(DdNode) h(\(node) f(for) f(short\)) g
(is) g(a) 5978 34979 y(structure) 340 b(with) h(se) -30
b(v) -18 b(eral) 341 b(\002elds.) 490 b(Those) 341 b(that) g(are) g(of)
g(interest) g(to) g(the) h(application) f(that) h(uses) 5978
36484 y(the) 315 b(CUDD) i(package) f(as) g(a) f(black) h(box) g(are) g
(the) f(v) -30 b(ariable) 316 b(inde) -18 b(x,) 319 b(the) c(reference)
h(count,) j(and) 5978 37990 y(the) d(v) -30 b(alue.) 415
b(The) 316 b(remaining) g(\002elds) g(are) g(pointers) f(that) i
(connect) f(nodes) g(among) h(themselv) -18 b(es) 5978
39495 y(and) 303 b(that) g(are) g(used) g(to) g(implement) g(the) h
(unique) f(table.) 376 b(\(See) 303 b(Section) g(3.2.2.\)) 7859
41000 y(The) p Fn 339 w(inde) -24 b(x) p Fo 342 w(\002eld) 338
b(holds) g(the) g(name) h(of) f(the) h(v) -30 b(ariable) 338
b(that) g(labels) g(the) h(node.) 482 b(The) 338 b(inde) -18
b(x) 5978 42506 y(of) 477 b(a) h(v) -30 b(ariable) 478
b(is) f(a) h(permanent) g(attrib) -24 b(ute) 478 b(that) g(re\003ects) f
(the) h(order) f(of) h(creation.) 900 b(Inde) -18 b(x) 5978
44011 y(0) 337 b(corresponds) f(to) h(the) h(v) -30 b(ariable) 337
b(created) h(\002rst.) 477 b(On) 338 b(a) f(machine) h(with) g(32-bit) f
(pointers,) 345 b(the) 5978 45517 y(maximum) 265 b(number) g(of) g(v)
-30 b(ariables) 264 b(is) h(the) g(lar) -22 b(gest) 264
b(v) -30 b(alue) 266 b(that) f(can) g(be) g(stored) g(in) g(an) g
(unsigned) 5978 47022 y(short) 331 b(inte) -18 b(ger) 332
b(minus) g(1.) 463 b(The) 332 b(lar) -22 b(gest) 332
b(inde) -18 b(x) 332 b(is) g(reserv) -18 b(ed) 331 b(for) h(the) g
(constant) g(nodes.) 464 b(When) 5978 48528 y(64-bit) 282
b(pointers) g(are) g(used,) 287 b(the) 282 b(maximum) h(number) g(of) f
(v) -30 b(ariables) 282 b(is) g(the) g(lar) -22 b(gest) 282
b(v) -30 b(alue) 283 b(that) 5978 50033 y(can) 303 b(be) g(stored) g
(in) g(an) g(unsigned) g(inte) -18 b(ger) 303 b(minus) f(1.) 7859
51539 y(When) 359 b(v) -30 b(ariables) 357 b(are) h(reordered) f(to) h
(reduce) g(the) g(size) g(of) f(the) h(decision) g(diagrams,) 371
b(the) 5978 53044 y(v) -30 b(ariables) 374 b(may) h(shift) f(in) i(the)
f(order) -48 b(,) 392 b(b) -24 b(ut) 375 b(the) -18 b(y) 375
b(retain) g(their) g(indices.) 591 b(The) 375 b(package) h(k) -12
b(eeps) 5978 54550 y(track) 342 b(of) g(the) h(v) -30
b(ariable) 343 b(permutation) f(\(and) h(its) f(in) -48
b(v) -18 b(erse\).) 493 b(The) 343 b(application) g(is) f(not) g(af) -30
b(fected) 5978 56055 y(by) 303 b(v) -30 b(ariable) 303
b(reordering,) f(e) -18 b(xcept) 304 b(in) f(the) g(follo) -30
b(wing) 302 b(cases.) p Black Fm 7796 58557 a(\262) p
Black Fo 606 w(If) 229 b(the) i(application) g(uses) e(generators) h
(\() p Fn(Cudd) p 28073 58557 364 45 v 437 w(F) -127
b(or) -45 b(eac) -18 b(hCube) p Fo 230 w(and) p Fn 231
w(Cudd) p 39822 58557 V 437 w(F) -127 b(or) -45 b(eac) -18
b(hNode) p Fo 9008 60062 a(\)) 359 b(and) g(reordering) f(is) h
(enabled,) 373 b(then) 360 b(it) f(must) f(tak) -12 b(e) 359
b(care) h(not) f(to) g(call) g(an) -18 b(y) 359 b(operation) 9008
61568 y(that) 367 b(may) g(create) f(ne) -30 b(w) 367
b(nodes) g(\(and) f(hence) h(possibly) f(trigger) g(reordering\).) 566
b(This) 366 b(is) 9008 63073 y(because) 343 b(the) g(cubes) g(\(i.e.,)
353 b(paths\)) 342 b(and) h(nodes) g(of) g(a) g(diagram) g(change) h
(as) e(a) h(result) f(of) 9008 64579 y(reordering.) p
Black 25600 69672 a(6) p Black 90 rotate dyy eop
%%Page: 7 7
7 6 bop Black Black Black Fm 7796 7638 a(\262) p Black
Fo 606 w(If) 345 b(the) g(application) h(uses) p Fn 345
w(Cudd) p 22851 7638 364 45 v 437 w(bddConstr) -18 b(ain) p
Fo 345 w(and) 346 b(reordering) f(tak) -12 b(es) 345
b(place,) 357 b(then) 9008 9143 y(the) 303 b(property) g(of) p
Fn 302 w(Cudd) p 19213 9143 V 438 w(bddConstr) -18 b(ain) p
Fo 302 w(of) 303 b(being) g(an) g(image) h(restrictor) e(is) g(lost.)
7859 11645 y(The) 356 b(CUDD) g(package) g(relies) f(on) h(g) -6
b(arbage) 355 b(collection) h(to) g(reclaim) f(the) h(memory) f(used)
5978 13151 y(by) 456 b(diagrams) g(that) g(are) g(no) g(longer) g(in) h
(use.) 835 b(The) 456 b(scheme) g(emplo) -12 b(yed) 456
b(for) g(g) -6 b(arbage) 456 b(col-) 5978 14656 y(lection) 384
b(is) g(based) g(on) g(k) -12 b(eeping) 385 b(a) g(reference) f(count) g
(for) g(each) h(node.) 619 b(The) 384 b(references) g(that) 5978
16162 y(are) 332 b(counted) i(are) e(both) h(the) g(internal) g
(references) f(\(references) g(from) g(other) g(nodes\)) g(and) h(e) -18
b(x-) 5978 17667 y(ternal) 459 b(references) h(\(typically) f
(references) h(from) f(the) h(calling) g(en) -48 b(vironment\).) 846
b(When) 460 b(an) 5978 19173 y(application) 279 b(creates) g(a) h(ne)
-30 b(w) 279 b(BDD,) h(ADD,) f(or) g(ZDD,) g(it) h(must) e(increase) h
(its) g(reference) g(count) 5978 20678 y(e) -18 b(xplicitly) -79
b(,) 508 b(through) 468 b(a) f(call) h(to) p Fn 467 w(Cudd) p
22842 20678 V 437 w(Ref) p Fo(.) 868 b(Similarly) -79
b(,) 508 b(when) 468 b(a) g(diagram) f(is) g(no) g(longer) 5978
22183 y(needed,) 337 b(the) 331 b(application) g(must) e(call) p
Fn 331 w(Cudd) p 25046 22183 V 437 w(Recur) -12 b(siveDer) -45
b(ef) p Fo 506 w(\(for) 330 b(BDDs) g(and) h(ADDs\)) e(or) p
Fn 5978 23689 a(Cudd) p 8677 23689 V 437 w(Recur) -12
b(s) n(iveDer) -45 b(efZdd) p Fo 337 w(\(for) 302 b(ZDDs\)) g(to) h
(\223rec) -18 b(ycle\224) 303 b(the) h(nodes) e(of) h(the) g(diagram.)
7859 25194 y(T) -85 b(erminal) 478 b(nodes) g(carry) g(a) g(v) -30
b(alue.) 901 b(This) 477 b(is) g(especially) i(important) f(for) f
(ADDs.) 901 b(By) 5978 26700 y(def) -12 b(ault,) 357
b(the) 348 b(v) -30 b(alue) 347 b(is) f(a) h(double.) 508
b(T) -97 b(o) 347 b(change) h(to) f(something) g(dif) -30
b(fer) n(ent) 348 b(\(e.g.,) 357 b(an) 348 b(inte) -18
b(ger\),) 5978 28205 y(the) 263 b(package) h(must) f(be) g(modi\002ed) g
(and) h(recompiled.) 363 b(Support) 262 b(for) h(this) g(process) f(is)
g(currently) 5978 29711 y(v) -18 b(ery) 302 b(rudimentary) -79
b(.) p Fp 5978 32989 a(3.2.2) 1212 b(The) 304 b(Manager) p
Fo 5978 35313 a(All) 359 b(nodes) g(used) f(in) h(BDDs,) 374
b(ADDs,) f(and) 359 b(ZDDs) g(are) g(k) -12 b(ept) 359
b(in) g(special) g(hash) g(tables) g(called) 5978 36818
y(the) p Fn 465 w(unique) 466 b(tables) p Fo(.) 863 b(Speci\002cally)
-79 b(,) 506 b(BDDs) 466 b(and) g(ADDs) f(share) g(the) h(same) f
(unique) h(table,) 5978 38324 y(whereas) 292 b(ZDDs) f(ha) -24
b(v) -18 b(e) 293 b(their) f(o) -30 b(wn) 292 b(table.) 372
b(As) 292 b(the) h(name) f(implies,) i(the) f(main) f(purpose) g(of) g
(the) 5978 39829 y(unique) g(table) f(is) h(to) f(guarantee) h(that) g
(each) g(node) g(is) f(unique;) 296 b(that) c(is,) h(there) f(is) f(no)
g(other) h(node) 5978 41335 y(labeled) 284 b(by) g(the) g(same) f(v) -30
b(ariable) 284 b(and) g(with) g(the) g(same) g(children.) 369
b(This) 283 b(uniqueness) h(property) 5978 42840 y(mak) -12
b(es) 434 b(decision) h(diagrams) f(canonical.) 773 b(The) 434
b(unique) h(tables) g(and) g(some) g(auxiliary) g(data) 5978
44345 y(structures) 400 b(mak) -12 b(e) 401 b(up) h(the) f(DdManager) g
(\(manager) h(for) e(short\).) 670 b(Though) 401 b(the) h(application)
5978 45851 y(that) 342 b(uses) g(only) h(the) g(e) -18
b(xported) 342 b(functions) g(needs) h(not) f(be) h(concerned) g(with) g
(most) f(details) g(of) 5978 47356 y(the) 246 b(manager) -48
b(,) 258 b(it) 246 b(has) g(to) h(deal) g(with) f(the) h(manager) g(in)
f(the) h(follo) -30 b(wing) 246 b(sense.) 356 b(The) 247
b(application) 5978 48862 y(must) 353 b(initialize) h(the) g(manager) g
(by) g(calling) g(an) g(appropriate) g(function.) 528
b(\(See) 353 b(Section) h(3.3.\)) 5978 50367 y(Subsequently) -79
b(,) 281 b(it) c(must) e(pass) h(a) g(pointer) h(to) f(the) g(manager) h
(to) f(all) g(the) h(functions) f(that) g(operate) 5978
51873 y(on) 303 b(decision) g(diagrams.) 7859 53378 y(W) -48
b(ith) 382 b(the) g(e) -18 b(xception) 383 b(of) e(a) h(fe) -30
b(w) 382 b(statistical) f(counters,) 402 b(there) 382
b(are) f(no) i(global) f(v) -30 b(ariables) 5978 54884
y(in) 385 b(the) h(CUDD) g(package.) 623 b(Therefore,) 406
b(it) 385 b(is) g(quite) g(possible) g(to) g(ha) -24
b(v) -18 b(e) 386 b(multiple) f(managers) 5978 56389
y(simultaneously) 363 b(acti) -30 b(v) -18 b(e) 363 b(in) h(the) g
(same) f(application.) p Fg 28586 55949 a(1) p Fo 29642
56389 a(It) g(is) g(the) h(pointers) f(to) h(the) f(managers) 5978
57895 y(that) 303 b(tell) g(the) g(functions) g(on) g(what) g(data) g
(the) -18 b(y) 304 b(should) e(operate.) p Black 5978
58714 15940 45 v Ff 7383 59455 a(1) p Fe 7771 59878 a(The) 240
b(global) g(statistical) f(counters) h(are) g(used) g(locally;) j
(hence) e(the) -15 b(y) 240 b(are) g(compatible) h(with) f(the) g(use) g
(of) f(multi-) 5978 61095 y(ple) 249 b(managers.) p Black
Black Fo 25600 69672 a(7) p Black 90 rotate dyy eop
%%Page: 8 8
8 7 bop Black Black Fp 5978 7638 a(3.2.3) 1212 b(Cache) p
Fo 5978 9962 a(Ef) -30 b(\002) n(cient) 299 b(recursi) -30
b(v) -20 b(e) 298 b(manipulation) h(of) e(decision) h(diagrams) f
(requires) g(the) h(use) g(of) f(a) h(table) g(to) 5978
11467 y(store) 317 b(computed) h(results.) 419 b(This) 317
b(table) h(is) f(called) h(here) g(the) p Fn 318 w(cac) -18
b(he) p Fo 318 w(because) 318 b(it) g(is) f(ef) -30 b(fecti) g(v) -18
b(ely) 5978 12973 y(handled) 281 b(lik) -12 b(e) 282
b(a) f(cache) h(of) f(v) -30 b(ariable) 281 b(b) -24
b(ut) 281 b(limited) g(capacity) -79 b(.) 370 b(The) 281
b(CUDD) h(package) g(starts) e(by) 5978 14478 y(def) -12
b(ault) 376 b(with) h(a) g(small) f(cache,) 396 b(and) 377
b(increases) f(its) g(size) g(until) h(either) f(no) h(further) f
(bene\002t) h(is) 5978 15984 y(achie) -30 b(v) -18 b(ed,) 302
b(or) g(a) g(limit) g(size) g(is) f(reached.) 376 b(The) 302
b(user) f(can) i(in\003uence) f(this) g(polic) -18 b(y) 302
b(by) g(choosing) 5978 17489 y(initial) h(and) g(limit) g(v) -30
b(alues) 302 b(for) h(the) g(cache) h(size.) 7859 18994
y(T) -97 b(oo) 279 b(small) g(a) h(cache) g(will) f(cause) g(frequent) g
(o) -18 b(v) g(erwriting) 279 b(of) f(useful) h(results.) 367
b(T) -97 b(oo) 279 b(lar) -22 b(ge) 279 b(a) 5978 20500
y(cache) 285 b(will) g(cause) h(o) -18 b(v) g(erhead,) 288
b(because) e(the) f(whole) g(cache) h(is) f(scanned) g(e) -30
b(v) -18 b(ery) 285 b(time) g(g) -6 b(arbage) 5978 22005
y(collection) 314 b(tak) -12 b(es) 314 b(place.) 410
b(The) 314 b(optimal) h(parameters) f(depend) g(on) h(the) f
(speci\002c) h(application.) 5978 23511 y(The) 302 b(def) -12
b(ault) 303 b(parameters) g(w) -12 b(ork) 303 b(reasonably) g(well) g
(for) f(a) h(lar) -22 b(ge) 304 b(spectrum) e(of) h(applications.) 7859
25016 y(The) 418 b(cache) h(of) f(the) g(CUDD) g(package) h(is) f(used)
f(by) i(most) e(recursi) -30 b(v) -18 b(e) 417 b(functions) g(of) h
(the) 5978 26522 y(package,) 304 b(and) f(can) g(be) h(used) e(by) i
(user) -24 b(-) n(supplied) 303 b(functions) g(as) f(well.) 376
b(\(See) 303 b(Section) h(4.4.\)) p Fi 5978 29820 a(3.3) 1328
b(Initializing) 333 b(and) e(Shutting) h(Do) -13 b(wn) 332
b(a) g(DdManager) p Fo 5978 32143 a(T) -97 b(o) 353 b(use) h(the) h
(functions) e(in) h(the) h(CUDD) g(package,) 368 b(one) 354
b(has) g(\002rst) f(to) h(initialize) h(the) f(package) 5978
33649 y(itself) 302 b(by) h(calling) p Fn 303 w(Cudd) p
16521 33649 364 45 v 437 w(Init) p Fo(.) 376 b(This) 302
b(function) h(tak) -12 b(es) 303 b(four) f(parameters:) p
Black Fm 7796 36026 a(\262) p Black Fo 606 w(numV) -135
b(ars:) 362 b(It) 274 b(is) h(the) g(initial) g(number) g(of) f(v) -30
b(ariables) 275 b(for) f(BDDs) h(and) h(ADDs.) 366 b(If) 274
b(the) h(to-) 9008 37531 y(tal) 265 b(number) g(of) f(v) -30
b(ariables) 264 b(needed) i(by) f(the) g(application) g(is) f(kno) -30
b(wn,) 273 b(then) 265 b(it) f(is) h(slightly) 9008 39037
y(more) 274 b(ef) -30 b(\002cient) 274 b(to) h(create) f(a) h(manager) f
(with) h(that) f(number) h(of) f(v) -30 b(ariables.) 365
b(If) 274 b(the) g(num-) 9008 40542 y(ber) e(is) h(unkno) -30
b(wn,) 279 b(it) 272 b(can) h(be) g(set) g(to) g(0,) 278
b(or) 273 b(to) g(an) -18 b(y) 272 b(other) h(lo) -30
b(wer) 272 b(bound) h(on) g(the) g(number) 9008 42048
y(of) 374 b(v) -30 b(ariables.) 588 b(Requesting) 375
b(more) f(v) -30 b(ariables) 373 b(than) h(are) g(actually) h(needed) g
(is) e(not) h(in-) 9008 43553 y(correct,) 303 b(b) -24
b(ut) 303 b(is) f(not) h(ef) -30 b(\002cient.) p Black
Fm 7796 46005 a(\262) p Black Fo 606 w(numV) -135 b(arsZ:) 356
b(It) h(is) f(the) i(initial) f(number) g(of) f(v) -30
b(ariables) 357 b(for) f(ZDDs.) 537 b(See) 357 b(Sections) g(3.9) 9008
47511 y(and) 303 b(3.11) g(for) g(a) g(discussion) f(of) h(the) g(v) -30
b(alue) 303 b(of) g(this) f(ar) -22 b(gument.) p Black
Fm 7796 49963 a(\262) p Black Fo 606 w(numSlots:) 541
b(Determines) 385 b(the) i(initial) e(size) h(of) g(each) g(subtable) g
(of) f(the) i(unique) f(table.) 9008 51468 y(There) 362
b(is) g(a) h(subtable) g(for) f(each) i(v) -30 b(ariable.) 554
b(The) 363 b(size) g(of) f(each) h(subtable) g(is) f(dynami-) 9008
52974 y(cally) 334 b(adjusted) f(to) h(re\003ect) g(the) g(number) f
(of) h(nodes.) 467 b(It) 333 b(is) g(normally) h(O.K.) g(to) g(use) f
(the) 9008 54479 y(def) -12 b(ault) 303 b(v) -30 b(alue) 303
b(for) f(this) h(parameter) -48 b(,) 302 b(which) i(is) e(CUDD) p
32620 54479 V 438 w(UNIQ) -12 b(UE) p 37691 54479 V 436
w(SLO) -48 b(T) n(S.) p Black Fm 7796 56931 a(\262) p
Black Fo 606 w(cacheSize:) 494 b(It) 361 b(is) g(the) h(initial) g
(size) f(\(number) h(of) f(entries\)) g(of) g(the) h(cache.) 552
b(Its) 361 b(def) -12 b(ault) 9008 58436 y(v) -30 b(alue) 303
b(is) g(CUDD) p 16524 58436 V 437 w(CA) -48 b(CHE) p
21020 58436 V 437 w(SLO) g(T) n(S.) p Black Fm 7796 60888
a(\262) p Black Fo 606 w(maxMemory:) 372 b(It) 297 b(is) f(the) h(tar)
-22 b(get) 297 b(v) -30 b(alue) 297 b(for) g(the) g(maximum) g(memory) g
(occupation) g(\(in) 9008 62394 y(bytes\).) 375 b(The) 303
b(package) h(uses) e(this) h(v) -30 b(alue) 303 b(to) g(decide) g(tw)
-12 b(o) 303 b(parameters.) p Black Fp 10462 64846 a(\226) p
Black Fo 607 w(the) 373 b(maximum) g(size) g(to) g(which) h(the) f
(cache) h(will) f(gro) -30 b(w) -79 b(,) 390 b(re) -18
b(g) -6 b(ardless) 372 b(of) h(the) g(hit) 11675 66351
y(rate) 303 b(or) f(the) h(size) g(of) g(the) g(unique) h(table.) p
Black 25600 69672 a(8) p Black 90 rotate dyy eop
%%Page: 9 9
9 8 bop Black Black Black Fp 10462 7638 a(\226) p Black
Fo 607 w(the) 245 b(maximum) h(size) f(to) g(which) h(gro) -30
b(wth) 245 b(of) g(the) h(unique) f(table) h(will) f(be) h(preferred)
11675 9143 y(to) 303 b(g) -6 b(arbage) 303 b(collection.) 9008
11645 y(If) 370 b(maxMemory) g(is) g(set) g(to) h(0,) 388
b(CUDD) 371 b(tries) f(to) g(guess) g(a) h(good) g(v) -30
b(alue) 371 b(based) f(on) h(the) 9008 13151 y(a) -24
b(v) -30 b(ailable) 303 b(memory) -79 b(.) 5978 15652
y(A) 303 b(typical) g(call) g(to) p Fn 303 w(Cudd) p
16756 15652 364 45 v 437 w(Init) p Fo 325 w(may) g(look) g(lik) -12
b(e) 303 b(this:) p Black Black Fh 7432 18154 a(manage) r(r) 727
b(=) h(Cudd_In) r(it\(0,0,) r(CUDD_UN) r(IQUE_SLO) r(TS,CUDD) r
(_CACHE_) r(SLOTS,0\)) r(;) p Fo 5978 20656 a(T) -97
b(o) 454 b(reclaim) g(all) h(the) f(memory) h(associated) f(with) g(a) h
(manager) -48 b(,) 492 b(an) 455 b(application) g(must) f(call) p
Fn 5978 22161 a(Cudd) p 8677 22161 V 437 w(Quit) p Fo(.) 376
b(This) 302 b(is) g(normally) h(done) g(before) g(e) -18
b(xiting.) p Fi 5978 25484 a(3.4) 1328 b(Setting) 332
b(P) -13 b(arameters) p Fo 5978 27807 a(The) 369 b(package) h(pro) -18
b(vides) 369 b(se) -30 b(v) -18 b(eral) 369 b(functions) g(to) g(set) g
(the) h(parameters) f(that) h(control) f(v) -30 b(arious) 5978
29313 y(functions.) 372 b(F) -18 b(or) 294 b(instance,) j(the) e
(package) h(has) f(an) g(automatic) g(w) -12 b(ay) 295
b(of) g(determining) g(whether) 5978 30818 y(a) 310 b(lar) -22
b(ger) 310 b(unique) g(table) h(w) -12 b(ould) 310 b(mak) -12
b(e) 310 b(the) h(application) f(run) g(f) -12 b(aster) -67
b(.) 397 b(In) 310 b(that) g(case,) i(the) e(pack-) 5978
32324 y(age) 238 b(enters) f(a) h(\223f) -12 b(ast) 237
b(gro) -30 b(wth\224) 238 b(mode) g(in) g(which) g(resizing) g(of) f
(the) h(unique) g(subtables) g(is) f(f) -12 b(a) -24
b(v) g(ored) 5978 33829 y(o) -18 b(v) g(er) 319 b(g) -6
b(arbage) 320 b(collection.) 427 b(When) 320 b(the) g(unique) g(table) h
(reaches) e(a) h(gi) -30 b(v) -18 b(en) 320 b(size,) k(ho) -30
b(we) g(v) -18 b(er) -48 b(,) 323 b(the) 5978 35335 y(package) 246
b(returns) f(to) h(the) g(normal) g(\223slo) -30 b(w) 246
b(gro) -30 b(wth\224) 245 b(mode,) 258 b(e) -30 b(v) -18
b(en) 246 b(though) g(the) g(conditions) g(that) 5978
36840 y(caused) 326 b(the) g(transition) f(to) h(f) -12
b(ast) 325 b(gro) -30 b(wth) 326 b(still) f(pre) -30
b(v) g(ail.) 444 b(The) 325 b(limit) h(size) g(for) f(f) -12
b(ast) 325 b(gro) -30 b(wth) 326 b(can) 5978 38346 y(be) 388
b(read) g(by) p Fn 388 w(Cudd) p 14283 38346 V 437 w(ReadLooseUpT) -112
b(o) p Fo 388 w(and) 388 b(changed) h(by) p Fn 388 w(Cudd) p
33935 38346 V 437 w(SetLooseUpT) -112 b(o) p Fo(.) 631
b(Similar) 5978 39851 y(pairs) 302 b(of) h(functions) f(e) -18
b(xist) 303 b(for) f(se) -30 b(v) -18 b(eral) 302 b(other) h
(parameters.) 375 b(See) 304 b(also) e(Section) i(4.8.) p
Fi 5978 43174 a(3.5) 1328 b(Constant) 332 b(Functions) p
Fo 5978 45497 a(The) 233 b(CUDD) h(P) -18 b(ackage) 234
b(de\002nes) f(se) -30 b(v) -18 b(eral) 233 b(constant) g(functions.)
353 b(These) 232 b(functions) h(are) h(created) 5978
47003 y(when) 303 b(the) g(manager) h(is) e(initialized,) i(and) f(are)
g(accessible) g(through) g(the) g(manager) g(itself.) p
Fp 5978 50281 a(3.5.1) 1212 b(One,) 303 b(Logic) h(Zer) -22
b(o,) 304 b(and) f(Arithmetic) f(Zer) -22 b(o) p Fo 5978
52605 a(The) 466 b(constant) g(1) g(\(returned) g(by) p
Fn 466 w(Cudd) p 23193 52605 V 437 w(ReadOne) p Fo(\)) h(is) e(common) i
(to) f(BDDs,) 508 b(ADDs,) f(and) 5978 54110 y(ZDDs.) 566
b(Ho) -30 b(we) g(v) -18 b(er) -48 b(,) 382 b(its) 366
b(meaning) h(is) f(dif) -30 b(ferent) 366 b(for) g(ADDs) g(and) h
(BDDs,) 383 b(on) 367 b(the) g(one) g(hand,) 5978 55616
y(and) 319 b(ZDDs,) j(on) c(the) h(other) g(hand.) 423
b(The) 319 b(diagram) f(consisting) g(of) h(the) g(constant) f(1) h
(node) g(only) 5978 57121 y(represents) 387 b(the) h(constant) h(1) f
(function) g(for) g(ADDs) g(and) h(BDDs.) 632 b(F) -18
b(or) 388 b(ZDDs,) 409 b(its) 388 b(meaning) 5978 58626
y(depends) 378 b(on) h(the) g(number) g(of) f(v) -30
b(ariables:) 527 b(It) 378 b(is) g(the) h(conjunction) g(of) g(the) g
(complements) f(of) 5978 60132 y(all) 442 b(v) -30 b(ariables.) 795
b(Con) -48 b(v) -18 b(ersely) -79 b(,) 477 b(the) 443
b(representation) f(of) h(the) g(constant) g(1) f(function) h(depends)
5978 61637 y(on) 351 b(the) g(number) g(of) g(v) -30
b(ariables.) 519 b(The) 351 b(constant) g(1) g(function) g(of) p
Fk 351 w(n) p Fo 350 w(v) -30 b(ariables) 351 b(is) f(returned) h(by) p
Fn 5978 63143 a(Cudd) p 8677 63143 V 437 w(ReadZddOne) p
Fo(.) p Black 25600 69672 a(9) p Black 90 rotate dyy
eop
%%Page: 10 10
10 9 bop Black Black Fo 7859 7638 a(The) 379 b(constant) f(0) g(is) g
(common) g(to) h(ADDs) f(and) g(ZDDs,) 397 b(b) -24 b(ut) 378
b(not) g(to) h(BDDs.) 601 b(The) 378 b(BDD) 5978 9143
y(logic) 257 b(0) g(is) p Fp 256 w(not) p Fo 256 w(associated) g(with) g
(the) g(constant) g(0) g(function:) 353 b(It) 256 b(is) g(obtained) i
(by) f(complemen-) 5978 10649 y(tation) 318 b(\() p Fn(Cudd) p
12160 10649 364 45 v 437 w(Not) p Fo 22 w(\)) g(of) g(the) h(constant) f
(1.) 422 b(\(It) 317 b(is) h(also) g(returned) g(by) p
Fn 318 w(Cudd) p 37282 10649 V 437 w(ReadLo) -12 b(gicZer) -55
b(o) p Fo(.\)) 5978 12154 y(All) 303 b(other) g(constants) f(are) h
(speci\002c) g(to) g(ADDs.) p Fp 5978 15433 a(3.5.2) 1212
b(Pr) -22 b(ede\002ned) 303 b(Constants) p Fo 5978 17756
a(Besides) 422 b(0) g(\(returned) f(by) p Fn 422 w(Cudd) p
20396 17756 V 437 w(ReadZer) -55 b(o) p Fo(\)) 422 b(and) h(1,) 452
b(the) 422 b(follo) -30 b(wing) 422 b(constant) g(functions) 5978
19262 y(are) 303 b(created) g(at) g(initialization) h(time.) p
Black 7493 21763 a(1.) p Black 606 w(PlusIn\002nity) 322
b(and) i(MinusIn\002nity:) 415 b(On) 323 b(computers) g(implementing) h
(the) f(IEEE) f(stan-) 9008 23269 y(dard) 501 b(754) f(for) h
(\003oating-point) f(arithmetic,) 550 b(these) 501 b(tw) -12
b(o) 501 b(constants) f(are) h(set) f(to) h(the) 9008
24774 y(signed) 230 b(in\002nities.) 351 b(On) 231 b(the) f(DEC) h
(Alphas,) 244 b(the) 231 b(option) p Fh 230 w(-ieee) r(_with_n) r
(o_inexac) r(t) p Fo 9008 26280 a(or) p Fh 440 w(-ieee_) r(with_in) r
(exact) p Fo 441 w(must) 440 b(be) h(passed) f(to) h(the) f(DEC) h
(compiler) f(to) h(get) 9008 27785 y(support) 313 b(of) h(the) g(IEEE) f
(standard.) 408 b(\(The) 313 b(compiler) h(still) g(produces) f(a) i(w)
-12 b(arning,) 316 b(b) -24 b(ut) 314 b(it) 9008 29291
y(can) 397 b(be) f(ignored.\)) 655 b(Compiling) 397 b(with) f(those) g
(options) g(may) h(cause) f(substantial) g(per) -24 b(-) 9008
30796 y(formance) 499 b(de) -18 b(gradation) 499 b(on) g(the) g(Ev) -24
b(olution) 499 b(IV) f(CPUs.) 964 b(\(Especially) 498
b(if) h(the) g(ap-) 9008 32302 y(plication) 428 b(does) f(use) g(the) h
(in\002nities.\)) 748 b(The) 427 b(problem) g(is) g(reportedly) g(solv)
-18 b(ed) 428 b(in) f(the) 9008 33807 y(Ev) -24 b(olution) 422
b(V) i(CPUs.) 736 b(If) p Fh 422 w(gcc) p Fo 424 w(is) 422
b(used) h(to) g(compile) h(CUDD) g(on) f(the) g(Alphas,) 453
b(the) 9008 35313 y(symbol) p Fh 329 w(HAVE) p 15888
35313 V 437 w(IEEE) p 19233 35313 V 438 w(754) p Fo 330
w(must) 329 b(be) g(unde\002ned.) 455 b(\(See) 330 b(the) f(Mak) -12
b(e\002le) 329 b(for) g(the) g(de-) 9008 36818 y(tails.\)) 499
b(The) 344 b(v) -30 b(alues) 345 b(of) f(these) g(constants) g(are) g
(returned) h(by) p Fn 344 w(Cudd) p 37384 36818 V 437
w(ReadPlusIn\002nity) p Fo 9008 38324 a(and) p Fn 303
w(Cudd) p 13760 38324 V 437 w(ReadMinusIn\002nity) p
Fo(.) p Black 7493 40825 a(2.) p Black 606 w(Epsilon:) 488
b(This) 359 b(constant,) 374 b(initially) 360 b(set) f(to) p
Fl 360 w(10) p Fd 29123 40385 a(\241) p Fc(12) p Fo 30851
40825 a(,) 374 b(is) 359 b(used) g(in) h(comparing) g(\003oating) 9008
42331 y(point) 338 b(v) -30 b(alues) 337 b(for) g(equality) -79
b(.) 481 b(Its) 337 b(v) -30 b(alue) 338 b(is) f(returned) h(by) p
Fn 338 w(Cudd) p 35858 42331 V 437 w(ReadEpsilon) p Fo(,) 345
b(and) 338 b(it) 9008 43836 y(can) 366 b(be) g(modi\002ed) g(by) g
(calling) p Fn 367 w(Cudd) p 25185 43836 V 437 w(SetEpsilon) p
Fo(.) 563 b(Unlik) -12 b(e) 366 b(the) g(other) g(constants,) 381
b(it) 9008 45342 y(does) 303 b(not) g(correspond) f(to) h(a) h(node.) p
Fp 5978 48620 a(3.5.3) 1212 b(Backgr) -22 b(ound) p Fo
5978 50944 a(The) 289 b(background) h(v) -30 b(alue) 290
b(is) f(a) h(constant) f(typically) h(used) f(to) h(represent) f(non-e)
-18 b(xisting) 289 b(arcs) g(in) 5978 52449 y(graphs.) 385
b(Consider) 306 b(a) h(shortest) e(path) i(problem.) 385
b(T) -97 b(w) -12 b(o) 307 b(nodes) f(that) g(are) h(not) f(connected) h
(by) g(an) 5978 53954 y(arc) 391 b(can) g(be) g(re) -18
b(g) -6 b(arded) 391 b(as) f(being) i(joined) f(by) g(an) g(arc) g(of) g
(in\002nite) g(length.) 639 b(In) 391 b(shortest) f(path) 5978
55460 y(problems,) 321 b(it) d(is) g(therefore) f(con) -48
b(v) -18 b(enient) 319 b(to) f(set) g(the) g(background) h(v) -30
b(alue) 318 b(to) g(PlusIn\002nity.) 420 b(In) 5978 56965
y(netw) -12 b(ork) 320 b(\003o) -30 b(w) 320 b(problems,) k(on) c(the) h
(other) f(hand,) 325 b(tw) -12 b(o) 320 b(nodes) g(not) h(connected) g
(by) f(an) h(arc) f(can) 5978 58471 y(be) 359 b(re) -18
b(g) -6 b(arded) 359 b(as) g(joined) h(by) g(an) f(arc) h(of) f(0) g
(capacity) -79 b(.) 546 b(F) -18 b(or) 359 b(these) g(problems,) 373
b(therefore,) g(it) 360 b(is) 5978 59976 y(more) 370
b(con) -48 b(v) -18 b(enient) 371 b(to) f(set) g(the) h(background) g
(v) -30 b(alue) 370 b(to) h(0.) 578 b(In) 370 b(general,) 388
b(when) 371 b(representing) 5978 61482 y(spars) n(e) 304
b(matrices,) e(the) i(background) f(v) -30 b(alue) 303
b(is) g(the) g(v) -30 b(alue) 303 b(that) g(is) g(assumed) f
(implicitly) -79 b(.) 7859 62987 y(At) 231 b(initialization,) 245
b(the) 231 b(background) f(v) -30 b(alue) 231 b(is) e(set) h(to) h(0.)
351 b(It) 230 b(can) h(be) f(read) h(with) p Fn 230 w(Cudd) p
43176 62987 V 437 w(ReadBac) -24 b(kgr) -55 b(ound) p
Fo(,) 5978 64493 y(and) 265 b(modi\002ed) h(with) p Fn
266 w(Cudd) p 17689 64493 V 437 w(SetBac) -24 b(kgr) -55
b(ound) p Fo(.) 363 b(The) 266 b(background) g(v) -30
b(alue) 265 b(af) -30 b(fects) 265 b(procedures) p Black
25297 69672 a(10) p Black 90 rotate dyy eop
%%Page: 11 11
11 10 bop Black Black Fo 5978 7638 a(that) 427 b(read) h(sparse) f
(matrices/graphs) g(\() p Fn(Cudd) p 25400 7638 364 45
v 437 w(addRead) p Fo 460 w(and) p Fn 428 w(Cudd) p 35410
7638 V 437 w(addHarwell) p Fo 1 w(\),) 459 b(proce-) 5978
9143 y(dures) 379 b(that) h(print) g(out) g(sum-of-) n(product) g(e) -18
b(xpressions) 379 b(for) g(ADDs) h(\() p Fn(Cudd) p 38091
9143 V 437 w(PrintMinter) n(m) p Fo(\),) 5978 10649 y(generators) 520
b(of) h(cubes) h(\() p Fn(Cudd) p 19463 10649 V 436 w(F) -127
b(or) -45 b(eac) -18 b(hCube) p Fo(\),) 576 b(and) 522
b(procedures) f(that) g(count) h(minterms) 5978 12154
y(\() p Fn(Cudd) p 9081 12154 V 436 w(CountMinterm) p
Fo(\).) p Fp 5978 15433 a(3.5.4) 1212 b(New) 303 b(Constants) p
Fo 5978 17756 a(Ne) -30 b(w) 260 b(constant) h(can) g(be) g(created) g
(by) f(calling) p Fn 261 w(Cudd) p 27636 17756 V 437
w(addConst) p Fo(.) 362 b(This) 260 b(function) g(will) h(retrie) -30
b(v) -18 b(e) 5978 19262 y(the) 397 b(ADD) h(for) f(the) g(desired) g
(constant,) 421 b(if) 397 b(it) h(already) f(e) -18 b(xist,) 421
b(or) 397 b(it) g(will) h(create) g(a) f(ne) -30 b(w) 398
b(one.) 5978 20767 y(Ob) -18 b(viously) -79 b(,) 303
b(ne) -30 b(w) 303 b(constants) f(should) h(only) g(be) g(used) g(when)
h(manipulating) f(ADDs.) p Fi 5978 24090 a(3.6) 1328
b(Cr) -24 b(eating) 333 b(V) -122 b(ariables) p Fo 5978
26413 a(Decision) 339 b(diagrams) g(are) h(typically) g(created) g(by) f
(combining) h(simpler) f(decision) h(diagrams.) 5978
27919 y(The) 282 b(simplest) f(decision) i(diagrams,) j(of) c(course,) k
(cannot) d(be) g(created) f(in) h(that) g(w) -12 b(ay) -79
b(.) 369 b(Constant) 5978 29424 y(functions) 296 b(ha) -24
b(v) -18 b(e) 297 b(been) g(discussed) f(in) h(Section) h(3.5.) 373
b(In) 297 b(this) g(section) f(we) i(discuss) d(the) i(simple) 5978
30930 y(v) -30 b(ariable) 302 b(functions,) h(also) g(kno) -30
b(wn) 303 b(as) p Fn 303 w(pr) -55 b(ojection) 303 b(functions) p
Fo(.) p Fp 5978 34208 a(3.6.1) 1212 b(New) 303 b(BDD) h(and) f(ADD) h
(V) -112 b(ariables) p Fo 5978 36532 a(The) 353 b(projection) h
(functions) f(are) h(distinct) f(for) g(BDDs) i(and) f(ADDs.) 527
b(A) 354 b(projection) g(function) 5978 38037 y(for) 296
b(BDDs) i(consists) e(of) h(an) h(internal) f(node) h(with) g(both) f
(outgoing) h(arcs) f(pointing) g(to) h(the) f(con-) 5978
39542 y(stant) 302 b(1.) 376 b(The) p Fn 303 w(else) p
Fo 303 w(arc) 303 b(is) f(complemented.) 7859 41048 y(An) 269
b(ADD) f(projection) g(function,) 275 b(on) 268 b(the) g(other) g
(hand,) 275 b(has) 268 b(the) p Fn 268 w(else) p Fo 268
w(pointer) g(directed) g(to) 5978 42553 y(the) 448 b(arithmetic) g
(zero) g(function.) 811 b(One) 448 b(should) g(ne) -30
b(v) -18 b(er) 448 b(mix) g(the) g(tw) -12 b(o) 448 b(types) g(of) g(v)
-30 b(ariables.) 5978 44059 y(BDD) 522 b(v) -30 b(ariables) 521
b(should) g(be) h(used) f(when) h(manipulating) g(BDDs,) 577
b(and) 522 b(ADD) g(v) -30 b(ariables) 5978 45564 y(should) 417
b(be) g(used) h(when) f(manipulating) h(ADDs.) 719 b(Three) 417
b(functions) g(are) h(pro) -18 b(vided) 417 b(to) h(cre-) 5978
47070 y(ate) 303 b(BDD) h(v) -30 b(ariables:) p Black
Fm 7796 49572 a(\262) p Black Fn 606 w(Cudd) p 11707
49572 V 437 w(bddIthV) -135 b(ar) p Fo 28 w(:) 493 b(Returns) 361
b(the) h(projection) g(function) g(with) g(inde) -18
b(x) p Fk 362 w(i) p Fo(.) 552 b(If) 361 b(the) h(func-) 9008
51077 y(tion) 303 b(does) g(not) g(e) -18 b(xist,) 302
b(it) h(is) g(created.) p Black Fm 7796 53579 a(\262) p
Black Fn 606 w(Cudd) p 11707 53579 V 437 w(bddNe) -18
b(wV) -135 b(ar) p Fo 28 w(:) 637 b(Returns) 433 b(a) h(ne) -30
b(w) 433 b(projection) g(function,) 466 b(whose) 434
b(inde) -18 b(x) 433 b(is) g(the) 9008 55084 y(lar) -22
b(gest) 303 b(inde) -18 b(x) 303 b(in) g(use) g(at) g(the) g(time) g
(of) g(the) g(call,) g(plus) g(1.) p Black Fm 7796 57586
a(\262) p Black Fn 606 w(Cudd) p 11707 57586 V 437 w(bddNe) -18
b(wV) -135 b(arAtLe) -18 b(vel) p Fo 1 w(:) 652 b(Similar) 440
b(to) p Fn 440 w(Cudd) p 30476 57586 V 437 w(bddNe) -18
b(w) r(V) -135 b(ar) p Fo(.) 788 b(In) 440 b(addition) h(it) f(al-) 9008
59091 y(lo) -30 b(ws) 360 b(to) h(specify) g(the) g(position) f(in) h
(the) g(v) -30 b(ariable) 361 b(order) g(at) g(which) g(the) g(ne) -30
b(w) 361 b(v) -30 b(ariable) 9008 60597 y(should) 341
b(be) h(inserted.) 492 b(By) 342 b(contrast,) p Fn 351
w(Cudd) p 27648 60597 V 437 w(bddNe) -18 b(wV) -135 b(ar) p
Fo 370 w(adds) 342 b(the) g(ne) -30 b(w) 341 b(v) -30
b(ariable) 342 b(at) 9008 62102 y(the) 303 b(end) g(of) g(the) g(order)
-67 b(.) 5978 64604 y(The) 438 b(analogous) h(functions) g(for) f(ADDs)
h(are) p Fn 439 w(Cudd) p 28612 64604 V 437 w(addIthV) -135
b(ar) p Fo(,) p Fn 472 w(Cudd) p 37299 64604 V 437 w(addNe) -18
b(wV) -135 b(ar) p Fo(,) 474 b(and) p Fn 5978 66110 a(Cudd) p
8677 66110 V 437 w(addNe) -18 b(wV) -135 b(arAtLe) -18
b(vel) p Fo(.) p Black 25297 69672 a(11) p Black 90 rotate
dyy eop
%%Page: 12 12
12 11 bop Black Black Fp 5978 7638 a(3.6.2) 1212 b(New) 303
b(ZDD) h(V) -112 b(ariables) p Fo 5978 9962 a(Unlik) -12
b(e) 411 b(the) g(projection) g(functions) g(of) f(BDDs) h(and) h
(ADDs,) 438 b(the) 411 b(projection) g(functions) f(of) 5978
11467 y(ZDDs) 277 b(ha) -24 b(v) -18 b(e) 279 b(diagrams) e(with) p
Fk 279 w(n) p Fl 178 w(+) 178 b(1) p Fo 276 w(nodes,) 283
b(where) p Fk 279 w(n) p Fo 278 w(is) 277 b(the) i(number) f(of) g(v)
-30 b(ariables.) 367 b(There-) 5978 12973 y(fore) k(the) i(ZDDs) f(of) g
(the) g(projection) h(functions) e(change) i(when) g(ne) -30
b(w) 373 b(v) -30 b(ariables) 371 b(are) i(added.) 5978
14478 y(This) 273 b(will) h(be) g(discussed) f(in) h(Section) g(3.9.)
366 b(Here) 274 b(we) h(assume) e(that) h(the) g(number) g(of) g(v) -30
b(ariables) 5978 15984 y(is) 302 b(\002x) -18 b(ed.) 376
b(The) 303 b(ZDD) g(of) f(the) p Fk 304 w(i) p Fo(-th) g(projection) h
(function) g(is) g(returned) f(by) p Fn 303 w(Cudd) p
39548 15984 364 45 v 437 w(zddIthV) -135 b(ar) p Fo(.) p
Fi 5978 19306 a(3.7) 1328 b(Basic) 332 b(BDD) h(Manipulation) p
Fo 5978 21630 a(Common) 441 b(manipulations) f(of) g(BDDs) g(can) h(be)
g(accomplished) f(by) h(calling) p Fn 440 w(Cudd) p 42064
21630 V 437 w(bddIte) p Fo(.) 5978 23135 y(This) 236
b(function) h(tak) -12 b(es) 237 b(three) g(BDDs,) p
Fk 250 w(f) p Fo 130 w(,) p Fk 252 w(g) p Fo 43 w(,) 251
b(and) p Fk 237 w(h) p Fo(,) g(as) 236 b(ar) -22 b(guments) 237
b(and) h(computes) p Fk 237 w(f) p Fm 156 w(\242) p Fk
25 w(g) p Fl 69 w(+) p Fk 25 w(f) p Fd 44129 22695 a(0) p
Fm 44465 23135 a(\242) p Fk 25 w(h) p Fo(.) 5978 24641
y(Lik) -12 b(e) 374 b(all) g(the) h(functions) f(that) h(create) f(ne)
-30 b(w) 375 b(BDDs) g(or) f(ADDs,) p Fn 392 w(Cudd) p
35994 24641 V 437 w(bddIte) p Fo 375 w(returns) f(a) i(re-) 5978
26146 y(sult) 390 b(that) h(must) g(be) g(e) -18 b(xplicitly) 391
b(referenced) g(by) g(the) g(caller) -67 b(.) p Fn 640
w(Cudd) p 34812 26146 V 437 w(bddIte) p Fo 391 w(can) 391
b(be) g(used) g(to) 5978 27652 y(implement) 409 b(all) g(tw) -12
b(o-ar) -22 b(gument) 409 b(boolean) h(functions.) 693
b(Ho) -30 b(we) g(v) -18 b(er) -48 b(,) 435 b(the) 409
b(package) h(also) f(pro-) 5978 29157 y(vides) p Fn 284
w(Cudd) p 11520 29157 V 437 w(bddAnd) p Fo 318 w(as) 285
b(well) g(as) f(the) i(other) e(tw) -12 b(o-operand) 285
b(boolean) h(functions,) i(which) d(are) 5978 30662 y(slightly) 389
b(more) i(ef) -30 b(\002cient) 390 b(when) h(a) f(tw) -12
b(o-operand) 391 b(function) f(is) g(called) h(for) -67
b(.) 637 b(The) 391 b(follo) -30 b(wing) 5978 32168 y(fragment) 291
b(of) h(code) g(illustrates) f(ho) -30 b(w) 292 b(to) g(b) -24
b(uild) 292 b(the) g(BDD) g(for) g(the) g(function) p
Fk 292 w(f) p Fl 467 w(=) p Fk 337 w(x) p Fd 41344 31728
a(0) p Fc 41344 32476 a(0) p Fk 41869 32168 a(x) p Fd
42562 31728 a(0) p Fc 42562 32476 a(1) p Fk 43088 32168
a(x) p Fd 43781 31728 a(0) p Fc 43781 32476 a(2) p Fk
44307 32168 a(x) p Fd 45000 31728 a(0) p Fc 45000 32476
a(3) p Fo 45525 32168 a(.) p Black Black Fh 11796 34670
a(DdManag) r(er) 727 b(*man) r(ager;) 11796 36175 y(DdNode) i(*f,) f
(*var,) g(*tmp;) 11796 37681 y(int) g(i;) 11796 40692
y(...) 11796 43702 y(f) f(=) h(Cudd_Re) r(adOne\(m) r(anager\)) r(;)
11796 45208 y(Cudd_Re) r(f\(f\);) 11796 46713 y(for) g(\(i) g(=) f(3;) h
(i) g(>=) f(0;) h(i--\)) h({) 14705 48219 y(var) f(=) f(Cudd) r
(_bddIthV) r(ar\(mana) r(ger,i\);) 14705 49724 y(tmp) h(=) f(Cudd) r
(_bddAnd\() r(manager) r(,Cudd_N) r(ot\(var\),) r(f\);) 14705
51230 y(Cudd_Re) r(f\(tmp\);) 14705 52735 y(Cudd_Re) r(cursive) r
(Deref\(m) r(anager,f) r(\);) 14705 54241 y(f) g(=) h(tmp;) 11796
55746 y(}) p Fo 5978 58248 a(This) 302 b(e) -18 b(xample) 303
b(illustrates) f(the) h(follo) -30 b(wing) 303 b(points:) p
Black Fm 7796 60750 a(\262) p Black Fo 606 w(Intermediate) 230
b(results) f(must) h(be) h(\223referenced\224) f(and) h
(\223dereferenced.) -85 b(\224) 231 b(Ho) -30 b(we) g(v) -18
b(er) -48 b(,) p Fh 244 w(var) p Fo 9008 62255 a(is) 463
b(a) h(projection) g(function,) 505 b(and) 464 b(its) f(reference) h
(count) g(is) f(al) -12 b(w) g(ays) 464 b(greater) g(than) g(0.) 9008
63761 y(Therefore,) 302 b(there) h(is) g(no) g(call) g(to) p
Fn 303 w(Cudd) p 25743 63761 V 437 w(Ref) p Fo(.) p Black
25297 69672 a(12) p Black 90 rotate dyy eop
%%Page: 13 13
13 12 bop Black Black Black Fm 7796 7638 a(\262) p Black
Fo 606 w(The) 317 b(ne) -30 b(w) p Fh 318 w(f) p Fo 318
w(must) 318 b(be) g(assigned) f(to) h(a) g(temporary) f(v) -30
b(ariable) 318 b(\() p Fh(tmp) p Fo 318 w(in) g(this) f(e) -18
b(xample\).) 9008 9143 y(If) 273 b(the) h(result) e(of) p
Fn 274 w(Cudd) p 18793 9143 364 45 v 437 w(bddAnd) p
Fo 306 w(were) i(assigned) f(directly) g(to) p Fh 274
w(f) p Fo(,) 280 b(the) 274 b(old) p Fh 273 w(f) p Fo
274 w(w) -12 b(ould) 274 b(be) 9008 10649 y(lost,) 302
b(and) i(there) f(w) -12 b(ould) 303 b(be) g(no) g(w) -12
b(ay) 304 b(to) f(free) f(its) h(nodes.) p Black Fm 7796
13103 a(\262) p Black Fo 606 w(The) g(statement) p Fh
303 w(f) 727 b(=) h(tmp) p Fo 304 w(has) 302 b(the) i(same) f(ef) -30
b(fect) 302 b(as:) p Black Black Fh 17735 15958 a(f) 728
b(=) f(tmp;) 17735 17464 y(Cudd_) r(Ref\(f\);) 17735
18969 y(Cudd_) r(Recursiv) r(eDeref\() r(manager,) r(tmp\);) p
Fo 9008 21825 a(b) -24 b(ut) 344 b(is) g(more) h(ef) -30
b(\002cient.) 500 b(The) 344 b(reference) h(is) f(\223passed\224) g
(from) p Fh 344 w(tmp) p Fo 346 w(to) p Fh 344 w(f) p
Fo(,) 355 b(and) p Fh 345 w(tmp) p Fo 346 w(is) 9008
23330 y(no) -30 b(w) 303 b(ready) g(to) g(be) g(reutilized.) p
Black Fm 7796 25784 a(\262) p Black Fo 606 w(It) 429
b(is) f(normally) h(more) g(ef) -30 b(\002cient) 429
b(to) g(b) -24 b(uild) 429 b(BDDs) g(\223bottom-up.) -85
b(\224) 430 b(This) e(is) h(wh) -6 b(y) 429 b(the) 9008
27290 y(loop) 273 b(goes) f(from) g(3) h(to) g(0.) 366
b(Notice,) 279 b(ho) -30 b(we) g(v) -18 b(er) -48 b(,) 278
b(that) 273 b(after) f(v) -30 b(ariable) 273 b(reordering,) 278
b(higher) 9008 28795 y(inde) -18 b(x) 404 b(does) g(not) g(necessarily)
g(mean) g(\223closer) g(to) g(the) h(bottom.) -85 b(\224) 404
b(Of) g(course,) 429 b(in) 405 b(this) 9008 30301 y(simple) 303
b(e) -18 b(xample,) 303 b(ef) -30 b(\002cienc) -18 b(y) 303
b(is) f(not) i(a) f(concern.) p Black Fm 7796 32754 a(\262) p
Black Fo 606 w(Had) 412 b(we) h(w) -12 b(anted) 412 b(to) g(conjoin) g
(the) h(v) -30 b(ariables) 411 b(in) h(a) g(bottom-up) g(f) -12
b(ashion) 412 b(e) -30 b(v) -18 b(en) 412 b(after) 9008
34260 y(reordering,) 300 b(we) h(should) f(ha) -24 b(v) -18
b(e) 301 b(used) p Fn 300 w(Cudd) p 27675 34260 V 437
w(ReadIn) -48 b(vP) -97 b(erm) p Fo(.) 374 b(One) 301
b(has) f(to) h(be) f(careful,) 9008 35765 y(though,) 346
b(to) 338 b(\002x) f(the) h(order) f(of) g(conjunction) h(before) g
(entering) f(the) h(loop.) 479 b(Otherwise,) 9008 37271
y(if) 432 b(reordering) g(tak) -12 b(es) 433 b(place,) 465
b(it) 433 b(is) f(possible) g(to) h(use) f(one) h(v) -30
b(ariable) 433 b(twice) g(and) g(skip) 9008 38776 y(another) 303
b(v) -30 b(ariable.) p Fi 5978 42075 a(3.8) 1328 b(Basic) 332
b(ADD) h(Manipulation) p Fo 5978 44399 a(The) 305 b(most) f(common) i
(w) -12 b(ay) 306 b(to) f(manipulate) h(ADDs) f(is) g(via) p
Fn 305 w(Cudd) p 33632 44399 V 437 w(addApply) p Fo(.) 383
b(This) 304 b(function) 5978 45904 y(can) 440 b(apply) h(a) f(wide) h
(v) -30 b(ariety) 440 b(of) g(operators) f(to) h(a) h(pair) f(of) g
(ADDs.) 787 b(Among) 441 b(the) f(a) -24 b(v) -30 b(ailable) 5978
47409 y(operators) 307 b(are) i(addition,) h(multiplication,) g(di) -30
b(vision,) 309 b(minimum,) h(maximum,) g(and) f(boolean) 5978
48915 y(operators) 302 b(that) h(w) -12 b(ork) 303 b(on) g(ADDs) g
(whose) g(lea) -24 b(v) -18 b(es) 303 b(are) g(restr) n(icted) h(to) f
(0) g(and) g(1) g(\(0-1) g(ADDs\).) 7859 50420 y(The) k(follo) -30
b(wing) 306 b(fragment) g(of) h(code) g(illustrates) e(ho) -30
b(w) 307 b(to) f(b) -24 b(uild) 307 b(the) g(ADD) g(for) f(the) h
(func-) 5978 51926 y(tion) p Fk 303 w(f) p Fl 467 w(=) 337
b(5) p Fk(x) p Fc 11806 52108 a(0) p Fk 12331 51926 a(x) p
Fc 13024 52108 a(1) p Fk 13550 51926 a(x) p Fc 14243
52108 a(2) p Fk 14768 51926 a(x) p Fc 15461 52108 a(3) p
Fo 15987 51926 a(.) p Black Black Fh 11796 54307 a(DdManag) r(er) 727
b(*man) r(ager;) 11796 55813 y(DdNode) i(*f,) f(*var,) g(*tmp;) 11796
57318 y(int) g(i;) 11796 60329 y(...) 11796 63340 y(f) f(=) h(Cudd_ad) r
(dConst\() r(manager) r(,5\);) 11796 64846 y(Cudd_Re) r(f\(f\);) 11796
66351 y(for) g(\(i) g(=) f(3;) h(i) g(>=) f(0;) h(i--\)) h({) p
Black Fo 25297 69672 a(13) p Black 90 rotate dyy eop
%%Page: 14 14
14 13 bop Black Black Fh 14705 7638 a(var) 728 b(=) f(Cudd) r(_addIthV)
r(ar\(mana) r(ger,i\);) 14705 9143 y(Cudd_Re) r(f\(var\);) 14705
10649 y(tmp) h(=) f(Cudd) r(_addAppl) r(y\(manag) r(er,Cudd) r
(_addTime) r(s,var,f) r(\);) 14705 12154 y(Cudd_Re) r(f\(tmp\);) 14705
13660 y(Cudd_Re) r(cursive) r(Deref\(m) r(anager,f) r(\);) 14705
15165 y(Cudd_Re) r(cursive) r(Deref\(m) r(anager,v) r(ar\);) 14705
16671 y(f) g(=) h(tmp;) 11796 18176 y(}) p Fo 5978 20512
a(This) 325 b(e) -18 b(xample,) 331 b(contrasted) 326
b(to) g(the) g(e) -18 b(xample) 326 b(of) g(BDD) g(manipulation,) 332
b(illustrates) 325 b(the) h(fol-) 5978 22017 y(lo) -30
b(wing) 303 b(points:) p Black Fm 7796 24353 a(\262) p
Black Fo 606 w(The) 281 b(ADD) g(projection) h(function) f(are) g(not) g
(maintained) h(by) f(the) g(manager) -67 b(.) 369 b(It) 281
b(is) g(there-) 9008 25858 y(fore) 302 b(necessary) h(to) g(reference) g
(and) g(dereference) g(them.) p Black Fm 7796 28293 a(\262) p
Black Fo 606 w(The) 230 b(product) g(of) g(tw) -12 b(o) 231
b(ADDs) f(is) g(computed) h(by) f(calling) p Fn 231 w(Cudd) p
35381 28293 364 45 v 437 w(addApply) p Fo 230 w(with) p
Fn 230 w(Cudd) p 45705 28293 V 437 w(addT) -67 b(imes) p
Fo 9008 29799 a(as) 250 b(parameter) -67 b(.) 358 b(There) 250
b(is) g(no) h(\223apply\224) g(function) f(for) g(BDDs,) 261
b(because) p Fn 251 w(Cudd) p 41661 29799 V 437 w(bddAnd) p
Fo 9008 31304 a(and) p Fn 266 w(Cudd) p 13723 31304 V
437 w(bddXor) p Fo 293 w(plus) 266 b(complementation) h(are) f(suf) -30
b(\002cient) 265 b(to) h(implement) g(all) g(tw) -12
b(o-) 9008 32810 y(ar) -22 b(gument) 303 b(boolean) h(functions.) p
Fi 5978 36099 a(3.9) 1328 b(Basic) 332 b(ZDD) h(Manipulation) p
Fo 5978 38423 a(ZDDs) 291 b(are) h(often) h(generated) f(by) h(con) -48
b(v) -18 b(erting) 291 b(e) -18 b(xisting) 292 b(BDDs.) 373
b(\(See) 292 b(Section) g(3.11.\)) 372 b(Ho) -30 b(w-) 5978
39928 y(e) g(v) -18 b(er) -48 b(,) 246 b(it) 233 b(is) f(also) h
(possible) f(to) h(b) -24 b(uild) 233 b(ZDDs) f(by) h(applying) g
(boolean) h(operators) e(to) h(other) g(ZDDs,) 5978 41434
y(starting) 345 b(from) h(constants) g(and) h(projection) f(functions.)
506 b(The) 346 b(follo) -30 b(wing) 346 b(fragment) h(of) f(code) 5978
42939 y(illustrates) 406 b(ho) -30 b(w) 408 b(to) g(b) -24
b(uild) 408 b(the) g(ZDD) f(for) h(the) g(function) p
Fk 407 w(f) p Fl 662 w(=) p Fk 531 w(x) p Fd 34158 42499
a(0) p Fc 34158 43247 a(0) p Fl 35030 42939 a(+) p Fk
347 w(x) p Fd 37013 42499 a(0) p Fc 37013 43247 a(1) p
Fl 37886 42939 a(+) p Fk 346 w(x) p Fd 39868 42499 a(0) p
Fc 39868 43247 a(2) p Fl 40741 42939 a(+) p Fk 347 w(x) p
Fd 42724 42499 a(0) p Fc 42724 43247 a(3) p Fo 43249
42939 a(.) 691 b(W) -97 b(e) 5978 44445 y(assume) 308
b(that) i(the) f(four) g(v) -30 b(ariables) 308 b(already) i(e) -18
b(xist) 309 b(in) g(the) g(manager) h(when) f(the) h(ZDD) f(for) p
Fk 309 w(f) p Fo 440 w(is) 5978 45950 y(b) -24 b(uilt.) 375
b(Note) 303 b(the) h(use) e(of) h(De) h(Mor) -22 b(g) -6
b(an') -67 b(s) 302 b(la) -18 b(w) -79 b(.) p Black Black
Fh 11796 48286 a(DdManag) r(er) 727 b(*man) r(ager;) 11796
49791 y(DdNode) i(*f,) f(*var,) g(*tmp;) 11796 51297
y(int) g(i;) 11796 54307 y(manager) h(=) e(Cudd) r(_Init\(0,) r
(4,CUDD_) r(UNIQUE_) r(SLOTS,) 26341 55813 y(CUDD_) r(CACHE_SL) r
(OTS,0\);) 11796 57318 y(...) 11796 60329 y(tmp) h(=) f(Cudd_) r
(ReadZdd) r(One\(man) r(ager,0\);) 11796 61835 y(Cudd_Re) r(f\(tmp\);)
11796 63340 y(for) h(\(i) g(=) f(3;) h(i) g(>=) f(0;) h(i--\)) h({)
14705 64846 y(var) f(=) f(Cudd) r(_zddIthV) r(ar\(mana) r(ger,i\);)
14705 66351 y(Cudd_Re) r(f\(var\);) p Black Fo 25297
69672 a(14) p Black 90 rotate dyy eop
%%Page: 15 15
15 14 bop Black Black Fh 14705 7638 a(f) 727 b(=) h(Cudd_z) r(ddInters)
r(ect\(man) r(ager,va) r(r,tmp\);) 14705 9143 y(Cudd_Re) r(f\(f\);)
14705 10649 y(Cudd_Re) r(cursive) r(DerefZd) r(d\(manage) r(r,tmp\);)
14705 12154 y(Cudd_Re) r(cursive) r(DerefZd) r(d\(manage) r(r,var\);)
14705 13660 y(tmp) g(=) f(f;) 11796 15165 y(}) 11796
16671 y(f) g(=) h(Cudd_zd) r(dDiff\(m) r(anager,) r(Cudd_Rea) r
(dZddOne) r(\(manage) r(r,0\),tmp) r(\);) 11796 18176
y(Cudd_Re) r(f\(f\);) 11796 19682 y(Cudd_Re) r(cursive) r(DerefZdd) r
(\(manage) r(r,tmp\);) p Fo 5978 22183 a(This) 302 b(e) -18
b(xample) 303 b(illustrates) f(the) h(follo) -30 b(wing) 303
b(points:) p Black Fm 7796 24685 a(\262) p Black Fo 606
w(The) k(projection) h(functions) g(are) f(referenced,) i(because) f
(the) -18 b(y) 308 b(are) g(not) g(maintained) g(by) 9008
26191 y(the) 303 b(manager) -67 b(.) p Black Fm 7796
28692 a(\262) p Black Fo 606 w(Complementation) 304 b(is) f(obtained) g
(by) g(subtracting) g(from) f(the) h(constant) g(1) h(function.) p
Black Fm 7796 31194 a(\262) p Black Fo 606 w(The) f(result) f(of) p
Fn 303 w(Cudd) p 18204 31194 364 45 v 437 w(ReadZddOne) p
Fo 303 w(does) h(not) g(require) g(referencing.) 5978
33696 y(CUDD) 426 b(pro) -18 b(vides) 425 b(functions) g(for) g(the) h
(manipulation) g(of) f(co) -18 b(v) g(ers) 425 b(represented) g(by) h
(ZDDs.) 5978 35201 y(F) -18 b(or) 529 b(instance,) p
Fn 586 w(Cudd) p 15733 35201 V 437 w(zddIsop) p Fo 529
w(b) -24 b(uilds) 529 b(a) h(ZDD) f(representing) h(an) g(irredundant) f
(sum) g(of) 5978 36707 y(products) 368 b(for) h(the) g(incompletely) h
(speci\002ed) f(function) g(de\002ned) h(by) f(the) g(tw) -12
b(o) 369 b(BDDs) p Fk 370 w(L) p Fo 369 w(and) p Fk 5978
38212 a(U) p Fo 132 w(.) p Fn 594 w(Cudd) p 10534 38212
V 437 w(zddW) -112 b(eakDiv) p Fo 377 w(performs) 375
b(the) h(weak) h(di) -30 b(vision) 375 b(of) h(tw) -12
b(o) 377 b(co) -18 b(v) g(ers) 375 b(gi) -30 b(v) -18
b(en) 376 b(as) g(ZDDs.) 5978 39718 y(These) 308 b(functions) g(e) -18
b(xpect) 308 b(the) h(tw) -12 b(o) 309 b(ZDD) f(v) -30
b(ariables) 308 b(corresponding) g(to) g(the) h(tw) -12
b(o) 309 b(literals) e(of) 5978 41223 y(the) 387 b(function) g(v) -30
b(ariable) 388 b(to) f(be) g(adjacent.) 630 b(One) 388
b(has) f(to) g(create) h(v) -30 b(ariable) 387 b(groups) f(\(see) h
(Sec-) 5978 42729 y(tion) 288 b(3.14\)) f(for) h(reordering) f(of) h
(the) g(ZDD) g(v) -30 b(ariables) 287 b(to) h(w) -12
b(ork.) 371 b(BDD) 288 b(automatic) h(reordering) 5978
44234 y(is) 400 b(safe) h(e) -30 b(v) -18 b(en) 401 b(without) h
(groups:) 572 b(If) 400 b(realignment) i(of) f(ZDD) g(and) h(ADD/BDD) g
(v) -30 b(ariables) 401 b(is) 5978 45740 y(requested) 302
b(\(see) h(Section) g(3.15\)) g(groups) g(will) g(be) g(k) -12
b(ept) 303 b(adjacent.) p Fi 5978 49062 a(3.10) 1329
b(Con) -53 b(v) -13 b(erting) 331 b(ADDs) h(to) h(BDDs) f(and) f(V) -49
b(ice) 332 b(V) -133 b(ersa) p Fo 5978 51386 a(Se) -30
b(v) -18 b(eral) 310 b(procedures) h(are) g(pro) -18
b(vided) 311 b(to) h(con) -48 b(v) -18 b(ert) 310 b(ADDs) i(to) f
(BDDs,) i(according) f(to) f(dif) -30 b(ferent) 5978
52891 y(criteria.) 351 b(\() p Fn(Cudd) p 13168 52891
V 436 w(addBddP) -97 b(attern) p Fo(,) p Fn 245 w(Cudd) p
24089 52891 V 437 w(addBddInterval) p Fo(,) 244 b(and) p
Fn 230 w(Cudd) p 37288 52891 V 437 w(addBddThr) -45 b(eshold) p
Fo(.\)) 5978 54397 y(The) 437 b(con) -48 b(v) -18 b(ersion) 437
b(from) g(BDDs) h(to) g(ADDs) g(\() p Fn(Cudd) p 28271
54397 V 436 w(BddT) -112 b(oAdd) p Fo 33 w(\)) 438 b(is) f(based) h(on)
f(the) h(simple) 5978 55902 y(principle) 305 b(of) h(mapping) g(the) g
(logical) g(0) g(and) g(1) f(on) h(the) g(arithmetic) g(0) g(and) g(1.)
384 b(It) 305 b(is) g(also) g(possi-) 5978 57408 y(ble) f(to) h(con) -48
b(v) -18 b(ert) 304 b(an) g(ADD) h(with) g(inte) -18
b(ger) 304 b(v) -30 b(alues) 304 b(\(more) g(precisely) -79
b(,) 305 b(\003oating) f(point) h(numbers) 5978 58913
y(with) e(0) g(fractional) g(part\)) f(to) h(an) g(array) g(of) g(BDDs)
g(by) g(repeatedly) h(calling) p Fn 303 w(Cudd) p 40184
58913 V 437 w(addIthBit) p Fo(.) p Fi 5978 62236 a(3.11) 1329
b(Con) -53 b(v) -13 b(erting) 331 b(BDDs) h(to) h(ZDDs) f(and) f(V) -49
b(ice) 332 b(V) -133 b(ersa) p Fo 5978 64559 a(Man) -18
b(y) 282 b(applications) g(\002rst) f(b) -24 b(uild) 283
b(a) f(set) g(of) g(BDDs) h(and) f(then) h(deri) -30
b(v) -18 b(e) 282 b(ZDDs) g(from) f(the) i(BDDs.) 5978
66065 y(These) 299 b(applications) g(should) h(create) g(the) f
(manager) h(with) g(0) g(ZDD) f(v) -30 b(ariables) 299
b(and) h(create) g(the) p Black 25297 69672 a(15) p Black
90 rotate dyy eop
%%Page: 16 16
16 15 bop Black Black Fo 5978 7638 a(BDDs.) 536 b(Then) 356
b(the) -18 b(y) 357 b(should) f(call) p Fn 357 w(Cudd) p
23515 7638 364 45 v 437 w(zddV) -135 b(ar) -12 b(s) n(F) -67
b(r) -55 b(omBddV) -135 b(ar) -12 b(s) p Fo 356 w(to) 356
b(create) h(the) g(necessary) 5978 9143 y(ZDD) 425 b(v) -30
b(ariables\227whose) 424 b(number) i(is) e(lik) -12 b(ely) 426
b(to) f(be) g(kno) -30 b(wn) 426 b(once) f(the) h(BDDs) f(are) h(a) -24
b(v) -30 b(ail-) 5978 10649 y(able.) 416 b(This) 315
b(approach) i(eliminates) f(the) g(dif) -30 b(\002culties) 316
b(that) g(arise) g(when) h(the) f(number) g(of) g(ZDD) 5978
12154 y(v) -30 b(ariables) 302 b(changes) h(while) h(ZDDs) e(are) h
(being) g(b) -24 b(uilt.) 7859 13660 y(The) 331 b(simplest) f(con) -48
b(v) -18 b(ersion) 329 b(from) h(BDDs) h(to) g(ZDDs) f(is) g(a) h
(simple) f(change) i(of) e(represen-) 5978 15165 y(tation,) 493
b(which) 455 b(preserv) -18 b(es) 453 b(the) j(functions.) 830
b(Simply) 455 b(put,) 493 b(gi) -30 b(v) -18 b(en) 455
b(a) g(BDD) g(for) p Fk 454 w(f) p Fo 130 w(,) 494 b(a) 455
b(ZDD) 5978 16671 y(for) p Fk 437 w(f) p Fo 569 w(is) 437
b(requested.) 781 b(In) 437 b(this) h(case) g(the) g(correspondence) g
(between) h(the) f(BDD) h(v) -30 b(ariables) 5978 18176
y(and) 407 b(ZDD) h(v) -30 b(ariables) 407 b(is) g(one-to-one.) 689
b(Hence,) p Fn 435 w(Cudd) p 29778 18176 V 437 w(zddV) -135
b(ar) -12 b(s) n(F) -67 b(r) -55 b(omBddV) -135 b(ar) -12
b(s) p Fo 407 w(should) 407 b(be) 5978 19682 y(called) 353
b(with) f(the) p Fn 353 w(multiplicity) p Fo 353 w(parameter) h(equal) g
(to) g(1.) 524 b(The) 353 b(con) -48 b(v) -18 b(ersion) 352
b(proper) g(can) h(then) 5978 21187 y(be) 478 b(performed) g(by) g
(calling) p Fn 479 w(Cudd) p 21294 21187 V 437 w(zddP) -97
b(ortF) -69 b(r) -55 b(omBdd) p Fo(.) 902 b(The) 478
b(in) -48 b(v) -18 b(erse) 478 b(transf) n(ormation) h(is) 5978
22693 y(performed) 302 b(by) p Fn 303 w(Cudd) p 15543
22693 V 437 w(zddP) -97 b(ortT) -112 b(oBdd) p Fo(.) 7859
24198 y(ZDDs) 383 b(are) h(quite) g(often) f(used) g(for) g(the) h
(representation) f(of) p Fn 383 w(co) -12 b(ver) g(s) p
Fo(.) 617 b(This) 382 b(is) h(normally) 5978 25704 y(done) 459
b(by) g(associating) f(tw) -12 b(o) 459 b(ZDD) g(v) -30
b(ariables) 458 b(to) h(each) h(v) -30 b(ariable) 458
b(of) h(the) g(function.) 843 b(\(And) 5978 27209 y(hence,) 340
b(typically) -79 b(,) 341 b(to) 333 b(each) h(BDD) f(v) -30
b(ariable.\)) 465 b(One) 333 b(ZDD) g(v) -30 b(ariable) 332
b(is) g(associated) h(with) g(the) 5978 28715 y(positi) -30
b(v) -18 b(e) 428 b(literal) i(of) f(the) h(BDD) g(v) -30
b(ariable,) 461 b(while) 430 b(the) f(other) h(ZDD) f(v) -30
b(ariable) 429 b(is) g(associated) 5978 30220 y(with) 434
b(the) h(ne) -18 b(g) -6 b(ati) -30 b(v) -18 b(e) 434
b(literal.) 770 b(A) 435 b(call) g(to) p Fn 434 w(Cudd) p
26423 30220 V 437 w(zddV) -135 b(ar) -12 b(sF) -69 b(r) -55
b(omBddV) -135 b(ar) -12 b(s) p Fo 434 w(with) p Fn 435
w(multiplicity) p Fo 5978 31725 a(equal) 303 b(to) g(2) g(will) g
(associate) g(to) g(BDD) h(v) -30 b(ariable) p Fk 303
w(i) p Fo 302 w(the) 304 b(tw) -12 b(o) 303 b(ZDD) g(v) -30
b(ariables) p Fl 302 w(2) p Fk(i) p Fo 303 w(and) p Fl
303 w(2) p Fk(i) p Fl 269 w(+) 269 b(1) p Fo(.) 7859
33231 y(If) 291 b(a) h(BDD) h(v) -30 b(ariable) 291 b(group) h(tree) f
(e) -18 b(xists) 291 b(when) p Fn 292 w(Cudd) p 30683
33231 V 437 w(zddV) -135 b(ar) -12 b(sF) -67 b(r) -57
b(omBddV) -135 b(ar) -12 b(s) p Fo 291 w(is) 292 b(called) 5978
34736 y(\(see) 357 b(Section) i(3.13\)) f(the) h(function) f(generates)
h(a) f(ZDD) g(v) -30 b(ariable) 359 b(group) f(tree) g(consistent) g
(to) 5978 36242 y(it.) 758 b(In) 430 b(an) -18 b(y) 430
b(case,) 463 b(all) 430 b(the) h(ZDD) f(v) -30 b(ariables) 430
b(deri) -30 b(v) -18 b(ed) 430 b(from) g(the) g(same) h(BDD) g(v) -30
b(ariable) 430 b(are) 5978 37747 y(clustered) 302 b(into) h(a) h
(group.) 7859 39253 y(If) 313 b(the) h(ZDD) f(for) p
Fk 313 w(f) p Fo 445 w(is) g(created) h(and) f(later) h(a) f(ne) -30
b(w) 314 b(ZDD) g(v) -30 b(ariable) 313 b(is) g(added) h(to) g(the) f
(man-) 5978 40758 y(ager) -48 b(,) 277 b(the) 271 b(function) h
(represented) f(by) g(the) g(e) -18 b(xisting) 271 b(ZDD) g(changes.)
366 b(Suppose,) 277 b(for) 271 b(instance,) 5978 42264
y(that) 323 b(tw) -12 b(o) 322 b(v) -30 b(ariables) 323
b(are) f(initially) h(created,) 328 b(and) 323 b(that) g(the) g(ZDD) g
(for) p Fk 322 w(f) p Fl 504 w(=) p Fk 373 w(x) p Fc
38617 42446 a(0) p Fl 39427 42264 a(+) p Fk 284 w(x) p
Fc 41347 42446 a(1) p Fo 42195 42264 a(is) f(b) -24 b(uilt.) 5978
43769 y(If) 430 b(a) i(third) f(v) -30 b(ariable) 431
b(is) g(added,) 464 b(say) p Fk 432 w(x) p Fc 22854 43951
a(2) p Fo 23379 43769 a(,) g(then) 431 b(the) h(ZDD) f(represents) p
Fk 431 w(g) p Fl 618 w(=) 574 b(\() p Fk(x) p Fc 40722
43951 a(0) p Fl 41612 43769 a(+) p Fk 365 w(x) p Fc 43613
43951 a(1) p Fl 44138 43769 a(\)) p Fk(x) p Fd 45302
43329 a(0) p Fc 45302 44077 a(2) p Fo 5978 45275 a(instead.) 446
b(This) 326 b(change) h(in) g(function) g(ob) -18 b(viously) 326
b(applies) h(re) -18 b(g) -6 b(ardless) 325 b(of) h(what) h(use) g(is) f
(made) 5978 46780 y(of) 358 b(the) h(ZDD.) 543 b(Ho) -30
b(we) g(v) -18 b(er) -48 b(,) 372 b(if) 358 b(the) h(ZDD) g(is) f(used)
h(to) g(represent) f(a) h(co) -18 b(v) g(er,) 372 b(the) 359
b(co) -18 b(v) g(er) 359 b(itself) f(is) 5978 48286 y(not) 376
b(changed) h(by) g(the) f(addition) h(of) f(ne) -30 b(w) 376
b(v) -30 b(ariable.) 596 b(\(What) 376 b(changes) h(is) f(the) g
(characteristic) 5978 49791 y(function) 303 b(of) f(the) i(co) -18
b(v) g(er) -67 b(.\)) p Fi 5978 53114 a(3.12) 1329 b(V) -122
b(ariable) 332 b(Reorder) n(ing) h(f) -33 b(or) 332 b(BDDs) g(and) f
(ADDs) p Fo 5978 55437 a(The) 253 b(CUDD) g(package) h(pro) -18
b(vides) 253 b(a) g(rich) g(set) g(of) g(dynamic) g(reordering) g
(algorithms.) 358 b(Some) 253 b(of) 5978 56943 y(them) 303
b(are) g(slight) g(v) -30 b(ariations) 303 b(of) g(e) -18
b(xisting) 302 b(techniques) i([16,) f(6,) g(2,) h(10,) f(15,) h(11];) f
(some) g(others) 5978 58448 y(ha) -24 b(v) -18 b(e) 303
b(been) g(de) -30 b(v) -18 b(eloped) 303 b(speci\002cally) h(for) e
(this) g(package) i([14,) f(13].) 7859 59954 y(Reordering) 394
b(af) -30 b(fects) 393 b(a) g(unique) h(table.) 648 b(This) 393
b(means) g(that) h(BDDs) g(and) g(ADDs,) 416 b(which) 5978
61459 y(share) 456 b(the) i(same) f(unique) g(table) h(are) f
(simultaneously) g(reordered.) 837 b(ZDDs,) 496 b(on) 457
b(the) g(other) 5978 62965 y(hand,) 271 b(are) 264 b(reordered) f
(separately) -79 b(.) 363 b(In) 263 b(the) h(follo) -30
b(wing) 263 b(we) h(discuss) f(the) h(reordering) f(of) g(BDDs) 5978
64470 y(and) 303 b(ADDs.) 376 b(Reordering) 303 b(for) f(ZDDs) h(is) f
(the) h(subject) g(of) g(Section) g(3.14.) p Black 25297
69672 a(16) p Black 90 rotate dyy eop
%%Page: 17 17
17 16 bop Black Black Fo 7859 7638 a(Reordering) 324
b(of) g(the) f(v) -30 b(ariables) 323 b(can) h(be) g(in) -48
b(v) -24 b(ok) -12 b(ed) 323 b(directly) h(by) g(the) f(application) i
(by) e(call-) 5978 9143 y(ing) p Fn 325 w(Cudd) p 10551
9143 364 45 v 437 w(ReduceHeap) p Fo(.) 444 b(Or) 326
b(it) f(can) h(be) g(automatically) g(triggered) g(by) f(the) h
(package) h(when) 5978 10649 y(the) 394 b(number) h(of) f(nodes) h(has)
f(reached) h(a) g(gi) -30 b(v) -18 b(en) 394 b(threshold.) 650
b(\(The) 394 b(threshold) g(is) g(initialized) 5978 12154
y(and) k(automatically) g(adjusted) g(after) g(each) g(reordering) g
(by) g(the) g(package.\)) 661 b(T) -97 b(o) 398 b(enable) g(au-) 5978
13660 y(tomatic) 351 b(dynamic) h(reordering) f(\(also) g(called) p
Fn 352 w(async) -18 b(hr) -55 b(onous) p Fo 351 w(dynamic) 351
b(reordering) g(in) h(this) 5978 15165 y(document\)) 457
b(the) h(application) g(must) f(call) p Fn 457 w(Cudd) p
27123 15165 V 437 w(A) -24 b(utodynEnable) p Fo(.) 839
b(Automatic) 458 b(dynamic) 5978 16671 y(reordering) 302
b(can) h(subsequently) g(be) g(disabled) g(by) h(calling) p
Fn 303 w(Cudd) p 33554 16671 V 437 w(A) -24 b(utodynDisable) p
Fo(.) 7859 18176 y(All) 231 b(reordering) f(methods) g(are) g(a) -24
b(v) -30 b(ailable) 230 b(in) h(both) f(the) h(case) f(of) g(direct) g
(call) h(to) p Fn 230 w(Cudd) p 43187 18176 V 437 w(ReduceHeap) p
Fo 5978 19682 a(and) 289 b(the) h(case) f(of) g(automatic) h(in) -48
b(v) -24 b(ocation.) 371 b(F) -18 b(or) 289 b(man) -18
b(y) 290 b(methods,) i(the) d(reordering) g(procedure) 5978
21187 y(is) 433 b(iterated) h(until) g(no) h(further) e(impro) -18
b(v) g(ement) 434 b(is) g(obtained.) 769 b(W) -97 b(e) 435
b(call) f(these) g(methods) g(the) p Fn 5978 22693 a(con) -48
b(ver) j(ging) p Fo 473 w(methods.) 887 b(When) 474 b(constraints) f
(are) g(imposed) h(on) f(the) h(relati) -30 b(v) -18
b(e) 473 b(position) g(of) 5978 24198 y(v) -30 b(ariables) 363
b(\(see) g(Section) i(3.13\)) e(the) h(reordering) g(methods) f(apply) i
(inside) e(the) h(groups.) 558 b(The) 5978 25704 y(groups) 401
b(themselv) -18 b(es) 401 b(are) h(reordered) g(by) g(sifting.) 672
b(Each) 402 b(method) g(is) g(identi\002ed) g(by) g(a) g(con-) 5978
27209 y(stant) 297 b(of) g(the) g(enumerated) h(type) p
Fn 298 w(Cudd) p 22686 27209 V 437 w(Reor) -45 b(deringT) -90
b(ype) p Fo 298 w(de\002ned) 297 b(in) p Fn 298 w(cudd.h) p
Fo 298 w(\(the) g(e) -18 b(xternal) 5978 28715 y(header) 303
b(\002le) g(of) g(the) g(CUDD) h(package\):) p Black
Fp 5978 31548 a(CUDD) p 9551 31548 V 437 w(REORDER) p
16047 31548 V 437 w(NONE:) p Black Fo 607 w(This) e(method) h(causes) g
(no) g(reordering.) p Black Fp 5978 34050 a(CUDD) p 9551
34050 V 437 w(REORDER) p 16047 34050 V 437 w(SAME:) p
Black Fo 607 w(If) 229 b(passed) h(to) p Fn 231 w(Cudd) p
29295 34050 V 437 w(A) -24 b(utodynEnable) p Fo(,) 244
b(this) 230 b(method) h(lea) -24 b(v) -18 b(es) 9008
35556 y(the) 230 b(current) g(method) h(for) f(automatic) g(reordering)
g(unchanged.) 353 b(If) 229 b(passed) h(to) p Fn 230
w(Cudd) p 44459 35556 V 437 w(ReduceHeap) p Fo(,) 9008
37061 y(this) 302 b(method) i(causes) e(the) i(current) e(method) i
(for) e(automatic) i(reordering) e(to) h(be) g(used.) p
Black Fp 5978 39563 a(CUDD) p 9551 39563 V 437 w(REORDER) p
16047 39563 V 437 w(RANDOM:) p Black Fo 607 w(P) -18
b(airs) 229 b(of) h(v) -30 b(ariables) 230 b(are) g(randomly) h
(chosen,) 244 b(and) 231 b(sw) -12 b(apped) 9008 41068
y(in) 384 b(the) f(order) -67 b(.) 618 b(The) 383 b(sw) -12
b(ap) 384 b(is) f(performed) g(by) h(a) f(series) g(of) g(sw) -12
b(aps) 383 b(of) h(adjacent) g(v) -30 b(ari-) 9008 42574
y(ables.) 353 b(The) 234 b(best) h(order) f(among) h(those) g(obtained)
g(by) g(the) g(series) e(of) i(sw) -12 b(aps) 234 b(is) g(retained.)
9008 44079 y(The) 323 b(number) f(of) h(pairs) f(chosen) h(for) f(sw)
-12 b(apping) 323 b(equals) g(the) g(number) f(of) h(v) -30
b(ariables) 322 b(in) 9008 45585 y(the) 303 b(diagram.) p
Black Fp 5978 48086 a(CUDD) p 9551 48086 V 437 w(REORDER) p
16047 48086 V 437 w(RANDOM) p 22071 48086 V 438 w(PIV) -55
b(O) -48 b(T:) p Black Fo 605 w(Same) 231 b(as) f(CUDD) p
34851 48086 V 437 w(REORDER) p 40944 48086 V 437 w(RANDOM,) 9008
49592 y(b) -24 b(ut) 384 b(the) g(tw) -12 b(o) 384 b(v) -30
b(ariables) 384 b(are) g(chosen) g(so) f(that) i(the) f(\002rst) f(is) h
(abo) -18 b(v) g(e) 384 b(the) g(v) -30 b(ariable) 384
b(with) 9008 51097 y(the) 359 b(lar) -22 b(gest) 358
b(number) g(of) g(nodes,) 372 b(and) 359 b(the) g(second) f(is) g(belo)
-30 b(w) 359 b(that) f(v) -30 b(ariable.) 542 b(In) 358
b(case) 9008 52603 y(there) 372 b(are) g(se) -30 b(v) -18
b(eral) 372 b(v) -30 b(ariables) 371 b(tied) i(for) e(the) h(maximum) h
(number) f(of) g(nodes,) 389 b(the) 373 b(one) 9008 54108
y(closest) 302 b(to) h(the) h(root) e(is) h(used.) p
Black Fp 5978 56610 a(CUDD) p 9551 56610 V 437 w(REORDER) p
16047 56610 V 437 w(SIFT:) p Black Fo 606 w(This) 314
b(method) i(is) g(an) g(implementation) g(of) f(Rudell') -67
b(s) 316 b(sifting) 9008 58115 y(algorithm) 349 b([16].) 513
b(A) 349 b(simpli\002ed) g(description) f(of) h(sifting) f(is) h(as) f
(follo) -30 b(ws:) 467 b(Each) 349 b(v) -30 b(ari-) 9008
59621 y(able) 416 b(is) f(considered) g(in) h(turn.) 713
b(A) 415 b(v) -30 b(ariable) 416 b(is) f(mo) -18 b(v) g(ed) 415
b(up) h(and) g(do) -30 b(wn) 415 b(in) h(the) g(order) 9008
61126 y(so) 338 b(that) g(it) h(tak) -12 b(es) 338 b(all) g(possible) g
(positions.) 481 b(The) 338 b(best) g(position) g(is) g(identi\002ed) g
(and) h(the) 9008 62632 y(v) -30 b(ariable) 303 b(is) f(returned) h(to)
g(that) g(position.) 9008 64635 y(In) 399 b(reality) -79
b(,) 424 b(things) 399 b(are) h(a) f(bit) h(more) f(complicated.) 666
b(F) -18 b(or) 399 b(instance,) 424 b(there) 400 b(is) f(a) g(limit)
9008 66141 y(on) 390 b(the) h(number) f(of) g(v) -30
b(ariables) 389 b(that) i(will) f(be) h(sifted.) 636
b(This) 390 b(limit) g(can) g(be) h(read) f(with) p Black
25297 69672 a(17) p Black 90 rotate dyy eop
%%Page: 18 18
18 17 bop Black Black Fn 9008 7638 a(Cudd) p 11707 7638
364 45 v 437 w(ReadSiftMaxV) -135 b(ar) p Fo 352 w(and) 326
b(set) e(with) p Fn 325 w(Cudd) p 29295 7638 V 437 w(SetSiftMaxV) -135
b(ar) p Fo(.) 442 b(In) 324 b(addition,) 331 b(if) 325
b(the) 9008 9143 y(diagram) 399 b(gro) -30 b(ws) 399
b(too) g(much) h(while) f(mo) -18 b(ving) 400 b(a) f(v) -30
b(ariable) 399 b(up) h(or) f(do) -30 b(wn,) 423 b(that) 400
b(mo) -18 b(v) g(e-) 9008 10649 y(ment) 482 b(is) f(terminated) h
(before) g(the) g(v) -30 b(ariable) 482 b(has) g(reached) g(one) g(end)
g(of) g(the) g(order) -67 b(.) 9008 12154 y(The) 358
b(maximum) h(ratio) f(by) h(which) g(the) g(diagram) f(is) g(allo) -30
b(wed) 359 b(to) f(gro) -30 b(w) 358 b(while) h(a) g(v) -30
b(ari-) 9008 13660 y(able) 448 b(is) g(being) g(sifted) f(can) i(be) f
(read) g(with) p Fn 448 w(Cudd) p 30573 13660 V 437 w(ReadMaxGr) -55
b(owth) p Fo 449 w(and) 448 b(set) g(with) p Fn 9008
15165 a(Cudd) p 11707 15165 V 437 w(SetMaxGr) -55 b(owth) p
Fo(.) p Black Fp 5978 17574 a(CUDD) p 9551 17574 V 437
w(REORDER) p 16047 17574 V 437 w(SIFT) p 19179 17574
V 436 w(CONVERGE) r(:) p Black Fo 606 w(This) 229 b(is) h(the) g(con)
-48 b(v) -18 b(er) c(ging) 230 b(v) -30 b(ariant) 230
b(of) g(CUDD-) p 9008 19080 V 9372 19080 a(REORDER) p
15101 19080 V 437 w(SIFT) -90 b(.) p Black Fp 5978 21488
a(CUDD) p 9551 21488 V 437 w(REORDER) p 16047 21488 V
437 w(SYMM) p 20321 21488 V 437 w(SIFT:) p Black Fo 606
w(This) 441 b(method) h(is) f(an) h(implementation) g(of) g(sym-) 9008
22994 y(metric) 350 b(sifting) f([14].) 516 b(It) 350
b(is) f(similar) g(to) h(sifting,) 361 b(with) 350 b(one) h(addition:)
470 b(V) -135 b(ariables) 350 b(that) 9008 24499 y(become) 291
b(adjacent) g(during) g(sifting) f(are) g(tested) h(for) f(symmetry.)
371 b(If) 290 b(the) -18 b(y) 290 b(are) h(symmet-) 9008
26005 y(ric,) 450 b(the) -18 b(y) 421 b(are) g(link) -12
b(ed) 421 b(in) g(a) g(group.) 730 b(Sifting) 421 b(then) g(continues) g
(with) g(a) g(group) g(being) 9008 27510 y(mo) -18 b(v) g(ed,) 416
b(instead) 393 b(of) g(a) h(single) f(v) -30 b(ariable.) 647
b(After) 393 b(symmetric) g(sifting) f(has) h(been) h(run,) p
Fn 9008 29016 a(Cudd) p 11707 29016 V 437 w(SymmPr) -55
b(o\002le) p Fo 409 w(can) 409 b(be) g(called) g(to) g(report) f(on) h
(the) g(symmetry) f(groups) g(found.) 9008 30521 y(\(Both) 303
b(positi) -30 b(v) -18 b(e) 302 b(and) i(ne) -18 b(g) -6
b(ati) -30 b(v) -18 b(e) 303 b(symmetries) f(are) h(reported.\)) p
Black Fp 5978 32930 a(CUDD) p 9551 32930 V 437 w(REORDER) p
16047 32930 V 437 w(SYMM) p 20321 32930 V 437 w(SIFT) p
23453 32930 V 436 w(CONV:) p Black Fo 606 w(This) 230
b(is) g(the) g(con) -48 b(v) -18 b(er) c(ging) 230 b(v) -30
b(ariant) 230 b(of) g(CUDD-) p 9008 34435 V 9372 34435
a(REORDER) p 15101 34435 V 437 w(SYMM) p 19243 34435
V 435 w(SIFT) -90 b(.) p Black Fp 5978 36844 a(CUDD) p
9551 36844 V 437 w(REORDER) p 16047 36844 V 437 w(GR) -36
b(OUP) p 20825 36844 V 436 w(SIFT:) p Black Fo 606 w(This) 289
b(method) i(is) g(an) g(implementation) g(of) f(group) 9008
38350 y(sifting) 232 b([13].) 352 b(It) 233 b(is) f(similar) h(to) g
(symmetric) g(sifting,) 246 b(b) -24 b(ut) 233 b(aggre) -18
b(g) -6 b(ation) 233 b(is) g(not) g(restricted) 9008
39855 y(to) 303 b(symmetric) f(v) -30 b(ariables.) p
Black Fp 5978 42264 a(CUDD) p 9551 42264 V 437 w(REORDER) p
16047 42264 V 437 w(GR) -36 b(OUP) p 20825 42264 V 436
w(SIFT) p 23956 42264 V 436 w(CONV:) p Black Fo 606 w(This) 468
b(method) g(repeats) g(until) g(con) -48 b(v) -18 b(er) -24
b(-) 9008 43769 y(gence) 484 b(the) g(combination) h(of) e(CUDD) p
25827 43769 V 438 w(REORDER) p 31921 43769 V 437 w(GR) -48
b(OUP) p 36417 43769 V 437 w(SIFT) 482 b(and) j(CUDD-) p
9008 45275 V 9372 45275 a(REORDER) p 15101 45275 V 437
w(WINDO) -42 b(W4.) p Black Fp 5978 47683 a(CUDD) p 9551
47683 V 437 w(REORDER) p 16047 47683 V 437 w(WINDO) -61
b(W2:) p Black Fo 607 w(This) 392 b(method) i(implements) f(the) h
(windo) -30 b(w) 394 b(permu-) 9008 49189 y(tation) 434
b(approach) h(of) f(Fujita) h([8) o(]) f(and) h(Ishiura) e([10].) 769
b(The) 434 b(size) h(of) f(the) g(windo) -30 b(w) 435
b(is) 9008 50694 y(2.) p Black Fp 5978 53103 a(CUDD) p
9551 53103 V 437 w(REORDER) p 16047 53103 V 437 w(WINDO) -61
b(W3:) p Black Fo 607 w(Similar) 230 b(to) g(CUDD) p
32035 53103 V 437 w(REORDER) p 38128 53103 V 437 w(WINDO) -42
b(W2,) 246 b(b) -24 b(ut) 9008 54609 y(with) 303 b(a) g(windo) -30
b(w) 303 b(of) g(size) g(3.) p Black Fp 5978 57017 a(CUDD) p
9551 57017 V 437 w(REORDER) p 16047 57017 V 437 w(WINDO) -61
b(W4:) p Black Fo 607 w(Similar) 230 b(to) g(CUDD) p
32035 57017 V 437 w(REORDER) p 38128 57017 V 437 w(WINDO) -42
b(W2,) 246 b(b) -24 b(ut) 9008 58523 y(with) 303 b(a) g(windo) -30
b(w) 303 b(of) g(size) g(4.) p Black Fp 5978 60932 a(CUDD) p
9551 60932 V 437 w(REORDER) p 16047 60932 V 437 w(WINDO) -61
b(W2) p 22618 60932 V 437 w(CONV:) p Black Fo 606 w(This) 230
b(is) g(the) g(con) -48 b(v) -18 b(er) c(ging) 230 b(v) -30
b(ariant) 230 b(of) g(CUDD-) p 9008 62437 V 9372 62437
a(REORDER) p 15101 62437 V 437 w(WINDO) -42 b(W2.) p
Black Fp 5978 64846 a(CUDD) p 9551 64846 V 437 w(REORDER) p
16047 64846 V 437 w(WINDO) -61 b(W3) p 22618 64846 V
437 w(CONV:) p Black Fo 606 w(This) 230 b(is) g(the) g(con) -48
b(v) -18 b(er) c(ging) 230 b(v) -30 b(ariant) 230 b(of) g(CUDD-) p
9008 66351 V 9372 66351 a(REORDER) p 15101 66351 V 437
w(WINDO) -42 b(W3.) p Black 25297 69672 a(18) p Black
90 rotate dyy eop
%%Page: 19 19
19 18 bop Black Black Black Fp 5978 7638 a(CUDD) p 9551
7638 364 45 v 437 w(REORDER) p 16047 7638 V 437 w(WINDO) -61
b(W4) p 22618 7638 V 437 w(CONV:) p Black Fo 606 w(This) 230
b(is) g(the) g(con) -48 b(v) -18 b(er) c(ging) 230 b(v) -30
b(ariant) 230 b(of) g(CUDD-) p 9008 9143 V 9372 9143
a(REORDER) p 15101 9143 V 437 w(WINDO) -42 b(W4.) p Black
Fp 5978 11585 a(CUDD) p 9551 11585 V 437 w(REORDER) p
16047 11585 V 437 w(ANNEA) r(LING:) p Black Fo 605 w(This) 312
b(method) h(is) f(an) h(implementation) g(of) f(simu-) 9008
13091 y(lated) 271 b(annealing) g(for) f(v) -30 b(ariable) 271
b(ordering,) 277 b(v) -30 b(aguely) 271 b(resemblant) f(of) h(the) g
(algorithm) f(of) 9008 14596 y([2].) 375 b(This) 302
b(method) i(is) e(potentially) h(v) -18 b(ery) 303 b(slo) -30
b(w) -79 b(.) p Black Fp 5978 17038 a(CUDD) p 9551 17038
V 437 w(REORDER) p 16047 17038 V 437 w(GENE) r(TIC:) p
Black Fo 605 w(This) 344 b(method) i(is) e(an) h(implementation) h(of) e
(a) i(genetic) 9008 18543 y(algorithm) 328 b(for) f(v) -30
b(ariable) 329 b(ordering,) 334 b(inspired) 327 b(by) i(the) f(w) -12
b(ork) 328 b(of) g(Drechsler) f([6].) 451 b(This) 9008
20049 y(method) 303 b(is) g(potentially) g(v) -18 b(ery) 303
b(slo) -30 b(w) -79 b(.) p Black Fp 5978 22490 a(CUDD) p
9551 22490 V 437 w(REORDER) p 16047 22490 V 437 w(EXA) -67
b(C) r(T:) p Black Fo 606 w(This) 293 b(method) i(implements) f(a) h
(dynamic) f(programming) 9008 23996 y(approach) 249 b(to) f(e) -18
b(xact) 248 b(reordering) g([9,) g(7,) g(10) q(],) 258
b(with) 249 b(impro) -18 b(v) g(ements) 247 b(described) h(in) h([11) o
(].) 9008 25501 y(It) 433 b(only) g(stores) f(one) h(BDD) h(at) f(the) g
(time.) 766 b(Therefore,) 465 b(it) 433 b(is) g(relati) -30
b(v) -18 b(ely) 432 b(ef) -30 b(\002cient) 433 b(in) 9008
27007 y(terms) 374 b(of) g(memory) -79 b(.) 592 b(Compared) 375
b(to) g(other) f(reordering) h(strate) -18 b(gies) n(,) 393
b(it) 375 b(is) f(v) -18 b(ery) 375 b(slo) -30 b(w) -79
b(,) 9008 28512 y(and) 303 b(is) g(not) g(recommended) g(for) g(more) g
(than) g(16) g(v) -30 b(ariables.) 5978 31166 y(So) 301
b(f) -12 b(ar) 301 b(we) h(ha) -24 b(v) -18 b(e) 302
b(described) g(methods) f(whereby) h(the) g(package) h(selects) e(an) h
(order) f(automati-) 5978 32671 y(cally) -79 b(.) 352
b(A) 230 b(gi) -30 b(v) -18 b(en) 230 b(order) g(of) g(the) h(v) -30
b(ariables) 229 b(can) i(also) f(be) g(imposed) h(by) f(calling) p
Fn 231 w(Cudd) p 40685 32671 V 437 w(Shuf) -22 b(\003eHeap) p
Fo(.) p Fi 5978 35964 a(3.13) 1329 b(Gr) -24 b(ouping) 331
b(V) -122 b(ariables) p Fo 5978 38288 a(CUDD) 400 b(allo) -30
b(ws) 400 b(the) g(application) h(to) f(specify) f(constraints) g(on) i
(the) f(positions) f(of) h(group) f(of) 5978 39793 y(v) -30
b(ariables.) 804 b(It) 446 b(is) f(possible) g(to) h(request) g(that) g
(a) h(group) e(of) h(contiguous) g(v) -30 b(ariables) 446
b(be) g(k) -12 b(ept) 5978 41299 y(contiguous) 463 b(by) g(the) g
(reordering) g(procedures.) 855 b(It) 463 b(is) g(also) f(possible) h
(to) g(request) g(that) g(the) 5978 42804 y(relati) -30
b(v) -18 b(e) 382 b(order) g(of) g(some) g(groups) g(of) g(v) -30
b(ariables) 382 b(be) g(left) g(unchanged.) 615 b(The) 383
b(constraints) e(on) 5978 44310 y(the) 303 b(order) f(are) h
(speci\002ed) g(by) h(means) f(of) f(a) h(tree,) g(which) h(is) e
(created) i(in) f(one) g(of) g(tw) -12 b(o) 303 b(w) -12
b(ays:) p Black Fm 7796 46661 a(\262) p Black Fo 606
w(By) 303 b(calling) p Fn 304 w(Cudd) p 17027 46661 V
437 w(Mak) -12 b(eT) -67 b(r) -45 b(eeNode) p Fo(.) p
Black Fm 7796 49103 a(\262) p Black Fo 606 w(By) 289
b(calling) f(the) h(functions) e(of) h(the) h(MTR) f(library) f(\(part)
h(of) g(the) h(distrib) -24 b(uti) n(on\),) 291 b(and) e(by) 9008
50608 y(re) -18 b(gistering) 286 b(the) h(result) f(with) h(the) g
(manager) g(using) p Fn 286 w(Cudd) p 33491 50608 V 437
w(SetT) -67 b(r) -45 b(ee) p Fo(.) 371 b(The) 287 b(current) f(tree)
9008 52114 y(re) -18 b(gistered) 302 b(with) h(the) g(manager) h(can) f
(be) g(read) h(with) p Fn 303 w(Cudd) p 33770 52114 V
437 w(ReadT) -67 b(r) -45 b(ee) p Fo(.) 7859 54465 y(Each) 469
b(node) f(in) h(the) f(tree) h(represents) e(a) h(range) h(of) f(v) -30
b(ariables.) 871 b(The) 468 b(lo) -30 b(wer) 468 b(bound) g(of) 5978
55971 y(the) 365 b(range) g(is) f(gi) -30 b(v) -18 b(en) 365
b(by) g(the) p Fn 365 w(low) p Fo 366 w(\002eld) g(of) g(the) g(node,)
381 b(and) 365 b(the) g(size) g(of) g(the) g(group) g(is) f(gi) -30
b(v) -18 b(en) 5978 57476 y(by) 425 b(the) p Fn 426 w(siz) n(e) p
Fo 426 w(\002eld) g(of) g(the) h(node.) p Fg 20346 57037
a(2) p Fo 21587 57476 a(The) f(v) -30 b(ariables) 425
b(in) g(each) h(range) f(are) h(k) -12 b(ept) 425 b(contiguous.) 5978
58982 y(Furthermore,) 263 b(if) 253 b(a) h(node) g(is) g(mark) -12
b(ed) 254 b(with) g(the) g(MTR) p 28784 58982 V 436 w(FIXED) f(\003ag,)
264 b(then) 254 b(the) g(relati) -30 b(v) -18 b(e) 254
b(order) 5978 60487 y(of) 415 b(the) g(v) -30 b(ariable) 416
b(ranges) f(associated) g(to) g(its) g(children) h(is) f(not) g
(changed.) 714 b(As) 415 b(an) h(e) -18 b(xample,) 5978
61993 y(suppose) 302 b(the) h(initial) g(v) -30 b(ariable) 303
b(order) g(is:) p Black 5978 62752 15940 45 v Ff 7383
63493 a(2) p Fe 7771 63916 a(When) 239 b(the) g(v) -25
b(ariables) 239 b(in) g(a) g(group) g(are) f(reordered,) k(the) d
(association) g(between) h(the) p Fb 238 w(low) p Fe
239 w(\002eld) e(and) h(the) g(inde) -15 b(x) 5978 65134
y(of) 291 b(the) h(\002rst) f(v) -25 b(ariable) 293 b(in) f(the) g
(group) g(is) g(lost.) 436 b(The) 292 b(packag) r(e) g(updates) g(the) g
(tree) g(to) g(k) -10 b(eep) 293 b(track) f(of) g(the) g(change) r(s.)
5978 66351 y(Ho) -25 b(we) g(v) -15 b(er) -40 b(,) 250
b(the) g(application) g(cannot) g(rely) g(on) p Fb 249
w(low) p Fe 249 w(to) f(determine) h(the) f(position) g(of) g(v) -25
b(ariables.) p Black Black Fo 25297 69672 a(19) p Black
90 rotate dyy eop
%%Page: 20 20
20 19 bop Black Black Black Black Fh 11796 7638 a(x0,) 728
b(y0,) g(z0,) g(x1,) g(y1,) g(z1,) g(...) g(,) g(x9,) g(y9,) g(z9.) p
Fo 5978 9977 a(Suppose) 334 b(we) g(w) -12 b(ant) 335
b(to) f(k) -12 b(eep) 335 b(each) g(group) f(of) g(three) g(v) -30
b(ariables) 334 b(with) g(the) h(same) f(inde) -18 b(x) 334
b(\(e.g.,) p Fh 5978 11483 a(x3,) 728 b(y3,) g(z3) p
Fo(\)) 299 b(contiguous,) g(while) h(allo) -30 b(wing) 299
b(the) g(package) g(to) g(change) h(the) f(order) f(of) h(the) 5978
12988 y(groups.) 375 b(W) -97 b(e) 303 b(can) h(accomplish) f(this) f
(with) h(the) h(follo) -30 b(wing) 302 b(code:) p Black
Black Fh 11796 15328 a(for) 728 b(\(i) g(=) f(0;) h(i) g(<) f(10;) h
(i++\)) h({) 14705 16833 y(\(void\)) g(Cudd_Ma) r(keTreeN) r(ode\(mana)
r(ger,i*3) r(,3,MTR_) r(DEFAULT\)) r(;) 11796 18339 y(}) p
Fo 5978 20678 a(If) 335 b(we) h(w) -12 b(ant) 336 b(to) g(k) -12
b(eep) 336 b(the) g(order) f(within) h(each) h(group) f(of) f(v) -30
b(ariables) 335 b(\002x) -18 b(ed) 336 b(\(i.e.,) p Fh
344 w(x) p Fo 336 w(before) p Fh 336 w(y) p Fo 5978 22184
a(before) p Fh 302 w(z) p Fo(\)) 303 b(we) h(need) f(to) g(change) h
(MTR) p 22800 22184 364 45 v 436 w(DEF) -90 b(A) -67
b(UL) -112 b(T) 303 b(into) g(MTR) p 33608 22184 V 436
w(FIXED.) 7859 23689 y(The) p Fn 411 w(low) p Fo 410
w(parameter) 411 b(passed) e(to) p Fn 411 w(Cudd) p 25267
23689 V 437 w(Mak) -12 b(eT) -67 b(r) -45 b(eeNode) p
Fo 411 w(is) 410 b(the) g(inde) -18 b(x) 411 b(of) f(a) g(v) -30
b(ariable) 5978 25195 y(\(as) 343 b(opposed) i(to) f(its) g(le) -30
b(v) -18 b(el) 344 b(or) g(position) g(in) h(the) f(order\).) 499
b(The) 344 b(group) h(tree) f(can) h(be) f(created) h(at) 5978
26700 y(an) -18 b(y) 353 b(time.) 528 b(The) 353 b(result) g(ob) -18
b(viously) 354 b(depends) f(on) h(the) g(v) -30 b(ariable) 353
b(order) h(in) f(ef) -30 b(fect) 353 b(at) h(creation) 5978
28206 y(time.) 7859 29711 y(It) 255 b(is) f(possible) g(to) g(create) h
(a) g(v) -30 b(ariable) 254 b(group) h(tree) f(also) h(before) f(the) h
(v) -30 b(ariables) 254 b(themselv) -18 b(es) 5978 31216
y(are) 263 b(created.) 363 b(The) 263 b(package) i(assumes) d(in) h
(this) g(case) h(that) f(the) h(inde) -18 b(x) 264 b(of) f(the) h(v) -30
b(ariables) 262 b(not) i(yet) 5978 32722 y(in) 280 b(e) -18
b(xistence) 281 b(will) g(equal) g(their) f(position) g(in) h(the) g
(order) f(when) h(the) -18 b(y) 281 b(are) f(created.) 369
b(Therefore,) 5978 34227 y(applications) 335 b(that) h(rely) f(on) p
Fn 336 w(Cudd) p 20792 34227 V 437 w(bddNe) -18 b(wV) -135
b(arAtLe) -18 b(vel) p Fo 337 w(or) p Fn 336 w(Cudd) p
34861 34227 V 437 w(addNe) g(wV) -135 b(arAtLe) -18 b(vel) p
Fo 337 w(to) 5978 35733 y(create) 303 b(ne) -30 b(w) 303
b(v) -30 b(ariables) 302 b(ha) -24 b(v) -18 b(e) 304
b(to) f(create) g(the) g(v) -30 b(ariables) 302 b(before) h(the) -18
b(y) 303 b(group) g(them.) 7859 37238 y(The) 407 b(reordering) e
(procedure) i(will) f(skip) g(all) g(groups) g(whose) g(v) -30
b(ariables) 406 b(are) g(not) h(yet) f(in) 5978 38744
y(e) -18 b(xistence.) 393 b(F) -18 b(or) 308 b(groups) h(that) g(are) g
(only) g(partially) f(in) h(e) -18 b(xistence,) 311 b(the) e
(reordering) f(procedure) 5978 40249 y(will) 232 b(try) f(to) h
(reorder) g(the) g(v) -30 b(ariables) 231 b(already) h(instantiated,)
247 b(without) 232 b(violating) g(the) g(adjacenc) -18
b(y) 5978 41755 y(constraints.) p Fi 5978 45045 a(3.14) 1329
b(V) -122 b(ariable) 332 b(Reorder) n(ing) h(f) -33 b(or) 332
b(ZDDs) p Fo 5978 47369 a(Reordering) 288 b(of) f(ZDDs) g(is) g(done) h
(in) g(much) g(the) g(same) f(w) -12 b(ay) 288 b(as) g(the) f
(reordering) h(of) f(BDDs) h(and) 5978 48874 y(ADDs.) 379
b(The) 304 b(functions) g(corresponding) f(to) p Fn 305
w(Cudd) p 27947 48874 V 437 w(ReduceHeap) p Fo 305 w(and) p
Fn 304 w(Cudd) p 39561 48874 V 437 w(Shuf) -22 b(\003eHeap) p
Fo 5978 50380 a(are) p Fn 310 w(Cudd) p 10467 50380 V
437 w(zddReduceHeap) p Fo 311 w(and) p Fn 311 w(Cudd) p
23778 50380 V 437 w(zddShuf) g(\003eHeap) p Fo(.) 399
b(T) -97 b(o) 310 b(enable) h(dynamic) g(reorder) -24
b(-) 5978 51885 y(ing,) 473 b(the) 439 b(application) h(must) e(call) p
Fn 440 w(Cudd) p 23734 51885 V 437 w(A) -24 b(utodynEnableZdd) p
Fo(,) 472 b(and) 440 b(to) f(disable) g(dynamic) 5978
53391 y(reordering,) 344 b(it) 337 b(must) f(call) p
Fn 337 w(Cudd) p 20165 53391 V 437 w(A) -24 b(utodynDisableZdd) p
Fo(.) 477 b(In) 336 b(the) h(current) g(implementation,) 5978
54896 y(ho) -30 b(we) g(v) -18 b(er) -48 b(,) 296 b(the) f(choice) h
(of) g(reordering) f(methods) g(for) g(ZDDs) g(is) g(more) g(limited.)
373 b(Speci\002cally) -79 b(,) 5978 56402 y(these) 302
b(methods) h(are) g(a) -24 b(v) -30 b(ailable:) p Black
Fp 5978 59041 a(CUDD) p 9551 59041 V 437 w(REORDER) p
16047 59041 V 437 w(NONE;) p Black Black 5978 61478 a(CUDD) p
9551 61478 V 437 w(REORDER) p 16047 61478 V 437 w(SAME;) p
Black Black 5978 63914 a(CUDD) p 9551 63914 V 437 w(REORDER) p
16047 63914 V 437 w(RANDOM;) p Black Black 5978 66351
a(CUDD) p 9551 66351 V 437 w(REORDER) p 16047 66351 V
437 w(RANDOM) p 22071 66351 V 438 w(PIV) -55 b(O) -48
b(T;) p Black Black Fo 25297 69672 a(20) p Black 90 rotate
dyy eop
%%Page: 21 21
21 20 bop Black Black Black Fp 5978 7638 a(CUDD) p 9551
7638 364 45 v 437 w(REORDER) p 16047 7638 V 437 w(SIFT;) p
Black Black 5978 10140 a(CUDD) p 9551 10140 V 437 w(REORDER) p
16047 10140 V 437 w(SIFT) p 19179 10140 V 436 w(CONVERGE) r(;) p
Black Black 5978 12641 a(CUDD) p 9551 12641 V 437 w(REORDER) p
16047 12641 V 437 w(SYMM) p 20321 12641 V 437 w(SIFT;) p
Black Black 5978 15143 a(CUDD) p 9551 15143 V 437 w(REORDER) p
16047 15143 V 437 w(SYMM) p 20321 15143 V 437 w(SIFT) p
23453 15143 V 436 w(CONV.) p Black Fo 7859 17977 a(T) -97
b(o) 270 b(create) h(ZDD) f(v) -30 b(ariable) 270 b(groups,) 276
b(the) 270 b(application) h(calls) p Fn 270 w(Cudd) p
35926 17977 V 437 w(Mak) -12 b(eZddT) -67 b(r) -45 b(eeNode) p
Fo(.) p Fi 5978 21300 a(3.15) 1329 b(K) -33 b(eeping) 331
b(Consistent) h(V) -122 b(ariable) 332 b(Orders) f(f) -33
b(or) 332 b(BDDs) g(and) f(ZDDs) p Fo 5978 23623 a(Se) -30
b(v) -18 b(eral) 298 b(applications) g(that) h(manipulate) g(both) g
(BDDs) g(and) f(ZDDs) g(bene\002t) h(from) f(k) -12 b(eeping) 299
b(a) 5978 25129 y(\002x) -18 b(ed) 314 b(correspondence) g(between) h
(the) g(order) f(of) g(the) g(BDD) h(v) -30 b(ariables) 314
b(and) h(the) f(order) g(of) g(the) 5978 26634 y(ZDD) 390
b(v) -30 b(ariables.) 638 b(If) 390 b(each) h(BDD) h(v) -30
b(ariable) 390 b(corresponds) g(to) h(a) f(group) h(of) f(ZDD) h(v) -30
b(ariables,) 5978 28140 y(then) 423 b(it) h(is) f(often) g(desirable) g
(that) h(the) g(groups) f(of) g(ZDD) g(v) -30 b(ariables) 423
b(be) h(in) f(the) h(same) g(order) 5978 29645 y(as) 414
b(the) h(corresponding) f(BDD) i(v) -30 b(ariables.) 710
b(CUDD) 415 b(allo) -30 b(ws) 415 b(the) g(ZDD) f(order) g(to) h(track)
g(the) 5978 31150 y(BDD) 371 b(order) g(and) h(vice) f(v) -18
b(ersa.) 579 b(T) -97 b(o) 371 b(ha) -24 b(v) -18 b(e) 371
b(the) h(ZDD) f(order) f(track) i(the) f(BDD) h(order) -48
b(,) 387 b(the) 371 b(ap-) 5978 32656 y(plication) 342
b(calls) p Fn 342 w(Cudd) p 15825 32656 V 437 w(zddRealignEnable) p
Fo(.) 491 b(The) 342 b(ef) -30 b(fect) 342 b(of) f(this) h(call) g(can)
g(be) g(re) -30 b(v) -18 b(ersed) 341 b(by) 5978 34161
y(calling) p Fn 374 w(Cudd) p 12350 34161 V 437 w(zddRealignDisable) p
Fo(.) 587 b(When) 374 b(ZDD) f(realignment) h(is) f(in) h(ef) -30
b(fect,) 391 b(automatic) 5978 35667 y(reordering) 302
b(of) h(ZDDs) f(should) h(be) g(disabled.) p Fi 5978
38989 a(3.16) 1329 b(Hooks) p Fo 5978 41313 a(Hooks) 268
b(in) h(CUDD) g(are) g(lists) f(of) g(application-speci\002ed) h
(functions) f(to) h(be) g(run) g(on) f(certain) h(oc-) 5978
42818 y(casions.) 351 b(Each) 230 b(hook) g(is) g(identi\002ed) h(by) f
(a) h(constant) f(of) g(the) g(enumerated) h(type) p
Fn 231 w(Cudd) p 41691 42818 V 437 w(HookT) -90 b(ype) p
Fo(.) 5978 44324 y(In) 302 b(V) -135 b(ersion) 303 b(2.4.1) h(hooks) e
(are) h(de\002ned) h(for) e(these) h(occasions:) p Black
Fm 7796 46826 a(\262) p Black Fo 606 w(before) g(g) -6
b(arbage) 303 b(collection) h(\(CUDD) p 25534 46826 V
436 w(PRE) p 28193 46826 V 437 w(GC) p 30313 46826 V
437 w(HOOK\);) p Black Fm 7796 49327 a(\262) p Black
Fo 606 w(after) e(g) -6 b(arbage) 304 b(collection) f(\(CUDD) p
24658 49327 V 437 w(POST) p 28059 49327 V 436 w(GC) p
30178 49327 V 437 w(HOOK\);) p Black Fm 7796 51829 a(\262) p
Black Fo 606 w(before) g(v) -30 b(ariable) 303 b(reordering) f(\(CUDD) p
25845 51829 V 437 w(PRE) p 28505 51829 V 436 w(REORDERING) p
36751 51829 V 438 w(HOOK\);) p Black Fm 7796 54331 a(\262) p
Black Fo 606 w(after) g(v) -30 b(ariable) 303 b(reordering) g(\(CUDD) p
24970 54331 V 437 w(POST) p 28371 54331 V 436 w(REORDERING) p
36617 54331 V 437 w(HOOK\).) 5978 56833 y(The) 315 b(current) g
(implementation) h(of) f(hooks) g(is) g(e) -18 b(xperimental.) 412
b(A) 316 b(function) f(added) h(to) f(a) h(hook) 5978
58338 y(recei) -30 b(v) -18 b(es) 232 b(a) g(pointer) h(to) g(the) f
(manager) -48 b(,) 247 b(a) 233 b(pointer) f(to) h(a) g(constant) f
(string,) 246 b(and) 233 b(a) g(pointer) g(to) f(v) -24
b(oid) 5978 59844 y(as) 342 b(ar) -22 b(guments;) 362
b(it) 343 b(must) f(return) h(1) f(if) h(successf) n(ul;) 363
b(0) 343 b(otherwise.) 494 b(The) 343 b(second) g(ar) -22
b(gument) 343 b(is) 5978 61349 y(one) 259 b(of) f(\223DD,) -85
b(\224) 259 b(\223BDD,) -85 b(\224) 260 b(and) f(\223ZDD.) -85
b(\224) 259 b(This) f(allo) -30 b(ws) 258 b(the) h(hook) g(functions) f
(to) h(tell) g(the) g(type) f(of) 5978 62854 y(diagram) 241
b(for) f(which) h(reordering) f(or) h(g) -6 b(arbage) 241
b(collection) g(tak) -12 b(es) 241 b(place.) 356 b(The) 240
b(third) h(ar) -22 b(gument) 5978 64360 y(v) -30 b(aries) 369
b(depending) h(on) g(the) g(hook.) 577 b(The) 369 b(hook) i(functions) e
(called) h(before) g(or) f(after) h(g) -6 b(arbage) 5978
65865 y(collection) 294 b(do) g(not) g(use) f(it.) 373
b(The) 293 b(hook) h(functions) f(called) i(before) e(reordering) g
(are) h(passed,) h(in) p Black 25297 69672 a(21) p Black
90 rotate dyy eop
%%Page: 22 22
22 21 bop Black Black Fo 5978 7638 a(addition) 382 b(to) h(the) g
(pointer) f(to) h(the) g(manager) -48 b(,) 402 b(also) 382
b(the) h(method) g(used) f(for) g(reordering.) 614 b(The) 5978
9143 y(hook) 331 b(functions) g(called) g(after) g(reordering) g(are) g
(passed) g(the) g(start) g(time.) 460 b(T) -97 b(o) 331
b(add) h(a) f(function) 5978 10649 y(to) 294 b(a) h(hook,) i(one) e
(uses) p Fn 293 w(Cudd) p 18197 10649 364 45 v 437 w(AddHook) p
Fo 21 w(.) 373 b(The) 295 b(function) f(of) g(a) h(gi) -30
b(v) -18 b(en) 295 b(hook) g(are) f(called) h(in) g(the) 5978
12154 y(order) 328 b(in) i(which) f(the) -18 b(y) 330
b(were) f(added) h(to) f(the) h(hook.) 455 b(F) -18 b(or) 328
b(sample) h(hook) h(functions,) 335 b(one) 330 b(may) 5978
13660 y(look) 303 b(at) p Fn 303 w(Cudd) p 12313 13660
V 437 w(StdPr) -45 b(eReor) g(dHook) p Fo 323 w(and) p
Fn 303 w(Cudd) p 26550 13660 V 437 w(StdP) -97 b(ostReor) -45
b(dHook) p Fo 21 w(.) p Fi 5978 16953 a(3.17) 1329 b(The) 331
b(SIS/VIS) f(Interface) p Fo 5978 19276 a(The) 357 b(CUDD) i(package) g
(contains) f(interf) -12 b(ace) 358 b(functions) f(that) h(emulate) g
(the) g(beha) -24 b(vior) 358 b(of) g(the) 5978 20782
y(original) j(BDD) g(package) h(used) f(in) g(SIS) g([17]) f(and) i(in)
f(the) g(ne) -30 b(wer) 361 b(VIS) p Fg 36244 20342 a(3) p
Fo 37103 20782 a([4) o(].) 550 b(Ho) -30 b(w) 361 b(to) g(b) -24
b(uild) 5978 22287 y(VIS) 408 b(with) h(CUDD) g(is) f(described) h(in) g
(the) g(installation) f(documents) h(of) f(VIS.) h(\(V) -135
b(ersion) 408 b(1.1) 5978 23793 y(and) 303 b(later) -67
b(.\)) p Fp 5978 27041 a(3.17.1) 1212 b(Using) 303 b(the) f(CUDD) i(P)
-12 b(ackage) 303 b(in) g(SIS) p Fo 5978 29365 a(This) 409
b(section) h(describes) f(ho) -30 b(w) 410 b(to) h(b) -24
b(uild) 410 b(SIS) f(with) h(the) h(CUDD) g(package.) 698
b(Let) p Fh 410 w(SISDIR) p Fo 5978 30870 a(designate) 496
b(the) h(root) g(of) f(the) h(directory) g(hierarch) -6
b(y) 497 b(where) g(the) g(sources) e(for) i(SIS) f(reside.) 5978
32376 y(Let) p Fh 355 w(CUDDD) r(IR) p Fo 356 w(be) 357
b(the) f(root) g(of) g(the) g(directory) g(hierarch) -6
b(y) 356 b(where) g(the) g(distrib) -24 b(ution) 355
b(of) h(the) 5978 33881 y(CUDD) 295 b(package) g(resides.) 372
b(T) -97 b(o) 294 b(b) -24 b(uild) 294 b(SIS) f(with) i(the) f(CUDD) h
(package,) i(follo) -30 b(w) 294 b(these) g(steps.) p
Black 7493 36232 a(1.) p Black 606 w(Create) 304 b(directories) p
Fh 302 w(SISDIR/) r(sis/cud) r(d) p Fo 303 w(and) p Fh
303 w(SISDI) r(R/sis/m) r(tr) p Fo(.) p Black 7493 38673
a(2.) p Black 606 w(Cop) -12 b(y) 231 b(all) f(\002les) g(from) p
Fh 230 w(CUDDDIR) r(/cudd) p Fo 231 w(and) p Fh 231 w(CUDDDIR) r(/sis) p
Fo 231 w(to) p Fh 230 w(SISDI) r(R/sis/c) r(udd) p Fo
9008 40178 a(and) 303 b(all) g(\002les) g(from) p Fh
302 w(CUDDD) r(IR/mtr) p Fo 304 w(to) p Fh 303 w(SISDI) r(R/sis/m) r
(tr) p Fo(.) p Black 7493 42620 a(3.) p Black 606 w(Cop) -12
b(y) p Fh 452 w(CUDDD) r(IR/cudd) r(/doc/cu) r(dd.doc) p
Fo 453 w(to) p Fh 452 w(SISDIR) r(/sis/cu) r(dd) p Fo(;) 526
b(also) 9008 44125 y(cop) -12 b(y) p Fh 303 w(CUDDD) r(IR/mtr/d) r
(oc/mtr.) r(doc) p Fo 303 w(to) p Fh 303 w(SISD) r(IR/sis/m) r(tr) p
Fo(.) p Black 7493 46566 a(4.) p Black 606 w(In) p Fh
499 w(SISDIR/s) r(is/cudd) p Fo 500 w(mak) g(e) p Fh
500 w(bdd.h) p Fo 500 w(a) 499 b(symbolic) g(link) g(to) p
Fh 499 w(cuddBdd) r(.h) p Fo(.) 9008 48072 y(\(That) 302
b(is:) p Fh 376 w(ln) 727 b(-s) h(cuddB) r(dd.h) g(bdd.h) p
Fo(.\)) p Black 7493 50513 a(5.) p Black 606 w(In) p
Fh 357 w(SISDIR) r(/sis/cud) r(d) p Fo 357 w(delete) p
Fh 358 w(Makef) r(ile) p Fo 358 w(and) 357 b(rename) p
Fh 358 w(Makefi) r(le.sis) p Fo 9008 52019 a(as) p Fh
303 w(Makefil) r(e) p Fo(.) 376 b(Do) 303 b(the) g(same) g(in) p
Fh 303 w(SISDIR) r(/sis/mtr) p Fo 2 w(.) p Black 7493
54460 a(6.) p Black 606 w(Cop) -12 b(y) p Fh 231 w(CUDDDIR) r(/sis/st) r
(.[ch]) p Fo 231 w(and) p Fh 231 w(CUDDDIR) r(/st/doc) r(/st.doc) p
Fo 232 w(to) p Fh 230 w(SISDIR) r(/sis/st) p Fo 2 w(.) 9008
55965 y(\(This) 385 b(will) i(o) -18 b(v) g(erwrite) 386
b(the) g(original) h(\002les:) 542 b(Y) -133 b(ou) 386
b(may) h(w) -12 b(ant) 387 b(to) f(sa) -24 b(v) -18 b(e) 386
b(them) h(before-) 9008 57471 y(hand.\)) p Black 7493
59912 a(7.) p Black 606 w(From) p Fh 230 w(CUDDDIR) r(/util) p
Fo 231 w(cop) -12 b(y) p Fh 231 w(datali) r(mit.c) p
Fo 231 w(to) p Fh 231 w(SISDIR/s) r(is/util) p Fo 2 w(.) 351
b(Up-) 9008 61418 y(date) p Fh 392 w(util.h) p Fo 394
w(and) p Fh 392 w(Makefil) r(e) p Fo 392 w(in) p Fh 392
w(SISDIR/) r(sis/util) p Fo 2 w(.) 642 b(Speci\002cally) -79
b(,) 415 b(add) 9008 62923 y(the) 501 b(declaration) p
Fh 501 w(EXTERN) 729 b(long) f(getSof) r(tDataLi) r(mit\(\);) p
Fo 601 w(to) p Fh 501 w(util.h) p Fo 9008 64429 a(and) 303
b(add) p Fh 304 w(datalimi) r(t.c) p Fo 304 w(to) g(the) g(list) f(of) h
(source) g(\002les) f(\(PSRC\)) h(in) p Fh 303 w(Makef) r(ile) p
Fo(.) p Black 5978 65187 15940 45 v Ff 7383 65928 a(3) p
Fe 7771 66351 a(http://vlsi.Colorado.EDU/) 249 b(vis/) p
Black Black Fo 25297 69672 a(22) p Black 90 rotate dyy
eop
%%Page: 23 23
23 22 bop Black Black Black Fo 7493 7638 a(8.) p Black
606 w(In) p Fh 296 w(SISDIR) r(/sis) p Fo 297 w(remo) -18
b(v) g(e) 296 b(the) g(link) h(from) p Fh 295 w(bdd) p
Fo 298 w(to) p Fh 296 w(bdd) p 34362 7638 364 45 v 437
w(cmu) p Fo 297 w(or) p Fh 296 w(bdd) p 40764 7638 V
437 w(ucb) p Fo 297 w(\(that) 9008 9143 y(is,) p Fh 481
w(rm) 728 b(bdd) p Fo(\)) 447 b(and) f(mak) -12 b(e) p
Fh 447 w(bdd) p Fo 447 w(a) 446 b(symbolic) g(link) g(to) p
Fh 446 w(cudd) p Fo 2 w(.) 805 b(\(That) 445 b(is:) p
Fh 662 w(ln) 728 b(-s) 9008 10649 y(cudd) g(bdd) p Fo(.\)) p
Black 7493 13113 a(9.) p Black 606 w(Still) 230 b(in) p
Fh 230 w(SISDI) r(R/sis) p Fo(,) 246 b(edit) p Fh 230
w(Makef) r(ile) p Fo(,) p Fh 245 w(Makef) r(ile.oct) p
Fo 2 w(,) f(and) p Fh 230 w(Makefi) r(le.nooc) r(t) p
Fo(.) 9008 14618 y(In) 303 b(all) g(three) g(\002les) f(add) i(mtr) e
(to) h(the) h(list) e(of) h(directories) f(to) h(be) g(made) h
(\(DIRS\).) p Black 6887 17082 a(10.) p Black 606 w(In) p
Fh 230 w(SISDIR) r(/sis/inc) r(lude) p Fo 231 w(mak) -12
b(e) p Fh 231 w(mtr.h) p Fo 231 w(a) 231 b(symbolic) f(link) g(to) p
Fh 231 w(../mtr/m) r(tr.h) p Fo(.) p Black 6887 19546
a(11.) p Black 606 w(In) p Fh 230 w(SISDIR) r(/sis/doc) p
Fo 232 w(mak) -12 b(e) p Fh 231 w(cudd.do) r(c) p Fo
230 w(a) 231 b(symbolic) f(link) g(to) p Fh 230 w(../cu) r(dd/cudd) r
(.doc) p Fo 9008 21051 a(and) p Fh 420 w(mtr.do) r(c) p
Fo 420 w(a) 420 b(symbolic) g(link) g(to) p Fh 419 w(../m) r(tr/mtr.d) r
(oc) p Fo(.) 727 b(\(That) 419 b(is:) p Fh 609 w(ln) 728
b(-s) 9008 22557 y(../cud) r(d/cudd.d) r(oc) g(.;) f(ln) h(-s) g
(../mtr) r(/mtr.doc) h(.) p Fo(.\)) p Black 6887 25021
a(12.) p Black 606 w(From) p Fh 338 w(SISDIR) p Fo 340
w(do) p Fh 338 w(make) g(clean) p Fo 340 w(follo) -30
b(wed) 338 b(by) p Fh 338 w(make) 729 b(-i) p Fo(.) 482
b(This) 337 b(should) i(cre-) 9008 26526 y(ate) 303 b(a) g(w) -12
b(orking) 303 b(cop) -12 b(y) 304 b(of) e(SIS) h(that) g(uses) f(the) h
(CUDD) h(package.) 7859 28933 y(The) 458 b(replacement) h(for) e(the) p
Fh 458 w(st) p Fo 459 w(library) h(is) f(because) h(the) h(v) -18
b(ersion) 457 b(shipped) h(with) g(the) 5978 30439 y(CUDD) 314
b(package) h(tests) e(for) g(out-of-memory) g(conditions.) 407
b(Notice) 315 b(that) f(the) f(v) -18 b(ersion) 314 b(of) f(the) p
Fh 5978 31944 a(st) p Fo 441 w(library) 440 b(to) g(be) h(used) f(for) g
(replacement) h(is) g(not) f(the) h(one) g(used) f(for) g(the) h
(normal) f(b) -24 b(uild,) 5978 33450 y(because) 304
b(the) g(latter) g(has) g(been) g(modi\002ed) g(for) g(C++) f
(compatibility) -79 b(.) 379 b(The) 304 b(abo) -18 b(v) g(e) 304
b(installation) 5978 34955 y(procedure) 408 b(has) h(been) g(tested) g
(on) f(SIS) h(1.3.) 693 b(SIS) 408 b(can) h(be) g(obtained) g(via) g
(anon) -18 b(ymous) 409 b(FTP) 5978 36461 y(from) p Fh
229 w(ic.ee) r(cs.berke) r(ley.edu) p Fo 2 w(.) 351 b(T) -97
b(o) 230 b(b) -24 b(uild) 230 b(SIS) g(1.3,) 245 b(you) 231
b(need) p Fh 230 w(sis-1) r(.2.tar.) r(Z) p Fo 5978 37966
a(and) p Fh 238 w(sis-1.2.) r(patch1.) r(Z) p Fo(.) 238
b(When) g(compiling) g(on) g(a) g(DEC) f(Alpha,) 252
b(you) 238 b(should) f(add) h(the) p Fh 5978 39471 a(-ieee) p
9686 39471 V 437 w(with) p 13031 39471 V 438 w(no) p
14923 39471 V 437 w(inexact) p Fo 260 w(\003ag.) 361
b(\(See) 258 b(Section) h(3.5.2.\)) 361 b(Refer) 258
b(to) h(the) p Fh 259 w(Makefile) p Fo 260 w(in) 5978
40977 y(the) 303 b(top) g(le) -30 b(v) -18 b(el) 303
b(directory) g(of) f(the) h(distrib) -24 b(ution) 302
b(for) h(ho) -30 b(w) 303 b(to) g(compile) g(with) g(32-bit) g
(pointers.) p Fi 5978 44281 a(3.18) 1329 b(Writing) 332
b(Decision) g(Diagrams) g(to) h(a) f(File) p Fo 5978
46604 a(The) 271 b(CUDD) h(package) h(pro) -18 b(vides) 271
b(se) -30 b(v) -18 b(eral) 270 b(functions) h(to) h(write) f(decision) h
(diagrams) f(to) g(a) h(\002le.) p Fn 5978 48110 a(Cudd) p
8677 48110 V 437 w(DumpBlif) p Fo 465 w(writes) 287 b(a) i(\002le) f
(in) p Fn 288 w(blif) p Fo 465 w(format.) 370 b(It) 288
b(is) g(restricted) f(to) h(BDDs.) 372 b(The) 288 b(diagrams) 5978
49615 y(are) 314 b(written) g(as) f(a) i(netw) -12 b(ork) 314
b(of) g(multiple) -18 b(x) g(ers,) 316 b(one) e(multiple) -18
b(x) g(er) 314 b(for) f(each) i(internal) f(node) g(of) 5978
51121 y(the) 303 b(BDD.) p Fn 7859 52626 a(Cudd) p 10558
52626 V 437 w(DumpDot) p Fo 494 w(produces) 471 b(input) g(suitable) g
(to) g(the) g(graph-dra) -18 b(wing) 471 b(program) p
Fn 471 w(dot) p Fg 45330 52186 a(4) p Fo 5978 54132 a(written) 367
b(by) h(Eleftherios) e(K) -42 b(outso\002os) 366 b(and) i(Stephen) g
(C.) g(North.) 569 b(An) 367 b(e) -18 b(xample) 368 b(of) f(dra) -18
b(wing) 5978 55637 y(produced) 320 b(by) h(dot) f(from) g(the) h
(output) f(of) p Fn 320 w(Cudd) p 26136 55637 V 437 w(DumpDot) p
Fo 343 w(is) g(sho) -30 b(wn) 320 b(in) h(Figure) f(1.) 428
b(It) 320 b(is) g(re-) 5978 57143 y(stricted) 313 b(to) h(BDDs) g(and) h
(ADDs.) p Fn 409 w(Cudd) p 23034 57143 V 437 w(zddDumpDot) p
Fo 336 w(is) e(the) h(analog) h(of) p Fn 314 w(Cudd) p
40684 57143 V 437 w(DumpDot) p Fo 5978 58648 a(for) 302
b(ZDDs.) p Fn 7859 60154 a(Cudd) p 10558 60154 V 437
w(DumpDaV) -90 b(inci) p Fo 531 w(produces) 529 b(input) g(suitable) g
(to) h(the) g(graph-dra) -18 b(wing) 529 b(program) p
Fn 5978 61659 a(daV) -90 b(inci) p Fg 9659 61219 a(5) p
Fo 10651 61659 a(de) -30 b(v) -18 b(eloped) 494 b(at) g(the) g(Uni) -30
b(v) -18 b(ersity) 492 b(of) i(Bremen.) 948 b(It) 494
b(is) f(restricted) g(to) h(BDDs) g(and) 5978 63164 y(ADDs.) p
Black 5978 63946 15940 45 v Ff 7383 64687 a(4) p Fe 7771
65110 a(http://www) -65 b(.research) r(.att.com/sw/tools/graphviz) p
Ff 7383 65928 a(5) p Fe 7771 66351 a(ftp://ftp.uni-bremen.de/pub/graph)
r(ics/daV) -60 b(inci) p Black Black Fo 25297 69672 a(23) p
Black 90 rotate dyy eop
%%Page: 24 24
24 23 bop Black Black Black 9619 56347 a @beginspecial
66 @llx 36 @lly 547 @urx 757 @ury 4393 @rhi @setspecial
%%BeginDocument: phase.ps
%!PS-Adobe-2.0
%%Creator: dot version 95 (4-10-95)
%%For: (fabio) Fabio Somenzi,OT4-11,2-3466,ECE faculty
%%Title: DD
%%Pages: (atend)
%%BoundingBox: 66 36 547 757
%%EndComments
%%BeginProlog
save
/DotDict 200 dict def
DotDict begin

%%BeginResource: procset
/coord-font-family /Times-Roman def
/default-font-family /Times-Roman def
/coordfont coord-font-family findfont 8 scalefont def

/InvScaleFactor 1.0 def
/set_scale {
        dup 1 exch div /InvScaleFactor exch def
        dup scale
} bind def

% styles
/solid { } bind def
/dashed { [9 InvScaleFactor mul dup ] 0 setdash } bind def
/dotted { [1 InvScaleFactor mul 6 InvScaleFactor mul] 0 setdash } bind def
/invis {/fill {newpath} def /stroke {newpath} def /show {pop newpath} def} bind def
/bold { 2 setlinewidth } bind def
/filled { } bind def
/unfilled { } bind def
/rounded { } bind def
/diagonals { } bind def

% hooks for setting color 
/nodecolor { sethsbcolor } bind def
/edgecolor { sethsbcolor } bind def
/graphcolor { sethsbcolor } bind def
/nopcolor {pop pop pop} bind def

/beginpage {    % i j npages
        /npages exch def
        /j exch def
        /i exch def
        /str 10 string def
        npages 1 gt {
                gsave
                        coordfont setfont
                        0 0 moveto
                        (() show i str cvs show (,) show j str cvs show ()) show
                grestore
        } if
} bind def

/set_font {
        findfont exch
        scalefont setfont
} def

/arrowhead {
        /arrowwidth exch def
        /arrowlength exch def
        gsave
                3 1 roll
                translate
                        rotate
                        newpath
                        arrowlength arrowwidth 2 div moveto
                        0 0 lineto
                        arrowlength arrowwidth -2 div lineto
                closepath fill
                stroke
        grestore
} def

% draw aligned label in bounding box aligned to current point
% alignfactor tells what fraction to place on the left.
% -.5 is centered.
/alignedtext {                  % text labelwidth fontsz alignfactor
        /alignfactor exch def
        /fontsz exch def
        /width exch def
        /text exch def
        gsave
                % even if node or edge is dashed, don't paint text with dashes
                [] 0 setdash
                currentpoint newpath moveto
                text stringwidth pop
                alignfactor mul fontsz -.3 mul rmoveto
                text show
        grestore
} def

/boxprim {                              % xcorner ycorner xsize ysize
                4 2 roll
                moveto
                2 copy
                exch 0 rlineto
                0 exch rlineto
                pop neg 0 rlineto
                closepath
} bind def

/ellipse_path {
        /ry exch def
        /rx exch def
        /y exch def
        /x exch def
        matrix currentmatrix
        newpath
        x y translate
        rx ry scale
        0 0 1 0 360 arc
        setmatrix
} bind def

/endpage { showpage } bind def

/layercolorseq
        [       % layer color sequence - darkest to lightest
                [0 0 0]
                [.2 .8 .8]
                [.4 .8 .8]
                [.6 .8 .8]
                [.8 .8 .8]
        ]
def

/setlayer {/maxlayer exch def /curlayer exch def
        layercolorseq curlayer get
        aload pop sethsbcolor
        /nodecolor {nopcolor} def
        /edgecolor {nopcolor} def
        /graphcolor {nopcolor} def
} bind def

/onlayer { curlayer ne {invis} if } def

/onlayers {
        /myupper exch def
        /mylower exch def
        curlayer mylower lt
        curlayer myupper gt
        or
        {invis} if
} def

/curlayer 0 def

%%EndResource
%%EndProlog
%%BeginSetup
14 default-font-family set_font
% /arrowlength 10 def
% /arrowwidth 5 def
%%EndSetup
%%Page: 1 (atend)
%%PageBoundingBox: 66 36 547 757
gsave
65 35 482 722 boxprim clip newpath
66 36 translate
0 0 1 beginpage
0.7407 set_scale
0 0 translate 0 rotate
0.000 0.000 0.000 graphcolor
14.00 /Times-Roman set_font

%       CONST NODES
gsave 10 dict begin
invis
gsave 10 dict begin
55 19 moveto (CONST NODES) 96 14.00 -0.50 alignedtext
end grestore
end grestore

%       a110
gsave 10 dict begin
gsave 10 dict begin
55 883 moveto (a110) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a111
gsave 10 dict begin
gsave 10 dict begin
55 811 moveto (a111) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a110 -> a111
gsave 10 dict begin
invis
newpath 55 864 moveto
55 853 55 839 55 828 curveto
stroke
end grestore

%       a210
gsave 10 dict begin
gsave 10 dict begin
55 739 moveto (a210) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a111 -> a210
gsave 10 dict begin
invis
newpath 55 792 moveto
55 781 55 767 55 756 curveto
stroke
end grestore

%       a211
gsave 10 dict begin
gsave 10 dict begin
55 667 moveto (a211) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a210 -> a211
gsave 10 dict begin
invis
newpath 55 720 moveto
55 709 55 695 55 684 curveto
stroke
end grestore

%       a310
gsave 10 dict begin
gsave 10 dict begin
55 595 moveto (a310) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a211 -> a310
gsave 10 dict begin
invis
newpath 55 648 moveto
55 637 55 623 55 612 curveto
stroke
end grestore

%       a311
gsave 10 dict begin
gsave 10 dict begin
55 523 moveto (a311) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a310 -> a311
gsave 10 dict begin
invis
newpath 55 576 moveto
55 565 55 551 55 540 curveto
stroke
end grestore

%       a410
gsave 10 dict begin
gsave 10 dict begin
55 451 moveto (a410) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a311 -> a410
gsave 10 dict begin
invis
newpath 55 504 moveto
55 493 55 479 55 468 curveto
stroke
end grestore

%       a411
gsave 10 dict begin
gsave 10 dict begin
55 379 moveto (a411) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a410 -> a411
gsave 10 dict begin
invis
newpath 55 432 moveto
55 421 55 407 55 396 curveto
stroke
end grestore

%       a510
gsave 10 dict begin
gsave 10 dict begin
55 307 moveto (a510) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a411 -> a510
gsave 10 dict begin
invis
newpath 55 360 moveto
55 349 55 335 55 324 curveto
stroke
end grestore

%       a511
gsave 10 dict begin
gsave 10 dict begin
55 235 moveto (a511) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a510 -> a511
gsave 10 dict begin
invis
newpath 55 288 moveto
55 277 55 263 55 252 curveto
stroke
end grestore

%       a610
gsave 10 dict begin
gsave 10 dict begin
55 163 moveto (a610) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a511 -> a610
gsave 10 dict begin
invis
newpath 55 216 moveto
55 205 55 191 55 180 curveto
stroke
end grestore

%       a611
gsave 10 dict begin
gsave 10 dict begin
55 91 moveto (a611) 27 14.00 -0.50 alignedtext
end grestore
end grestore

%       a610 -> a611
gsave 10 dict begin
invis
newpath 55 144 moveto
55 133 55 119 55 108 curveto
stroke
end grestore

%       a611 -> CONST NODES
gsave 10 dict begin
invis
newpath 55 72 moveto
55 61 55 47 55 36 curveto
stroke
end grestore

%       o
gsave 10 dict begin
newpath 511 972 moveto
457 972 lineto
457 936 lineto
511 936 lineto
closepath
stroke
gsave 10 dict begin
484 955 moveto (o) 7 14.00 -0.50 alignedtext
end grestore
end grestore

%       a00
gsave 10 dict begin
484 882 27 18 ellipse_path
stroke
gsave 10 dict begin
484 883 moveto (a00) 20 14.00 -0.50 alignedtext
end grestore
end grestore

%       o -> a00
gsave 10 dict begin
solid
newpath 484 936 moveto
484 925 484 911 484 900 curveto
stroke
end grestore

%       9fc
gsave 10 dict begin
448 810 27 18 ellipse_path
stroke
gsave 10 dict begin
448 811 moveto (9fc) 17 14.00 -0.50 alignedtext
end grestore
end grestore

%       a00 -> 9fc
newpath 475 865 moveto
470 853 462 839 457 827 curveto
stroke

%       9ff
gsave 10 dict begin
520 810 27 18 ellipse_path
stroke
gsave 10 dict begin
520 811 moveto (9ff) 16 14.00 -0.50 alignedtext
end grestore
end grestore

%       a00 -> 9ff
gsave 10 dict begin
dashed
newpath 493 865 moveto
498 853 506 839 511 827 curveto
stroke
end grestore

%       995
gsave 10 dict begin
453 738 27 18 ellipse_path
stroke
gsave 10 dict begin
453 739 moveto (995) 21 14.00 -0.50 alignedtext
end grestore
end grestore

%       9fc -> 995
gsave 10 dict begin
dashed
newpath 449 792 moveto
450 781 451 767 452 756 curveto
stroke
end grestore

%       9fb
gsave 10 dict begin
381 738 27 18 ellipse_path
stroke
gsave 10 dict begin
381 739 moveto (9fb) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9fc -> 9fb
newpath 433 794 moveto
422 782 407 765 396 753 curveto
stroke

%       9fe
gsave 10 dict begin
584 738 27 18 ellipse_path
stroke
gsave 10 dict begin
584 739 moveto (9fe) 17 14.00 -0.50 alignedtext
end grestore
end grestore

%       9ff -> 9fe
gsave 10 dict begin
dashed
newpath 534 794 moveto
545 782 560 765 570 753 curveto
stroke
end grestore

%       95f
gsave 10 dict begin
512 666 27 18 ellipse_path
stroke
gsave 10 dict begin
512 667 moveto (95f) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9ff -> 95f
newpath 519 792 moveto
518 764 515 712 513 684 curveto
stroke

%       994
gsave 10 dict begin
347 594 27 18 ellipse_path
stroke
gsave 10 dict begin
347 595 moveto (994) 21 14.00 -0.50 alignedtext
end grestore
end grestore

%       995 -> 994
newpath 432 727 moveto
407 714 370 693 363 684 curveto
356 675 351 636 349 612 curveto
stroke

%       946
gsave 10 dict begin
newpath 401 36 moveto
347 36 lineto
347 0 lineto
401 0 lineto
closepath
stroke
gsave 10 dict begin
374 19 moveto (1) 7 14.00 -0.50 alignedtext
end grestore
end grestore

%       995 -> 946
gsave 10 dict begin
dotted
newpath 584 594 moveto
589 570 587 545 584 522 curveto
stroke
newpath 453 720 moveto
454 698 458 662 473 648 curveto
498 621 544 628 577 612 curveto
582 609 582 600 584 594 curveto
stroke
end grestore

%       9f7
gsave 10 dict begin
292 666 27 18 ellipse_path
stroke
gsave 10 dict begin
292 667 moveto (9f7) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9fb -> 9f7
newpath 363 724 moveto
347 711 325 693 309 680 curveto
stroke

%       9fa
gsave 10 dict begin
402 666 27 18 ellipse_path
stroke
gsave 10 dict begin
402 667 moveto (9fa) 17 14.00 -0.50 alignedtext
end grestore
end grestore

%       9fb -> 9fa
gsave 10 dict begin
dashed
newpath 386 720 moveto
389 709 393 695 397 684 curveto
stroke
end grestore

%       9fd
gsave 10 dict begin
584 666 27 18 ellipse_path
stroke
gsave 10 dict begin
584 667 moveto (9fd) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9fe -> 9fd
newpath 584 720 moveto
584 709 584 695 584 684 curveto
stroke

%       9fe -> 946
gsave 10 dict begin
dotted
newpath 600 723 moveto
611 711 625 696 632 684 curveto
637 673 637 658 632 648 curveto
632 648 584 594 584 594 curveto
stroke
end grestore

%       9f7 -> 994
gsave 10 dict begin
dashed
newpath 304 650 moveto
313 638 326 622 335 610 curveto
stroke
end grestore

%       9f6
gsave 10 dict begin
275 594 27 18 ellipse_path
stroke
gsave 10 dict begin
275 595 moveto (9f6) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f7 -> 9f6
newpath 288 648 moveto
285 637 282 623 279 612 curveto
stroke

%       9f9
gsave 10 dict begin
529 594 27 18 ellipse_path
stroke
gsave 10 dict begin
529 595 moveto (9f9) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9fa -> 9f9
gsave 10 dict begin
dashed
newpath 423 654 moveto
447 641 485 619 508 606 curveto
stroke
end grestore

%       95e
gsave 10 dict begin
457 522 27 18 ellipse_path
stroke
gsave 10 dict begin
457 523 moveto (95e) 20 14.00 -0.50 alignedtext
end grestore
end grestore

%       9fa -> 95e
newpath 465 594 moveto
464 579 462 556 460 540 curveto
stroke
newpath 420 652 moveto
439 638 464 614 465 594 curveto
stroke

%       95f -> 95e
newpath 497 651 moveto
483 636 464 612 465 594 curveto
stroke

%       95f -> 946
gsave 10 dict begin
dotted
newpath 531 653 moveto
551 639 579 615 584 594 curveto
stroke
end grestore

%       9fd -> 9f9
newpath 572 650 moveto
563 638 550 622 541 610 curveto
stroke

%       9fd -> 946
gsave 10 dict begin
dotted
newpath 582 648 moveto
581 631 580 608 584 594 curveto
stroke
end grestore

%       993
gsave 10 dict begin
292 450 27 18 ellipse_path
stroke
gsave 10 dict begin
292 451 moveto (993) 21 14.00 -0.50 alignedtext
end grestore
end grestore

%       994 -> 993
newpath 333 578 moveto
323 566 312 551 308 540 curveto
301 521 296 489 294 468 curveto
stroke

%       994 -> 946
gsave 10 dict begin
dotted
newpath 357 577 moveto
371 556 396 519 418 504 curveto
447 482 489 484 522 468 curveto
527 465 527 456 529 450 curveto
stroke
newpath 529 450 moveto
534 426 532 401 529 378 curveto
stroke
end grestore

%       9f5
gsave 10 dict begin
347 522 27 18 ellipse_path
stroke
gsave 10 dict begin
347 523 moveto (9f5) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f6 -> 9f5
gsave 10 dict begin
dashed
newpath 290 579 moveto
302 567 319 550 332 537 curveto
stroke
end grestore

%       9f2
gsave 10 dict begin
237 522 27 18 ellipse_path
stroke
gsave 10 dict begin
237 523 moveto (9f2) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f6 -> 9f2
newpath 266 577 moveto
260 566 252 551 246 539 curveto
stroke

%       9f8
gsave 10 dict begin
529 522 27 18 ellipse_path
stroke
gsave 10 dict begin
529 523 moveto (9f8) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f9 -> 9f8
newpath 529 576 moveto
529 565 529 551 529 540 curveto
stroke

%       9f9 -> 946
gsave 10 dict begin
dotted
newpath 546 580 moveto
563 565 587 541 584 522 curveto
stroke
newpath 584 522 moveto
579 492 522 479 529 450 curveto
stroke
end grestore

%       9f4
gsave 10 dict begin
474 450 27 18 ellipse_path
stroke
gsave 10 dict begin
474 451 moveto (9f4) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f5 -> 9f4
gsave 10 dict begin
dashed
newpath 368 510 moveto
392 497 430 475 453 462 curveto
stroke
end grestore

%       95d
gsave 10 dict begin
402 378 27 18 ellipse_path
stroke
gsave 10 dict begin
402 379 moveto (95d) 21 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f5 -> 95d
newpath 365 508 moveto
384 494 409 470 410 450 curveto
stroke
newpath 410 450 moveto
409 435 407 412 405 396 curveto
stroke

%       9f2 -> 993
gsave 10 dict begin
dashed
newpath 249 506 moveto
258 494 271 478 280 466 curveto
stroke
end grestore

%       9f1
gsave 10 dict begin
220 450 27 18 ellipse_path
stroke
gsave 10 dict begin
220 451 moveto (9f1) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f2 -> 9f1
newpath 233 504 moveto
230 493 227 479 224 468 curveto
stroke

%       95e -> 95d
newpath 442 507 moveto
428 492 409 468 410 450 curveto
stroke

%       95e -> 946
gsave 10 dict begin
dotted
newpath 476 509 moveto
496 495 524 471 529 450 curveto
stroke
end grestore

%       9f8 -> 9f4
newpath 517 506 moveto
508 494 495 478 486 466 curveto
stroke

%       9f8 -> 946
gsave 10 dict begin
dotted
newpath 527 504 moveto
526 487 525 464 529 450 curveto
stroke
end grestore

%       992
gsave 10 dict begin
237 306 27 18 ellipse_path
stroke
gsave 10 dict begin
237 307 moveto (992) 21 14.00 -0.50 alignedtext
end grestore
end grestore

%       993 -> 992
newpath 278 434 moveto
268 422 257 407 253 396 curveto
246 377 241 345 239 324 curveto
stroke

%       993 -> 946
gsave 10 dict begin
dotted
newpath 474 306 moveto
474 306 474 234 474 234 curveto
stroke
newpath 302 433 moveto
316 412 341 375 363 360 curveto
392 338 434 340 467 324 curveto
472 321 472 312 474 306 curveto
stroke
end grestore

%       9ed
gsave 10 dict begin
182 378 27 18 ellipse_path
stroke
gsave 10 dict begin
182 379 moveto (9ed) 20 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f1 -> 9ed
newpath 211 433 moveto
205 422 197 407 191 395 curveto
stroke

%       9f0
gsave 10 dict begin
292 378 27 18 ellipse_path
stroke
gsave 10 dict begin
292 379 moveto (9f0) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f1 -> 9f0
gsave 10 dict begin
dashed
newpath 235 435 moveto
247 423 264 406 277 393 curveto
stroke
end grestore

%       9f3
gsave 10 dict begin
474 378 27 18 ellipse_path
stroke
gsave 10 dict begin
474 379 moveto (9f3) 18 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f4 -> 9f3
newpath 474 432 moveto
474 421 474 407 474 396 curveto
stroke

%       9f4 -> 946
gsave 10 dict begin
dotted
newpath 491 436 moveto
508 421 532 397 529 378 curveto
stroke
newpath 529 378 moveto
528 371 525 365 522 360 curveto
522 360 474 306 474 306 curveto
stroke
end grestore

%       9ed -> 992
gsave 10 dict begin
dashed
newpath 194 362 moveto
203 350 216 334 225 322 curveto
stroke
end grestore

%       9ec
gsave 10 dict begin
165 306 27 18 ellipse_path
stroke
gsave 10 dict begin
165 307 moveto (9ec) 19 14.00 -0.50 alignedtext
end grestore
end grestore

%       9ed -> 9ec
newpath 178 360 moveto
175 349 172 335 169 324 curveto
stroke

%       9ef
gsave 10 dict begin
419 306 27 18 ellipse_path
stroke
gsave 10 dict begin
419 307 moveto (9ef) 17 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f0 -> 9ef
gsave 10 dict begin
dashed
newpath 313 366 moveto
337 353 375 331 398 318 curveto
stroke
end grestore

%       95c
gsave 10 dict begin
347 234 27 18 ellipse_path
stroke
gsave 10 dict begin
347 235 moveto (95c) 20 14.00 -0.50 alignedtext
end grestore
end grestore

%       9f0 -> 95c
newpath 310 364 moveto
329 350 354 326 355 306 curveto
stroke
newpath 355 306 moveto
354 291 352 268 350 252 curveto
stroke

%       95d -> 95c
newpath 387 363 moveto
373 348 354 324 355 306 curveto
stroke

%       95d -> 946
gsave 10 dict begin
dotted
newpath 421 365 moveto
441 351 469 327 474 306 curveto
stroke
end grestore

%       9f3 -> 9ef
newpath 462 362 moveto
453 350 440 334 431 322 curveto
stroke

%       9f3 -> 946
gsave 10 dict begin
dotted
newpath 472 360 moveto
471 343 470 320 474 306 curveto
stroke
end grestore

%       954
gsave 10 dict begin
165 162 27 18 ellipse_path
stroke
gsave 10 dict begin
165 163 moveto (954) 21 14.00 -0.50 alignedtext
end grestore
end grestore

%       992 -> 954
newpath 220 234 moveto
214 216 194 192 180 177 curveto
stroke
newpath 233 288 moveto
230 272 224 248 220 234 curveto
stroke

%       992 -> 946
gsave 10 dict begin
dotted
newpath 220 234 moveto
220 234 213 144 213 144 curveto
213 144 193 90 193 90 curveto
stroke
end grestore

%       987
gsave 10 dict begin
165 234 27 18 ellipse_path
stroke
gsave 10 dict begin
165 235 moveto (987) 21 14.00 -0.50 alignedtext
end grestore
end grestore

%       9ec -> 987
newpath 165 288 moveto
165 277 165 263 165 252 curveto
stroke

%       9eb
gsave 10 dict begin
275 234 27 18 ellipse_path
stroke
gsave 10 dict begin
275 235 moveto (9eb) 20 14.00 -0.50 alignedtext
end grestore
end grestore

%       9ec -> 9eb
gsave 10 dict begin
dashed
newpath 184 293 moveto
204 280 236 260 256 247 curveto
stroke
end grestore

%       9ee
gsave 10 dict begin
419 234 27 18 ellipse_path
stroke
gsave 10 dict begin
419 235 moveto (9ee) 19 14.00 -0.50 alignedtext
end grestore
end grestore

%       9ef -> 9ee
newpath 419 288 moveto
419 277 419 263 419 252 curveto
stroke

%       9ef -> 946
gsave 10 dict begin
dotted
newpath 474 234 moveto
477 210 461 184 469 162 curveto
stroke
newpath 435 291 moveto
450 276 471 252 474 234 curveto
stroke
end grestore

%       987 -> 954
gsave 10 dict begin
dashed
newpath 165 216 moveto
165 205 165 191 165 180 curveto
stroke
end grestore

%       987 -> 946
newpath 193 90 moveto
225 56 305 34 347 24 curveto
stroke
newpath 152 218 moveto
136 197 113 162 126 144 curveto
144 120 173 110 193 90 curveto
stroke

%       9ea
gsave 10 dict begin
410 162 27 18 ellipse_path
stroke
gsave 10 dict begin
410 163 moveto (9ea) 19 14.00 -0.50 alignedtext
end grestore
end grestore

%       9eb -> 9ea
gsave 10 dict begin
dashed
newpath 296 223 moveto
321 210 363 187 389 174 curveto
stroke
end grestore

%       955
gsave 10 dict begin
374 90 27 18 ellipse_path
stroke
gsave 10 dict begin
374 91 moveto (955) 21 14.00 -0.50 alignedtext
end grestore
end grestore

%       9eb -> 955
newpath 293 220 moveto
311 206 338 182 347 162 curveto
stroke
newpath 347 162 moveto
353 147 362 124 368 108 curveto
stroke

%       95c -> 955
newpath 344 216 moveto
342 199 341 175 347 162 curveto
stroke

%       95c -> 946
gsave 10 dict begin
dotted
newpath 368 222 moveto
372 220 376 217 380 216 curveto
407 203 436 195 462 180 curveto
467 176 466 168 469 162 curveto
stroke
newpath 469 162 moveto
476 139 475 113 469 90 curveto
stroke
end grestore

%       9ee -> 9ea
newpath 417 216 moveto
415 205 414 191 412 180 curveto
stroke

%       9ee -> 946
gsave 10 dict begin
dotted
newpath 432 218 moveto
442 206 454 190 462 180 curveto
465 174 466 168 469 162 curveto
stroke
end grestore

%       954 -> 946
newpath 169 144 moveto
174 127 182 101 193 90 curveto
stroke

%       954 -> 946
gsave 10 dict begin
dotted
end grestore

%       9ea -> 955
newpath 401 145 moveto
396 133 388 119 383 107 curveto
stroke

%       9ea -> 946
gsave 10 dict begin
dotted
newpath 429 149 moveto
448 133 474 109 469 90 curveto
stroke
newpath 469 90 moveto
462 66 427 44 401 30 curveto
stroke
end grestore

%       955 -> 946
newpath 374 72 moveto
374 61 374 47 374 36 curveto
stroke

%       955 -> 946
gsave 10 dict begin
dotted
end grestore
endpage
grestore
%%PageTrailer
%%Trailer
%%Pages: 1
end
restore
%%EOF

%%EndDocument
@endspecial Fo 5978 58959 a(Figure) 432 b(1:) 636 b(A) 433
b(BDD) g(representing) f(a) h(phase) g(constraint) f(for) h(the) g
(optimization) g(of) f(\002x) -18 b(ed-) 5978 60465 y(polarity) 321
b(Reed-Muller) g(forms.) 429 b(The) 321 b(label) g(of) g(each) h(node) g
(is) e(the) i(unique) f(part) g(of) g(the) h(node) 5978
61970 y(address.) 370 b(All) 289 b(nodes) g(on) g(the) h(same) f(le) -30
b(v) -18 b(el) 289 b(correspond) f(to) h(the) h(same) f(v) -30
b(ariable,) 292 b(whose) d(name) 5978 63476 y(is) 283
b(sho) -30 b(wn) 283 b(at) h(the) g(left) g(of) f(the) h(diagram.) 370
b(Dotted) 284 b(lines) f(indicate) i(complement) f(arcs.) 369
b(Dashed) 5978 64981 y(lines) 302 b(indicate) i(re) -18
b(gular) 302 b(\223else\224) i(arcs.) p Black Black 25297
69672 a(24) p Black 90 rotate dyy eop
%%Page: 25 25
25 24 bop Black Black Fo 7859 7638 a(Functions) 420 b(are) f(also) g(a)
-24 b(v) -30 b(ailable) 420 b(to) f(produce) h(the) g(input) f(format) g
(of) p Fn 419 w(DDcal) p Fo 421 w(\(see) g(Sec-) 5978
9143 y(tion) 303 b(2.2\)) f(and) i(f) -12 b(actored) 303
b(forms) n(.) p Fi 5978 12466 a(3.19) 1329 b(Sa) -33
b(ving) 331 b(and) h(Restoring) g(BDDs) p Fo 5978 14790
a(The) p Fn 298 w(dddmp) p Fg 11460 14350 a(6) p Fo 12256
14790 a(library) 298 b(by) g(Gianpiero) g(Cabodi) h(and) f(Stef) -12
b(ano) 298 b(Quer) g(allo) -30 b(ws) 298 b(a) g(CUDD) h(appli-) 5978
16295 y(cation) 365 b(to) h(sa) -24 b(v) -18 b(e) 365
b(BDDs) h(to) f(disk) g(in) h(compact) g(form) e(for) h(later) h
(retrie) -30 b(v) g(al.) 562 b(See) 366 b(the) f(library') -67
b(s) 5978 17801 y(o) -30 b(wn) 303 b(documentation) g(for) g(the) g
(details.) p Fq 5978 21702 a(4) 1594 b(Pr) -29 b(ogrammer) n(') -59
b(s) 399 b(Manual) p Fo 5978 24462 a(This) 348 b(section) i(pro) -18
b(vides) 349 b(additional) h(detail) g(on) g(the) g(w) -12
b(orking) 349 b(of) h(the) g(CUDD) g(package) h(and) 5978
25968 y(on) 475 b(the) g(programming) g(con) -48 b(v) -18
b(entions) 475 b(follo) -30 b(wed) 475 b(in) g(its) f(writing.) 892
b(The) 475 b(additional) h(detail) 5978 27473 y(should) 246
b(help) i(those) f(who) g(w) -12 b(ant) 248 b(to) f(write) g
(procedures) g(that) g(directly) g(manipulate) h(the) f(CUDD) 5978
28979 y(data) 303 b(structures.) p Fi 5978 32301 a(4.1) 1328
b(Compiling) 332 b(and) g(Linking) p Fo 5978 34625 a(If) 420
b(you) i(plan) g(to) g(use) f(the) h(CUDD) g(package) g(as) g(a) f
(clear) h(box) g(\(for) e(instance,) 452 b(you) 421 b(w) -12
b(ant) 422 b(to) 5978 36130 y(write) 302 b(a) i(procedure) f(that) g
(tra) -24 b(v) -18 b(erses) 301 b(a) j(decision) f(diagram\)) f(you) h
(need) h(to) f(add) p Black Black Fh 5978 38632 a(#include) 729
b("cuddI) r(nt.h") p Fo 5978 41134 a(to) 310 b(your) g(source) h
(\002les.) 397 b(In) 311 b(addition,) h(you) f(should) f(link) p
Fh 311 w(libcudd) r(.a) p Fo 311 w(to) g(your) g(e) -18
b(x) g(ecutable.) 5978 42639 y(Some) 254 b(platforms) g(require) g
(speci\002c) h(compiler) f(and) h(link) -12 b(er) 255
b(\003ags.) 359 b(Refer) 255 b(to) f(the) p Fh 255 w(Makefi) r(le) p
Fo 5978 44145 a(in) 303 b(the) g(top) g(le) -30 b(v) -18
b(el) 303 b(directory) g(of) f(the) i(distrib) -24 b(u) n(tion.) p
Fi 5978 47467 a(4.2) 1328 b(Refer) -24 b(ence) 331 b(Counts) p
Fo 5978 49791 a(Garbage) 293 b(collection) h(in) g(the) f(CUDD) i
(package) f(is) f(based) g(on) h(reference) f(counts.) 372
b(Each) 294 b(node) 5978 51296 y(stores) 299 b(the) j(sum) e(of) h(the)
g(e) -18 b(xternal) 301 b(references) f(and) i(internal) f(references.)
374 b(An) 301 b(internal) g(BDD) 5978 52802 y(or) 427
b(ADD) h(node) g(is) g(created) g(by) g(a) g(call) g(to) p
Fn 428 w(cuddUniqueInter) p Fo(,) 459 b(an) 428 b(internal) g(ZDD) f
(node) i(is) 5978 54307 y(created) 352 b(by) h(a) f(call) h(to) p
Fn 352 w(cuddUniqueInterZdd) p Fo(,) 365 b(and) 352 b(a) h(terminal) f
(node) h(is) e(created) i(by) f(a) h(call) 5978 55813
y(to) p Fn 343 w(cuddUniqueConst) p Fo(.) 496 b(If) 342
b(the) h(node) g(returned) g(by) g(these) g(functions) f(is) h(ne) -30
b(w) -79 b(,) 353 b(its) 342 b(reference) 5978 57318
y(count) 401 b(is) g(zero.) 671 b(The) 401 b(function) h(that) f(calls)
p Fn 401 w(cuddUniqueInter) p Fo(,) p Fn 426 w(cuddUniqueInterZdd) p
Fo(,) 426 b(or) p Fn 5978 58823 a(cuddUniqueConst) p
Fo 474 w(is) 451 b(responsible) g(for) g(increasing) h(the) g
(reference) f(count) h(of) g(the) g(node.) 5978 60329
y(This) 302 b(is) g(accomplished) i(by) f(calling) p
Fn 303 w(Cudd) p 24332 60329 364 45 v 437 w(Ref) p Fo(.) 7859
61834 y(When) 272 b(a) f(function) g(is) f(no) h(longer) g(needed) h
(by) f(an) g(application,) 278 b(the) 271 b(memory) g(used) g(by) g
(its) 5978 63340 y(diagram) 403 b(can) h(be) g(rec) -18
b(ycled) 404 b(by) g(calling) p Fn 404 w(Cudd) p 26496
63340 V 437 w(Recur) -12 b(siveDer) -45 b(ef) p Fo 580
w(\(BDDs) 403 b(and) h(ADDs\)) f(or) p Black 5978 64159
15940 45 v Ff 7383 64900 a(6) p Fe 7771 65323 a
(ftp://ftp.polito.it/pub/research/dddmp/) p Black Black
Fo 25297 69672 a(25) p Black 90 rotate dyy eop
%%Page: 26 26
26 25 bop Black Black Fn 5978 7638 a(Cudd) p 8677 7638
364 45 v 437 w(Recur) -12 b(s) n(iveDer) -45 b(efZdd) p
Fo 432 w(\(ZDDs\).) 661 b(These) 398 b(functions) g(decrease) h(the) f
(reference) h(count) 5978 9143 y(of) 443 b(the) h(node) h(passed) e(to)
h(them.) 799 b(If) 443 b(the) h(reference) g(count) g(becomes) g(0,) 479
b(then) 445 b(tw) -12 b(o) 444 b(things) 5978 10649 y(happen:) p
Black 7493 13151 a(1.) p Black 606 w(The) 308 b(node) g(is) g(declared)
h(\223dead;\224) g(this) e(entails) h(increasing) g(the) h(counters) e
(of) h(the) h(dead) 9008 14656 y(nodes.) 727 b(\(One) 420
b(counter) h(for) e(the) i(subtable) f(to) g(which) h(the) f(node) h
(belongs,) 449 b(and) 421 b(one) 9008 16162 y(global) 406
b(counter) f(for) g(the) h(unique) f(table) h(to) g(which) g(the) f
(node) h(belongs.\)) 683 b(The) 405 b(node) 9008 17667
y(itself) 302 b(is) h(not) g(af) -30 b(fected.) p Black
7493 20169 a(2.) p Black 606 w(The) 303 b(function) g(is) f(recursi) -30
b(v) -18 b(ely) 302 b(called) i(on) f(the) g(tw) -12
b(o) 303 b(children) g(of) g(the) g(node.) 5978 22671
y(F) -18 b(or) 467 b(instance,) 509 b(if) 468 b(the) g(diagram) g(of) g
(a) g(function) g(does) g(not) g(share) g(an) -18 b(y) 468
b(nodes) g(with) g(other) 5978 24176 y(diagrams,) 482
b(then) 447 b(calling) p Fn 447 w(Cudd) p 20186 24176
V 437 w(Recur) -12 b(siveDer) -45 b(ef) p Fo 623 w(or) p
Fn 447 w(Cudd) p 32812 24176 V 437 w(Recur) -12 b(siveDer) -45
b(efZdd) p Fo 479 w(on) 447 b(its) 5978 25681 y(root) 302
b(will) h(cause) g(all) h(the) f(nodes) g(of) f(the) i(diagram) f(to) g
(become) g(dead.) 7859 27187 y(When) 255 b(the) e(number) h(of) f(dead)
h(nodes) g(reaches) f(a) h(gi) -30 b(v) -18 b(en) 254
b(le) -30 b(v) -18 b(el) 253 b(\(dynamically) h(determined) 5978
28692 y(by) 419 b(the) h(package\)) g(g) -6 b(arbage) 419
b(collection) h(tak) -12 b(es) 419 b(place.) 726 b(During) 419
b(g) -6 b(arbage) 420 b(collection) g(dead) 5978 30198
y(nodes) 302 b(are) h(returned) g(to) g(the) h(node) f(free) g(list.)
7859 31703 y(When) 469 b(a) f(ne) -30 b(w) 468 b(node) g(is) f
(created,) 510 b(it) 467 b(is) h(important) f(to) h(increase) g(its) f
(reference) h(count) 5978 33209 y(before) 302 b(one) i(of) e(the) i(tw)
-12 b(o) 303 b(follo) -30 b(wing) 302 b(e) -30 b(v) -18
b(ents) 303 b(occurs:) p Black 7493 35711 a(1.) p Black
606 w(A) 279 b(call) g(to) p Fn 279 w(cuddUniqueInter) p
Fo(,) k(to) p Fn 279 w(cuddUniqueInterZdd) p Fo(,) h(to) p
Fn 279 w(cuddUniqueConst) p Fo(,) g(or) 9008 37216 y(to) 303
b(a) g(function) g(that) g(may) h(e) -30 b(v) -18 b(entually) 303
b(cause) g(a) g(call) g(to) g(them.) p Black 7493 39718
a(2.) p Black 606 w(A) 241 b(call) h(to) p Fn 241 w(Cudd) p
15999 39718 V 437 w(Recur) -12 b(siveDer) -45 b(ef) p
Fo(,) 253 b(to) p Fn 241 w(Cudd) p 28285 39718 V 437
w(Recur) -12 b(siveDer) -45 b(efZdd) p Fo(,) 253 b(or) 241
b(to) g(a) g(function) 9008 41223 y(that) 303 b(may) g(e) -30
b(v) -18 b(entually) 304 b(cause) f(a) g(call) g(to) g(them.) 5978
43725 y(In) 399 b(practice,) 424 b(it) 400 b(is) f(recommended) i(to) e
(increase) h(the) g(reference) f(count) h(as) g(soon) f(as) h(the) g
(re-) 5978 45230 y(turned) 303 b(pointer) f(has) h(been) h(tested) f
(for) f(not) h(being) g(NULL.) p Fp 5978 48509 a(4.2.1) 1212
b(NULL) 304 b(Retur) -18 b(n) 303 b(V) -112 b(alues) p
Fo 5978 50832 a(The) 321 b(interf) -12 b(ace) 321 b(to) h(the) f
(memory) h(management) g(functions) f(\(e.g.,) 326 b(malloc\)) 321
b(used) h(by) f(CUDD) 5978 52338 y(intercepts) 342 b(NULL) g(return) g
(v) -30 b(alues) 342 b(and) h(calls) g(a) f(handler) -67
b(.) 495 b(The) 343 b(def) -12 b(ault) 342 b(handler) h(e) -18
b(xits) 342 b(with) 5978 53843 y(an) 378 b(error) e(message.) 600
b(If) 377 b(the) h(application) g(does) f(not) h(install) f(another) h
(handler) -48 b(,) 396 b(therefore,) g(a) 5978 55349
y(NULL) 302 b(return) h(v) -30 b(alue) 303 b(from) f(an) h(e) -18
b(xported) 303 b(function) g(of) g(CUDD) h(signals) e(an) i(internal) f
(error) -67 b(.) 7859 56854 y(If) 288 b(the) g(aplication,) k(ho) -30
b(we) g(v) -18 b(er) -48 b(,) 290 b(installs) d(another) h(handler) g
(that) h(lets) e(e) -18 b(x) g(ecution) 289 b(continue,) 5978
58360 y(a) 343 b(NULL) g(pointer) g(returned) g(by) g(an) h(e) -18
b(xported) 343 b(function) g(typically) h(indicates) f(that) g(the) h
(pro-) 5978 59865 y(cess) 407 b(has) g(run) h(out) g(of) g(memory) -79
b(.) p Fn 690 w(Cudd) p 23480 59865 V 437 w(ReadErr) -55
b(orCode) p Fo 407 w(can) 409 b(be) f(used) f(to) h(ascertain) g(the)
5978 61371 y(nature) 303 b(of) f(the) i(problem.) 7859
62876 y(An) 483 b(application) g(that) f(tests) f(for) h(the) g(result)
g(being) g(NULL) g(can) g(try) g(some) g(remedial) 5978
64381 y(action,) 302 b(if) f(it) h(runs) f(out) g(of) h(memory) -79
b(.) 375 b(F) -18 b(or) 301 b(instance,) h(it) g(may) g(free) f(some) h
(memory) f(that) h(is) f(not) 5978 65887 y(strictly) 350
b(necessary) -79 b(,) 363 b(or) 351 b(try) f(a) i(slo) -30
b(wer) 350 b(algorithm) h(that) g(tak) -12 b(es) 351
b(less) f(space.) 521 b(As) 350 b(an) i(e) -18 b(xample,) p
Black 25297 69672 a(26) p Black 90 rotate dyy eop
%%Page: 27 27
27 26 bop Black Black Fo 5978 7638 a(CUDD) 354 b(o) -18
b(v) g(errides) 352 b(the) i(def) -12 b(ault) 354 b(handler) f(when) h
(trying) g(to) f(enlar) -22 b(ge) 354 b(the) g(cache) g(or) f(increase)
5978 9143 y(the) 365 b(number) g(of) g(slots) f(of) h(the) g(unique) g
(table.) 563 b(If) 364 b(the) h(allocation) h(f) -12
b(ails,) 380 b(the) 365 b(package) h(prints) 5978 10649
y(out) 303 b(a) g(message) g(and) g(continues) g(without) g(resizing) g
(the) g(cache.) p Fp 5978 13927 a(4.2.2) p Fa 1212 w(Cudd) p
12381 13927 364 45 v 437 w(Recursiv) -18 b(eDeref) p
Fp 439 w(vs.) p Fa 303 w(Cudd) p 25359 13927 V 437 w(Deref) p
Fo 5978 16251 a(It) 465 b(is) g(often) g(the) h(case) g(that) g(a) f
(recursi) -30 b(v) -18 b(e) 465 b(procedure) g(has) h(to) f(protect) h
(the) g(result) f(it) g(is) g(go-) 5978 17756 y(ing) 502
b(to) h(return,) 552 b(while) 502 b(it) h(disposes) e(of) h
(intermediate) h(results.) 973 b(\(See) 503 b(the) f(pre) -30
b(vious) 502 b(dis-) 5978 19262 y(cussion) 528 b(on) i(when) g(to) f
(increase) h(reference) f(counts.\)) 1055 b(Once) 530
b(the) g(intermediate) f(results) 5978 20767 y(ha) -24
b(v) -18 b(e) 463 b(been) g(properly) g(disposed) f(of,) 503
b(the) 463 b(\002nal) g(result) g(must) f(be) i(returned) e(to) h(its) g
(pristine) 5978 22273 y(state,) 458 b(in) 428 b(which) h(the) f(root) f
(node) i(may) f(ha) -24 b(v) -18 b(e) 428 b(a) g(reference) g(count) g
(of) f(0.) 751 b(One) 428 b(cannot) g(use) p Fn 5978
23778 a(Cudd) p 8677 23778 V 437 w(Recur) -12 b(s) n(iveDer) -45
b(ef) p Fo 606 w(\(or) p Fn 428 w(Cudd) p 21669 23778
V 437 w(Recur) -12 b(siveDer) -45 b(efZdd) p Fo 33 w(\)) 428
b(for) g(this) g(purpose,) 459 b(because) 429 b(it) 5978
25284 y(may) 281 b(erroneously) f(mak) -12 b(e) 281 b(some) f(nodes) h
(dead.) 369 b(Therefore,) 284 b(the) d(package) h(pro) -18
b(vides) 280 b(a) h(dif) -30 b(fer) -24 b(-) 5978 26789
y(ent) 332 b(function:) p Fn 434 w(Cudd) p 15301 26789
V 437 w(Der) -45 b(ef) p Fo(.) 463 b(This) 332 b(function) g(is) g(not)
g(recursi) -30 b(v) -18 b(e,) 338 b(and) 333 b(does) f(not) g(change) h
(the) 5978 28295 y(dead) 317 b(node) h(counts.) 419 b(Its) 317
b(use) g(is) g(almost) g(e) -18 b(xclusi) -30 b(v) -18
b(ely) 317 b(the) g(one) h(just) f(described:) 404 b(Decreasing) 5978
29800 y(the) 325 b(reference) h(count) g(of) f(the) h(root) f(of) g
(the) h(\002nal) f(result) g(before) h(returning) f(from) g(a) g
(recursi) -30 b(v) -18 b(e) 5978 31305 y(procedure.) p
Fp 5978 34584 a(4.2.3) 1212 b(When) 303 b(Incr) -22 b(easing) 303
b(the) g(Refer) -22 b(ence) 304 b(Count) e(is) h(Unnecessary) p
Fo 5978 36907 a(When) 366 b(a) h(cop) -12 b(y) 366 b(of) g(a) g
(prede\002ned) h(constant) f(or) g(of) f(a) i(simple) e(BDD) i(v) -30
b(ariable) 366 b(is) g(needed) h(for) 5978 38413 y(comparison) 353
b(purposes,) 366 b(then) 354 b(calling) p Fn 354 w(Cudd) p
25759 38413 V 437 w(Ref) p Fo 531 w(is) g(not) g(necessary) -79
b(,) 366 b(because) 354 b(these) g(sim-) 5978 39918 y(ple) 394
b(functions) g(are) g(guaranteed) g(to) g(ha) -24 b(v) -18
b(e) 395 b(reference) f(counts) g(greater) f(than) i(0) f(at) g(all) h
(times.) 5978 41424 y(If) 451 b(no) h(call) g(to) p Fn
453 w(Cudd) p 15198 41424 V 437 w(Ref) p Fo 628 w(is) g(made,) 490
b(then) 452 b(no) g(attempt) g(to) h(free) e(the) h(diagram) h(by) f
(calling) p Fn 5978 42929 a(Cudd) p 8677 42929 V 437
w(Recur) -12 b(s) n(iveDer) -45 b(ef) p Fo 481 w(or) p
Fn 303 w(Cudd) p 21015 42929 V 437 w(Recur) -12 b(si) n(veDer) -45
b(efZdd) p Fo 337 w(should) 302 b(be) i(made.) p Fp 5978
46207 a(4.2.4) 1212 b(Saturating) 302 b(Incr) -22 b(ements) 302
b(and) h(Decr) -22 b(ements) p Fo 5978 48531 a(On) 398
b(32-bit) g(machines,) 422 b(the) 399 b(CUDD) g(package) g(stores) e
(the) i(reference) f(counts) g(in) g(unsigned) 5978 50036
y(short) 475 b(int') -67 b(s.) 894 b(F) -18 b(or) 475
b(lar) -22 b(ge) 476 b(diagrams,) 519 b(it) 476 b(is) f(possible) g
(for) g(some) h(reference) g(counts) g(to) f(e) -18 b(x-) 5978
51542 y(ceed) 341 b(the) f(capacity) h(of) g(an) f(unsigned) h(short) e
(int.) 488 b(Therefore,) 349 b(increments) 340 b(and) h(decrements) 5978
53047 y(of) 445 b(reference) g(counts) h(are) p Fn 445
w(satur) -18 b(ating) p Fo(.) 803 b(This) 445 b(means) g(that) h(once) g
(a) g(reference) f(count) h(has) 5978 54553 y(reached) 278
b(the) h(maximum) g(possible) e(v) -30 b(alue,) 284 b(it) 278
b(is) g(no) h(longer) f(changed) h(by) g(calls) f(to) p
Fn 278 w(Cudd) p 43545 54553 V 437 w(Ref) p Fo(,) p Fn
5978 56058 a(Cudd) p 8677 56058 V 437 w(Recur) -12 b(s) n(iveDer) -45
b(ef) p Fo(,) p Fn 246 w(Cudd) p 19770 56058 V 437 w(Recur) -12
b(siveDer) -45 b(efZdd) p Fo(,) 244 b(or) p Fn 230 w(Cudd) p
33989 56058 V 437 w(Der) -45 b(ef) p Fo(.) 352 b(As) 230
b(a) g(consequence,) 5978 57564 y(some) 336 b(nodes) g(that) h(ha) -24
b(v) -18 b(e) 337 b(no) f(references) g(may) h(not) g(be) g(declared) g
(dead.) 477 b(This) 335 b(may) i(result) f(in) 5978 59069
y(a) 356 b(small) f(w) -12 b(aste) 356 b(of) f(memory) -79
b(,) 369 b(which) 356 b(is) g(normally) f(more) h(than) g(of) -30
b(fs) n(et) 356 b(by) g(the) g(reduction) g(in) 5978
60575 y(size) 302 b(of) h(the) g(node) h(structure.) 7859
62080 y(When) 342 b(using) f(64-bit) g(pointers,) 350
b(there) 341 b(is) f(normally) h(no) h(memory) f(adv) -30
b(antage) 341 b(from) g(us-) 5978 63586 y(ing) 302 b(short) f(int') -67
b(s) 301 b(instead) h(of) f(int') -67 b(s) 301 b(in) h(a) g(DdNode.) 376
b(Therefore,) 302 b(increments) f(and) h(decrements) 5978
65091 y(are) 401 b(not) h(saturating) f(in) h(that) g(case.) 671
b(What) 403 b(option) e(is) g(in) h(ef) -30 b(fect) 401
b(depends) h(on) g(tw) -12 b(o) 402 b(macros,) p Black
25297 69672 a(27) p Black 90 rotate dyy eop
%%Page: 28 28
28 27 bop Black Black Fo 5978 7638 a(SIZE) n(OF) p 10158
7638 364 45 v 437 w(V) -48 b(OID) p 13576 7638 V 436
w(P) 396 b(and) g(SIZEOF) p 21337 7638 V 435 w(INT,) g(de\002ned) g(in)
g(the) h(e) -18 b(xternal) 396 b(header) g(\002le) g(\() p
Fn(cudd.h) p Fo(\).) 5978 9143 y(The) 386 b(increments) g(and) h
(decrements) g(of) f(the) h(reference) f(counts) g(are) h(performed) f
(using) g(tw) -12 b(o) 5978 10649 y(macros:) p Fn 338
w(cuddSatInc) p Fo 231 w(and) p Fn 231 w(cuddSatDec) p
Fo(,) 245 b(whose) 231 b(de\002nitions) f(depend) h(on) f(SIZEOF) p
42255 10649 V 435 w(V) -48 b(OID) p 45671 10649 V 436
w(P) 5978 12154 y(and) 303 b(SIZEOF) p 12213 12154 V
435 w(INT.) p Fi 5978 15477 a(4.3) 1328 b(Complement) 331
b(Ar) -24 b(cs) p Fo 5978 17801 a(If) 377 b(ADDs) h(are) g(restricted) f
(to) h(use) g(only) g(the) g(constants) f(0) h(and) h(1,) 397
b(the) -18 b(y) 378 b(beha) -24 b(v) -18 b(e) 378 b(lik) -12
b(e) 378 b(BDDs) 5978 19306 y(without) 333 b(complement) h(arcs.) 466
b(It) 333 b(is) f(normally) i(easier) f(to) g(write) g(code) h(that) f
(manipulates) g(0-1) 5978 20811 y(ADDs,) 453 b(than) 424
b(to) f(write) g(code) h(for) f(BDDs.) 737 b(Ho) -30
b(we) g(v) -18 b(er) -48 b(,) 452 b(complementation) 424
b(is) f(tri) -30 b(vial) 423 b(with) 5978 22317 y(complement) 354
b(arcs,) 367 b(and) 354 b(is) f(not) i(tri) -30 b(vial) 353
b(without.) 529 b(As) 354 b(a) g(consequence,) 367 b(with) 354
b(complement) 5978 23822 y(arcs) 369 b(it) h(is) f(possible) g(to) h
(check) g(for) f(more) h(terminal) g(cases) f(and) h(it) g(is) f
(possible) g(to) h(apply) g(De) 5978 25328 y(Mor) -22
b(g) -6 b(an') -67 b(s) 291 b(la) -18 b(ws) 292 b(to) g(reduce) h
(problems) e(that) i(are) f(essentially) g(identical) g(to) h(a) f
(standard) g(form.) 5978 26833 y(This) 302 b(in) h(turn) g(increases) f
(the) h(utilization) g(of) g(the) g(cache.) 7859 28339
y(The) 490 b(complement) g(attrib) -24 b(ute) 490 b(is) f(stored) g(in)
g(the) h(least) g(signi\002cant) f(bit) h(of) f(the) h(\223else\224)
5978 29844 y(pointer) 300 b(of) h(each) g(node.) 376
b(An) 301 b(e) -18 b(xternal) 301 b(pointer) g(to) f(a) h(function) g
(can) h(also) e(be) h(complemented.) 5978 31350 y(The) 423
b(\223then\224) h(pointer) f(to) g(a) g(node,) 454 b(on) 423
b(the) h(other) f(hand,) 454 b(is) 423 b(al) -12 b(w) g(ays) p
Fn 423 w(r) -45 b(e) d(gular) p Fo(.) 735 b(It) 423 b(is) g(a) g(mis-)
5978 32855 y(tak) -12 b(e) 420 b(to) g(use) g(a) g(pointer) h(as) e(it)
h(is) g(to) g(address) g(memory) -79 b(.) 727 b(Instead,) 449
b(it) 420 b(is) g(al) -12 b(w) g(ays) 420 b(necessary) 5978
34361 y(to) 366 b(obtain) g(a) g(re) -18 b(gular) 365
b(v) -18 b(ersion) 366 b(of) f(it.) 565 b(This) 365 b(is) h(normally) f
(done) i(by) f(calling) p Fn 366 w(Cudd) p 41304 34361
V 437 w(Re) -48 b(gular) p Fo(.) 5978 35866 y(It) 355
b(is) g(also) g(a) h(mistak) -12 b(e) 355 b(to) g(call) p
Fn 356 w(cuddUniqueInter) p Fo 384 w(with) g(a) h(complemented) h
(\223then\224) f(child) f(as) 5978 37372 y(ar) -22 b(gument.) 369
b(The) 284 b(calling) f(procedure) h(must) f(apply) h(De) g(Mor) -22
b(g) -6 b(an') -67 b(s) 283 b(la) -18 b(ws) 283 b(by) g(complementing)
5978 38877 y(both) 406 b(pointers) h(passed) f(to) p
Fn 407 w(cuddUniqueInter) p Fo 434 w(and) h(then) g(taking) g(the) g
(complement) h(of) e(the) 5978 40383 y(result.) p Fi
5978 43705 a(4.4) 1328 b(The) 332 b(Cache) p Fo 5978
46029 a(Each) 488 b(entry) h(of) f(the) h(cache) g(consists) e(of) h
(\002) -30 b(v) -18 b(e) 489 b(\002elds:) 746 b(The) 488
b(operator) -48 b(,) 535 b(three) 488 b(pointers) g(to) 5978
47534 y(operands) 434 b(and) h(a) g(pointer) g(to) g(the) g(result.) 771
b(The) 434 b(operator) h(and) g(the) g(three) g(pointers) f(to) h(the)
5978 49040 y(operands) 302 b(are) h(combined) h(to) f(form) f(three) h
(w) -12 b(ords.) 375 b(The) 303 b(combination) h(relies) e(on) h(tw) -12
b(o) 304 b(f) -12 b(acts:) p Black Fm 7796 51541 a(\262) p
Black Fo 606 w(Most) 345 b(operations) g(ha) -24 b(v) -18
b(e) 346 b(one) g(or) f(tw) -12 b(o) 346 b(operands.) 503
b(A) 346 b(fe) -30 b(w) 346 b(bits) f(are) g(suf) -30
b(\002cient) 345 b(to) h(dis-) 9008 53047 y(criminate) 303
b(all) g(three-operands) g(operations.) p Black Fm 7796
55549 a(\262) p Black Fo 606 w(All) 383 b(nodes) g(are) g(aligned) h
(to) f(16-byte) h(boundaries.) 616 b(\(32-byte) 383 b(boundaries) g(if)
f(64-bit) 9008 57054 y(pointers) 397 b(are) h(used.\)) 660
b(Hence,) 423 b(there) 398 b(are) g(a) g(fe) -30 b(w) 397
b(bits) h(a) -24 b(v) -30 b(ailable) 398 b(to) g(distinguish) f(the)
9008 58559 y(three-operand) 303 b(operations) f(from) h(te) g(others) f
(and) i(to) f(assign) f(unique) h(codes) g(to) g(them.) 7859
61061 y(The) 386 b(cache) h(does) e(not) h(contrib) -24
b(ute) 386 b(to) g(the) g(reference) g(counts) g(of) f(the) h(nodes.)
625 b(The) 385 b(f) -12 b(act) 5978 62567 y(that) 391
b(the) h(cache) h(contains) f(a) g(pointer) f(to) h(a) g(node) g(does) g
(not) f(imply) h(that) g(the) g(node) g(is) f(ali) -30
b(v) -18 b(e.) 5978 64072 y(Instead,) 418 b(when) 396
b(g) -6 b(arbage) 396 b(collection) g(tak) -12 b(es) 396
b(place,) 419 b(all) 396 b(entries) f(of) g(the) h(cache) g(pointing) g
(to) 5978 65578 y(dead) 303 b(nodes) g(are) g(cleared.) p
Black 25297 69672 a(28) p Black 90 rotate dyy eop
%%Page: 29 29
29 28 bop Black Black Fo 7859 7638 a(The) 302 b(cache) g(is) f(also) g
(cleared) g(\(of) g(all) h(entries\)) e(when) i(dynamic) g(reordering) e
(tak) -12 b(es) 302 b(place.) 5978 9143 y(In) g(both) h(cases,) g(the) g
(entries) g(remo) -18 b(v) g(ed) 303 b(from) f(the) h(cache) h(are) f
(about) g(to) g(become) h(in) -48 b(v) -30 b(alid.) 7859
10649 y(All) 398 b(operands) f(and) g(results) f(in) h(a) g(cache) h
(entry) f(must) g(be) g(pointers) g(to) g(DdNodes.) 659
b(If) 396 b(a) 5978 12154 y(function) 352 b(produces) h(more) f(than) i
(one) f(result,) 364 b(or) 353 b(uses) f(more) g(than) h(three) g(ar)
-22 b(guments,) 365 b(there) 5978 13660 y(are) 303 b(currently) f(tw)
-12 b(o) 303 b(solutions:) p Black Fm 7796 16162 a(\262) p
Black Fo 606 w(Build) g(a) h(separate,) f(local,) g(cache.) 376
b(\(Using,) 303 b(for) f(instance,) h(the) p Fn 304 w(st) p
Fo 324 w(library.\)) p Black Fm 7796 18663 a(\262) p
Black Fo 606 w(Combine) 425 b(multiple) f(results) n(,) 455
b(or) 423 b(multiple) h(operands,) 454 b(into) 424 b(a) g(single) g
(diagram,) 454 b(by) 9008 20169 y(b) -24 b(uilding) 303
b(a) g(\223multiple) -18 b(xing) 303 b(structure\224) g(with) g(reserv)
-18 b(ed) 302 b(v) -30 b(ariables.) 5978 22671 y(Support) 442
b(of) h(the) g(former) g(solution) f(is) h(under) g(de) -30
b(v) -18 b(elopment.) 796 b(\(See) p Fh 443 w(cuddL) r(Cache.c) p
Fo(..) r(\)) 5978 24176 y(Support) 302 b(for) h(the) g(latter) g
(solution) f(may) i(be) f(pro) -18 b(vided) 303 b(in) g(future) g(v) -18
b(ersions) 301 b(of) i(the) g(package.) 7859 25681 y(There) 280
b(are) g(three) g(sets) f(of) h(interf) -12 b(ace) 280
b(functions) g(to) g(the) g(cache.) 369 b(The) 280 b(\002rst) f(set) h
(is) f(for) h(func-) 5978 27187 y(tions) 391 b(with) g(three) g
(operands:) p Fn 553 w(cuddCac) -18 b(heInsert) p Fo
413 w(and) p Fn 391 w(cuddCac) i(heLookup) p Fo(.) 641
b(The) 391 b(second) 5978 28692 y(set) 267 b(is) f(for) h(functions) g
(with) g(tw) -12 b(o) 268 b(operands:) p Fn 358 w(cuddCac) -18
b(heInsert2) p Fo 267 w(and) p Fn 268 w(cuddCac) g(heLookup2) p
Fo(.) 5978 30198 y(The) 435 b(second) g(set) g(is) g(for) g(functions) f
(with) i(one) g(operand:) p Fn 640 w(cuddCac) -18 b(heInsert1) p
Fo 436 w(and) p Fn 435 w(cudd-) 5978 31703 y(Cac) g(heLookup1) p
Fo(.) 516 b(The) 349 b(second) g(set) h(is) e(slightly) h(f) -12
b(aster) 349 b(than) g(the) h(\002rst,) 360 b(and) 350
b(the) g(third) f(set) g(is) 5978 33209 y(slightly) 302
b(f) -12 b(aster) 302 b(than) h(the) h(second.) p Fp
5978 36487 a(4.4.1) 1212 b(Cache) 303 b(Sizing) p Fo
5978 38811 a(The) 277 b(size) g(of) g(the) h(cache) g(can) g(increase) f
(during) g(the) h(e) -18 b(x) g(ecution) 277 b(of) h(an) f
(application.) 368 b(\(There) 277 b(is) 5978 40316 y(currently) 310
b(no) h(w) -12 b(ay) 310 b(to) h(decrease) g(the) f(size) h(of) f(the) h
(cache,) i(though) e(it) f(w) -12 b(ould) 311 b(not) g(be) g(dif) -30
b(\002cult) 5978 41822 y(to) 428 b(do) h(it.\)) 751 b(When) 429
b(a) g(cache) g(miss) f(occurs,) 459 b(the) 429 b(package) g(uses) f
(the) h(follo) -30 b(wing) 428 b(criteria) g(to) 5978
43327 y(decide) 303 b(whether) g(to) g(resize) g(the) g(cache:) p
Black 7493 45829 a(1.) p Black 606 w(If) 369 b(the) i(cache) g(already)
f(e) -18 b(xceeds) 371 b(the) f(limit) g(gi) -30 b(v) -18
b(en) 370 b(by) h(the) p Fh 370 w(maxCa) r(che) p Fo
371 w(\002eld) f(of) g(the) 9008 47334 y(manager) -48
b(,) 381 b(no) 366 b(resizing) g(tak) -12 b(es) 365 b(place.) 565
b(The) 365 b(limit) h(is) f(the) h(minimum) g(of) g(tw) -12
b(o) 366 b(v) -30 b(alues:) 9008 48840 y(a) 427 b(v) -30
b(alue) 427 b(set) g(at) g(initialization) g(time) g(and) h(possibly) e
(modi\002ed) h(by) g(the) h(application,) 9008 50345
y(which) d(constitutes) e(the) i(hard) f(limit) g(be) -18
b(yond) 424 b(which) h(the) f(cache) h(will) g(ne) -30
b(v) -18 b(er) 424 b(gro) -30 b(w;) 9008 51851 y(and) 293
b(a) g(number) g(that) f(depends) h(on) g(the) g(current) f(total) h
(number) g(of) f(slots) g(in) h(the) g(unique) 9008 53356
y(table.) p Black 7493 55858 a(2.) p Black 606 w(If) g(the) g(cache) i
(is) e(not) g(too) h(lar) -22 b(ge) 294 b(already) -79
b(,) 296 b(resizing) d(is) g(decided) h(based) f(on) h(the) g(hit) f
(rate.) 9008 57363 y(The) 395 b(polic) -18 b(y) 396 b(adopted) g(by) g
(the) g(CUDD) g(package) h(is) e(\223re) -30 b(w) -12
b(ard-based.) -85 b(\224) 395 b(If) g(the) g(cache) 9008
58869 y(hit) 303 b(rate) g(is) f(high,) i(then) f(it) g(is) f(w) -12
b(orthwhile) 303 b(to) g(increase) g(the) g(size) g(of) g(the) g
(cache.) 5978 61371 y(When) 324 b(resizing) f(tak) -12
b(es) 324 b(place,) 329 b(the) 324 b(statistical) f(counters) h(used) f
(to) h(compute) h(the) f(hit) f(rate) h(are) 5978 62876
y(reinitialized) 270 b(so) g(as) g(to) h(pre) -30 b(v) -18
b(ent) 270 b(immediate) h(resizing.) 364 b(The) 270 b(number) h(of) f
(entries) g(is) g(doubled.) 7859 64381 y(The) 306 b(rationale) g(for) f
(the) h(\223re) -30 b(w) -12 b(ard-based\224) 305 b(polic) -18
b(y) 305 b(is) h(as) f(follo) -30 b(ws.) 383 b(In) 305
b(man) -18 b(y) 306 b(BDD/ADD) 5978 65887 y(applications) 293
b(the) h(hit) f(rate) g(is) g(not) g(v) -18 b(ery) 293
b(sensiti) -30 b(v) -18 b(e) 293 b(to) g(the) h(size) f(of) g(the) g
(cache:) 372 b(It) 293 b(is) g(primarily) p Black 25297
69672 a(29) p Black 90 rotate dyy eop
%%Page: 30 30
30 29 bop Black Black Fo 5978 7638 a(a) 330 b(function) g(of) g(the) g
(problem) g(instance) h(at) f(hand.) 457 b(If) 330 b(a) g(lar) -22
b(ge) 330 b(hit) h(rate) f(is) f(observ) -18 b(ed,) 337
b(chances) 5978 9143 y(are) 289 b(that) g(by) g(using) g(a) g(lar) -22
b(ge) 289 b(cache,) k(the) c(results) f(of) g(lar) -22
b(ge) 290 b(problems) e(\(those) h(that) g(w) -12 b(ould) 289
b(tak) -12 b(e) 5978 10649 y(longer) 383 b(to) h(solv) -18
b(e\)) 383 b(will) h(survi) -30 b(v) -18 b(e) 382 b(in) i(the) g(cache)
h(without) f(being) g(o) -18 b(v) g(erwritten) 383 b(long) h(enough)
5978 12154 y(to) 418 b(cause) g(a) h(v) -30 b(aluable) 418
b(cache) h(hit.) 722 b(Notice) 418 b(that) h(when) g(a) f(lar) -22
b(ge) 418 b(problem) h(is) e(solv) -18 b(ed) 418 b(more) 5978
13660 y(than) 359 b(once,) 373 b(so) 358 b(are) h(its) f(recursi) -30
b(v) -18 b(ely) 358 b(generated) h(subproblems.) 542
b(If) 358 b(the) h(hit) g(rate) g(is) f(lo) -30 b(w) -79
b(,) 373 b(the) 5978 15165 y(probability) 303 b(of) f(lar) -22
b(ge) 303 b(problems) g(being) g(solv) -18 b(ed) 303
b(more) g(than) g(once) h(is) e(lo) -30 b(w) -79 b(.) 7859
16671 y(The) 258 b(other) g(observ) -30 b(ation) 257
b(about) h(the) g(cache) h(sizing) f(polic) -18 b(y) 258
b(is) f(that) h(there) g(is) f(little) h(point) g(in) 5978
18176 y(k) -12 b(eeping) 288 b(a) h(cache) g(which) g(is) f(much) g
(lar) -22 b(ger) 289 b(than) f(the) h(unique) g(table.) 371
b(Ev) -18 b(ery) 288 b(time) g(the) h(unique) 5978 19682
y(table) 366 b(\223\002lls) f(up,) -85 b(\224) 366 b(g) -6
b(arbage) 366 b(collection) g(is) f(in) -48 b(v) -24
b(ok) -12 b(ed) 366 b(and) g(the) g(cache) g(is) f(cleared) h(of) g
(all) g(dead) 5978 21187 y(entries.) 359 b(A) 257 b(cache) h(that) f
(is) f(much) h(lar) -22 b(ger) 257 b(than) g(the) g(unique) g(table) g
(is) f(therefore) h(less) e(than) i(fully) 5978 22693
y(utilized.) p Fp 5978 25971 a(4.4.2) 1212 b(Local) 304
b(Caches) p Fo 5978 28295 a(Sometimes) 350 b(it) h(may) g(be) g
(necessary) f(or) h(con) -48 b(v) -18 b(enient) 350 b(to) h(use) g(a) g
(local) g(cache.) 519 b(A) 351 b(local) g(cache) 5978
29800 y(can) 344 b(be) g(lossless) e(\(no) i(results) f(are) h(e) -30
b(v) -18 b(er) 344 b(o) -18 b(v) g(erwritten\),) 353
b(or) 344 b(it) g(may) g(store) f(objects) h(for) g(which) 5978
31305 y(canonical) 428 b(representations) e(are) h(not) h(a) -24
b(v) -30 b(ailable.) 749 b(One) 427 b(important) h(f) -12
b(act) 427 b(to) g(k) -12 b(eep) 428 b(in) f(mind) 5978
32811 y(when) 380 b(using) g(a) h(local) f(cache) h(is) f(that) g
(local) h(caches) f(are) h(not) f(cleared) h(during) f(g) -6
b(arbage) 380 b(col-) 5978 34316 y(lection) 351 b(or) f(before) h
(reordering.) 519 b(Therefore,) 362 b(it) 351 b(is) f(necessary) g(to) h
(increment) g(the) g(reference) 5978 35822 y(count) 256
b(of) g(all) h(nodes) f(pointed) g(by) h(a) f(local) h(cache.) 361
b(\(Unless) 255 b(their) h(reference) g(counts) h(are) f(guar) -24
b(-) 5978 37327 y(anteed) 305 b(positi) -30 b(v) -18
b(e) 305 b(in) g(some) g(other) g(w) -12 b(ay) -79 b(.) 383
b(One) 306 b(such) f(w) -12 b(ay) 305 b(is) g(by) g(including) h(all) f
(partial) g(results) 5978 38833 y(in) 347 b(the) h(global) g(result.\))
509 b(Before) 348 b(disposing) f(of) g(the) h(local) g(cache,) 360
b(all) 348 b(elements) f(stored) g(in) h(it) 5978 40338
y(must) 266 b(be) h(passed) f(to) p Fn 266 w(Cudd) p
17419 40338 364 45 v 437 w(Recur) -12 b(siveDer) -45
b(ef) p Fo(.) 363 b(As) 266 b(consequence) i(of) e(the) h(f) -12
b(act) 266 b(that) h(all) f(results) 5978 41844 y(in) 284
b(a) h(local) g(cache) h(are) e(referenced,) 289 b(it) 284
b(is) g(generally) h(con) -48 b(v) -18 b(enient) 285
b(to) g(store) f(in) g(the) h(local) g(cache) 5978 43349
y(also) k(the) h(result) g(of) f(tri) -30 b(vial) 290
b(problems,) i(which) e(are) g(not) g(usually) g(stored) f(in) h(the) g
(global) g(cache.) 5978 44855 y(Otherwise,) 441 b(after) 414
b(a) g(recursi) -30 b(v) -18 b(e) 413 b(call,) 442 b(it) 414
b(is) f(dif) -30 b(\002cult) 414 b(to) g(tell) g(whether) g(the) g
(result) f(is) h(in) g(the) 5978 46360 y(cache,) 303
b(and) h(therefore) e(referenced,) h(or) g(not) g(in) g(the) g(cache,) h
(and) f(therefore) g(not) g(referenced.) 7859 47866 y(An) 242
b(alternati) -30 b(v) -18 b(e) 242 b(approach) g(to) g(referencing) g
(the) g(results) e(in) i(the) g(local) g(caches) g(is) g(to) g(install)
5978 49371 y(hook) 303 b(functions) f(\(see) h(Section) g(3.16\)) g(to)
g(be) g(e) -18 b(x) g(ecuted) 304 b(before) f(g) -6 b(arbage) 303
b(collection.) p Fi 5978 52694 a(4.5) 1328 b(The) 332
b(Unique) f(T) -122 b(able) p Fo 5978 55017 a(A) 391
b(recursi) -30 b(v) -18 b(e) 390 b(procedure) h(typically) g(splits) f
(the) i(operands) e(by) i(e) -18 b(xpanding) 391 b(with) g(respect) g
(to) 5978 56523 y(the) 358 b(topmost) g(v) -30 b(ariable.) 543
b(T) -97 b(opmost) 358 b(in) g(this) g(conte) -18 b(xt) 359
b(refers) e(to) i(the) g(v) -30 b(ariable) 358 b(that) h(is) f(closest)
5978 58028 y(to) 381 b(the) g(roots) f(in) h(the) g(current) g(v) -30
b(ariable) 380 b(order) -67 b(.) 610 b(The) 381 b(nodes,) 400
b(on) 381 b(the) g(other) g(hand,) 401 b(hold) 381 b(the) 5978
59534 y(inde) -18 b(x,) 326 b(which) 321 b(is) g(in) -48
b(v) -30 b(ariant) 321 b(with) g(reordering.) 430 b(Therefore,) 325
b(when) d(splitting,) j(one) d(must) e(use) 5978 61039
y(the) 355 b(permutation) g(array) f(maintained) h(by) g(the) g
(package) h(to) f(get) g(the) g(right) g(le) -30 b(v) -18
b(el.) 531 b(Access) 354 b(to) 5978 62544 y(the) 272
b(permutation) h(array) f(is) g(pro) -18 b(vided) 273
b(by) f(the) h(macro) p Fn 273 w(cuddI) p Fo 334 w(for) f(BDDs) h(and) g
(ADDs,) 278 b(and) 273 b(by) 5978 64050 y(the) 303 b(macro) p
Fn 303 w(cuddIZ) p Fo 363 w(for) g(ZDDs.) 7859 65555
y(The) 338 b(unique) g(table) g(consists) e(of) h(as) g(man) -18
b(y) 338 b(hash) f(tables) h(as) f(there) g(are) h(v) -30
b(ariables) 337 b(in) g(use.) p Black 25297 69672 a(30) p
Black 90 rotate dyy eop
%%Page: 31 31
31 30 bop Black Black Fo 5978 7638 a(These) 296 b(has) g(tables) h(are)
f(called) p Fn 297 w(unique) h(subtables) p Fo(.) 373
b(The) 297 b(sizes) f(of) g(the) h(unique) g(subtables) f(are) 5978
9143 y(determined) 303 b(by) g(tw) -12 b(o) 303 b(criteria:) p
Black 7493 11645 a(1.) p Black 606 w(The) g(collision) f(lists) g
(should) h(be) g(short) g(to) g(k) -12 b(eep) 303 b(access) g(time) g
(do) -30 b(wn.) p Black 7493 14147 a(2.) p Black 606
w(There) 230 b(should) g(be) g(enough) h(room) f(for) g(dead) h(nodes,)
244 b(to) 231 b(pre) -30 b(v) -18 b(ent) 230 b(too) g(frequent) g(g) -6
b(arbage) 9008 15652 y(collections.) 5978 18154 y(While) 386
b(the) g(\002rst) f(criterion) h(is) f(f) -12 b(airly) 386
b(straightfor) n(w) -12 b(ard) 386 b(to) g(implement,) 407
b(the) 386 b(second) h(lea) -24 b(v) -18 b(es) 5978 19660
y(more) 278 b(room) g(to) g(creati) -30 b(vity) -79 b(.) 367
b(The) 278 b(CUDD) h(package) g(tries) f(to) g(\002gure) g(out) g
(whether) h(more) f(dead) 5978 21165 y(node) 295 b(should) g(be) g
(allo) -30 b(wed) 295 b(to) h(increase) e(performance.) 373
b(\(See) 295 b(also) g(Section) h(3.4.\)) 372 b(There) 295
b(are) 5978 22671 y(tw) -12 b(o) 344 b(reasons) f(for) h(not) g(doing) h
(g) -6 b(arbage) 345 b(collection) f(too) h(often.) 499
b(The) 344 b(ob) -18 b(vious) 344 b(one) h(is) f(that) g(it) 5978
24176 y(is) 272 b(e) -18 b(xpensi) -30 b(v) -18 b(e.) 365
b(The) 272 b(second) h(is) f(that) g(dead) h(nodes) g(may) f(be) h
(reclaimed,) 279 b(if) 272 b(the) -18 b(y) 273 b(are) f(the) h(result)
5978 25681 y(of) 325 b(a) g(successful) f(cache) i(lookup.) 443
b(Hence) 326 b(dead) g(nodes) f(may) g(pro) -18 b(vide) 325
b(a) h(substantial) f(speed-) 5978 27187 y(up) 445 b(if) g(the) -18
b(y) 446 b(are) f(k) -12 b(ept) 446 b(around) f(long) h(enough.) 803
b(The) 445 b(usefulness) f(of) h(k) -12 b(eeping) 446
b(man) -18 b(y) 446 b(dead) 5978 28692 y(nodes) 426 b(around) h(v) -30
b(aries) 426 b(from) g(application) h(to) g(application,) 458
b(and) 427 b(from) f(problem) h(instance) 5978 30198
y(to) 393 b(problem) g(instance.) 648 b(As) 393 b(in) g(the) h(sizing) f
(of) g(the) h(cache,) 416 b(the) 394 b(CUDD) g(package) h(adopts) e(a)
5978 31703 y(\223re) -30 b(w) -12 b(ard-based\224) 421
b(polic) -18 b(y) 423 b(to) f(decide) h(ho) -30 b(w) 422
b(much) h(room) f(should) g(be) h(used) f(for) f(the) i(unique) 5978
33209 y(table.) 809 b(If) 447 b(the) g(number) h(of) f(dead) h(nodes) f
(reclaimed) h(is) f(lar) -22 b(ge) 447 b(compared) h(to) g(the) f
(number) 5978 34714 y(of) 396 b(nodes) g(directly) h(requested) g(from)
f(the) g(memory) h(manager) -48 b(,) 420 b(then) 397
b(the) g(CUDD) g(package) 5978 36220 y(assumes) 425 b(that) i(it) f
(will) h(be) g(bene\002cial) g(to) f(allo) -30 b(w) 427
b(more) f(room) h(for) e(the) i(subtables,) 457 b(thereby) 5978
37725 y(reducing) 371 b(the) h(frequenc) -18 b(y) 371
b(of) g(g) -6 b(arbage) 372 b(collection.) 582 b(The) 371
b(package) h(does) g(so) f(by) g(switching) 5978 39231
y(between) 303 b(tw) -12 b(o) 303 b(modes) g(of) g(operation:) p
Black 7493 41732 a(1.) p Black 606 w(F) -18 b(ast) 287
b(gro) -30 b(wth:) 368 b(In) 287 b(this) h(mode,) j(the) d(ratio) f(of)
h(dead) g(nodes) g(to) g(total) g(nodes) f(required) h(for) 9008
43238 y(g) -6 b(arbage) 347 b(collection) g(is) f(higher) g(than) h(in)
g(the) g(slo) -30 b(w) 345 b(gro) -30 b(wth) 347 b(mode) g(to) f(f) -12
b(a) -24 b(v) g(or) 346 b(resizing) 9008 44743 y(of) 303
b(the) g(subtables.) p Black 7493 47245 a(2.) p Black
606 w(Slo) -30 b(w) 383 b(gro) -30 b(wth:) 535 b(In) 382
b(this) g(mode) i(k) -12 b(eeping) 383 b(man) -18 b(y) 383
b(dead) g(nodes) g(around) g(is) f(not) h(as) g(im-) 9008
48751 y(portant) 303 b(as) g(k) -12 b(eeping) 303 b(memory) g
(requirements) f(lo) -30 b(w) -79 b(.) 5978 51252 y(Switching) 303
b(from) f(one) i(mode) f(to) g(the) g(other) g(is) g(based) g(on) g
(the) g(follo) -30 b(wing) 303 b(criteria:) p Black 7493
53754 a(1.) p Black 606 w(If) f(the) h(unique) h(table) f(is) g
(already) g(lar) -22 b(ge,) 303 b(only) g(slo) -30 b(w) 303
b(gro) -30 b(wth) 302 b(is) h(possible.) p Black 7493
56256 a(2.) p Black 606 w(If) 467 b(the) g(table) h(is) f(small) g(and)
h(man) -18 b(y) 467 b(dead) h(nodes) f(are) h(being) f(reclaimed,) 509
b(then) 468 b(f) -12 b(ast) 9008 57761 y(gro) -30 b(wth) 303
b(is) f(selected.) 5978 60263 y(This) 329 b(polic) -18
b(y) 330 b(is) g(especially) g(ef) -30 b(fecti) g(v) -18
b(e) 330 b(when) h(the) f(diagrams) g(being) g(manipulated) h(ha) -24
b(v) -18 b(e) 331 b(lots) 5978 61768 y(of) 322 b(recombination.) 437
b(Notice) 324 b(the) f(interplay) g(of) g(the) g(cache) h(sizing) f
(and) h(unique) f(sizing:) 416 b(F) -18 b(ast) 5978 63274
y(gro) -30 b(wth) 298 b(normally) g(occurs) h(when) g(the) g(cache) g
(hit) g(rate) f(is) h(lar) -22 b(ge.) 374 b(The) 299
b(cache) g(and) g(the) g(unique) 5978 64779 y(table) k(then) g(gro) -30
b(w) 303 b(in) g(concert,) g(preserving) g(a) g(health) -6
b(y) 303 b(balance) h(between) g(their) f(sizes.) p Black
25297 69672 a(31) p Black 90 rotate dyy eop
%%Page: 32 32
32 31 bop Black Black Fi 5978 7638 a(4.6) 1328 b(Allo) -13
b(wing) 333 b(Asynchr) -24 b(on) n(ous) 332 b(Reordering) p
Fo 5978 9962 a(Asynchronous) 416 b(reordering) g(is) g(the) h
(reordering) f(that) h(is) f(triggered) h(automatically) g(by) g(the)
5978 11467 y(increase) 448 b(of) g(the) g(number) h(of) e(nodes.) 812
b(Asynchronous) 448 b(reordering) f(tak) -12 b(es) 448
b(place) h(when) g(a) 5978 12973 y(ne) -30 b(w) 367 b(internal) g(node)
h(must) f(be) g(created,) 384 b(and) 368 b(the) f(number) h(of) f
(nodes) g(has) g(reached) h(a) f(gi) -30 b(v) -18 b(en) 5978
14478 y(threshold.) 604 b(\(The) 378 b(threshold) h(is) g(adjusted) g
(by) h(the) f(package) h(e) -30 b(v) -18 b(ery) 379 b(time) h
(reordering) e(tak) -12 b(es) 5978 15984 y(place.\)) 7859
17489 y(Those) 302 b(procedures) h(that) f(do) h(not) g(create) g(ne)
-30 b(w) 303 b(nodes) f(\(e.g.,) h(procedures) f(that) h(count) g(the)
5978 18994 y(number) c(of) h(nodes) g(or) f(minterms\)) g(need) h(not) g
(w) -12 b(orry) 299 b(about) h(asynchronous) f(reordering:) 374
b(No) 5978 20500 y(special) 303 b(precaution) g(is) f(necessary) h(in) g
(writing) g(them.) 7859 22005 y(Procedures) e(that) g(only) g
(manipulate) g(decision) g(diagrams) f(through) h(the) g(e) -18
b(xported) 301 b(func-) 5978 23511 y(tions) 343 b(of) g(the) h(CUDD) h
(package) g(also) e(need) i(not) e(concern) i(themselv) -18
b(es) 343 b(with) h(asynchronous) 5978 25016 y(reordering.) 375
b(\(See) 303 b(Section) g(3.2.1) g(for) g(the) g(e) -18
b(xceptions.\)) 7859 26522 y(The) 331 b(remaining) g(class) f(of) g
(procedures) g(is) g(composed) h(of) f(functions) h(that) f(visit) g
(the) h(dia-) 5978 28027 y(grams) 344 b(and) h(may) g(create) g(ne) -30
b(w) 345 b(nodes.) 502 b(All) 345 b(such) f(procedures) h(in) g(the) g
(CUDD) g(package) h(are) 5978 29533 y(written) 435 b(so) h(that) g(the)
-18 b(y) 436 b(can) g(be) g(interrupted) g(by) g(dynamic) g
(reordering.) 774 b(The) 435 b(general) h(ap-) 5978 31038
y(proach) 320 b(follo) -30 b(wed) 320 b(goes) g(under) g(the) h(name) f
(of) g(\223abort) g(and) h(retry.) -85 b(\224) 320 b(As) g(the) g(name)
h(implies,) j(a) 5978 32544 y(computation) 303 b(that) g(is) g
(interrupted) g(by) g(dynamic) g(reordering) g(is) f(aborted) h(and) h
(tried) e(ag) -6 b(ain.) 7859 34049 y(A) 301 b(recursi) -30
b(v) -18 b(e) 300 b(procedure) g(that) h(can) g(be) g(interrupted) f
(by) h(dynamic) g(reordering) f(\(an) g(inter) -24 b(-) 5978
35555 y(ruptible) 284 b(procedure) h(from) f(no) -30
b(w) 285 b(on\)) f(is) g(composed) h(of) g(tw) -12 b(o) 285
b(functions.) 369 b(One) 285 b(is) f(responsible) 5978
37060 y(for) 378 b(the) i(real) g(computation.) 606 b(The) 379
b(other) h(is) f(a) g(simple) h(wrapper,) 398 b(which) 380
b(tests) f(whether) h(re-) 5978 38566 y(ordering) 302
b(occurred) h(and) h(restarts) d(the) i(computation) h(if) f(it) f
(did.) 7859 40071 y(Asynchronous) 238 b(reordering) g(of) g(BDDs) h
(and) g(ADDs) f(can) h(only) g(be) g(triggered) f(inside) p
Fn 238 w(cud-) 5978 41576 y(dUniqueInter) p Fo(,) 427
b(when) 402 b(a) h(ne) -30 b(w) 402 b(node) h(is) f(about) g(to) h(be) f
(created.) 674 b(Lik) -12 b(e) -30 b(wise,) 427 b(asynchronous) 5978
43082 y(reordering) 366 b(of) g(ZDDs) g(can) h(only) g(be) g(triggered)
f(inside) p Fn 367 w(cuddUniqueInterZdd) p Fo(.) 567
b(When) 367 b(re-) 5978 44587 y(ordering) 302 b(is) h(triggered,) f
(three) i(things) e(happen:) p Black 7493 46987 a(1.) p
Black Fn 606 w(cuddUniqueInter) p Fo 331 w(returns) g(a) h(NULL) g(v)
-30 b(alue;) p Black 7493 49447 a(2.) p Black 606 w(The) 304
b(\003ag) p Fn 305 w(r) -45 b(eor) g(der) g(ed) p Fo
336 w(of) 304 b(the) h(manager) g(is) f(set) g(to) g(1.) 380
b(\(0) 304 b(means) g(no) h(reordering,) f(while) 9008
50953 y(2) f(indicates) g(an) g(error) f(occurred) h(during) g
(reordering.\)) p Black 7493 53414 a(3.) p Black 606
w(The) 340 b(counter) p Fn 340 w(r) -45 b(eor) g(derings) p
Fo 339 w(of) 340 b(the) g(manager) g(is) g(incremented.) 487
b(The) 340 b(counter) g(is) g(ini-) 9008 54919 y(tialized) 466
b(to) g(0) g(when) g(the) g(manager) g(is) f(started) g(and) h(can) g
(be) g(accessed) g(by) g(calling) p Fn 9008 56425 a(Cudd) p
11707 56425 364 45 v 437 w(ReadReor) -45 b(derings) p
Fo(.) 489 b(By) 342 b(taking) f(tw) -12 b(o) 341 b(readings) g(of) g
(the) g(counter) -48 b(,) 351 b(an) 341 b(applica-) 9008
57930 y(tion) 413 b(can) h(determine) g(if) f(v) -30
b(ariable) 414 b(reordering) f(has) g(tak) -12 b(en) 414
b(place) g(between) g(the) g(\002rst) 9008 59436 y(and) 347
b(the) g(second) g(reading.) 507 b(The) 346 b(package) i(itself,) 357
b(ho) -30 b(we) g(v) -18 b(er) -48 b(,) 357 b(does) 346
b(not) h(mak) -12 b(e) 347 b(use) f(of) 9008 60941 y(the) 303
b(counter:) 376 b(It) 303 b(is) f(mentioned) i(here) f(for) f
(completeness.) 7859 63340 y(The) 453 b(recursi) -30
b(v) -18 b(e) 451 b(procedure) i(that) g(recei) -30 b(v) -18
b(es) 452 b(a) h(NULL) e(v) -30 b(alue) 453 b(from) p
Fn 452 w(cuddUniqueInter) p Fo 5978 64846 a(must) j(free) h(all) g
(intermediate) h(results) d(that) j(it) f(may) g(ha) -24
b(v) -18 b(e) 457 b(computed) h(before,) 495 b(and) 458
b(return) 5978 66351 y(NULL) 302 b(in) h(its) g(turn.) p
Black 25297 69672 a(32) p Black 90 rotate dyy eop
%%Page: 33 33
33 32 bop Black Black Fo 7859 7638 a(The) 398 b(wrapper) f(function) g
(does) g(not) h(decide) g(whether) f(reordering) g(occurred) h(based) f
(on) 5978 9143 y(the) 479 b(NULL) g(return) g(v) -30
b(alue,) 524 b(because) 480 b(the) f(NULL) g(v) -30 b(alue) 480
b(may) f(be) h(the) g(result) e(of) i(lack) f(of) 5978
10649 y(memory) -79 b(.) 376 b(Instead,) 302 b(it) h(checks) g(the) p
Fn 303 w(r) -45 b(eor) g(der) g(ed) p Fo 336 w(\003ag.) 7859
12154 y(When) 361 b(a) f(recursi) -30 b(v) -18 b(e) 360
b(procedure) g(calls) g(another) g(recursi) -30 b(v) -18
b(e) 359 b(procedure) h(that) h(may) f(cause) 5978 13660
y(reordering,) 342 b(it) 335 b(should) f(bypass) h(the) g(wrapper) g
(and) g(call) g(the) g(recursi) -30 b(v) -18 b(e) 334
b(procedure) h(directly) -79 b(.) 5978 15165 y(Otherwise,) 370
b(the) 357 b(calling) g(procedure) g(will) g(not) f(kno) -30
b(w) 357 b(whether) g(reordering) g(occurred,) 370 b(and) 5978
16671 y(will) 333 b(not) g(be) g(able) g(to) g(restart.) 465
b(This) 332 b(is) g(the) h(main) h(reason) e(wh) -6 b(y) 333
b(most) g(recursi) -30 b(v) -18 b(e) 332 b(procedures) 5978
18176 y(are) 391 b(internal,) 413 b(rather) 391 b(than) g(static.) 641
b(\(The) 390 b(wrappers,) 413 b(on) 391 b(the) h(other) f(hand,) 413
b(are) 392 b(mostly) e(e) -18 b(x-) 5978 19682 y(ported.\)) p
Fi 5978 23004 a(4.7) 1328 b(Deb) -27 b(ugging) p Fo 5978
25328 a(By) 467 b(de\002ning) h(the) f(symbol) g(DD) p
20108 25328 364 45 v 436 w(DEB) -12 b(UG) 468 b(during) f(compilation,)
508 b(numerous) 467 b(checks) g(are) 5978 26833 y(added) 230
b(to) h(the) f(code.) 352 b(In) 230 b(addition,) 245
b(the) 231 b(procedures) p Fn 230 w(Cudd) p 30650 26833
V 437 w(Deb) -24 b(ugChec) g(k) p Fo(,) p Fn 246 w(Cudd) p
40473 26833 V 437 w(Chec) g(kK) -42 b(e) -36 b(ys) p
Fo(,) 5978 28339 y(and) p Fn 257 w(cuddHeapPr) -55 b(o\002le) p
Fo 258 w(can) 258 b(be) g(called) g(at) g(an) -18 b(y) 257
b(point) h(to) f(v) -18 b(erify) 257 b(the) h(consistenc) -18
b(y) 257 b(of) g(the) h(data) 5978 29844 y(structure.) 542
b(\() p Fn(cuddHeapPr) -55 b(o\002le) p Fo 358 w(is) 359
b(an) g(internal) f(procedure.) 543 b(It) 358 b(is) h(declared) g(in) p
Fn 358 w(cuddInt.h) p Fo(.\)) 5978 31350 y(Procedures) p
Fn 450 w(Cudd) p 14513 31350 V 437 w(Deb) -24 b(ugChec) g(k) p
Fo 473 w(and) p Fn 452 w(Cudd) p 26462 31350 V 437 w(Chec) g(kK) -42
b(e) -36 b(ys) p Fo 451 w(are) 452 b(especially) f(useful) g(when) 5978
32855 y(CUDD) 282 b(reports) f(that) g(during) h(g) -6
b(arbage) 282 b(collection) g(the) f(number) h(of) f(nodes) h(actually)
g(deleted) 5978 34361 y(from) 365 b(the) h(unique) g(table) h(is) e
(dif) -30 b(ferent) 365 b(from) g(the) i(count) f(of) g(dead) g(nodes) g
(k) -12 b(ept) 366 b(by) g(the) g(man-) 5978 35866 y(ager) -67
b(.) 454 b(The) 328 b(error) g(causing) h(the) h(discrepanc) -18
b(y) 328 b(may) i(ha) -24 b(v) -18 b(e) 329 b(occurred) g(much) g
(earlier) g(than) g(it) g(is) 5978 37372 y(disco) -18
b(v) g(ered.) 522 b(A) 353 b(fe) -30 b(w) 351 b(strate) -18
b(gicaly) 352 b(placed) h(calls) f(to) g(the) g(deb) -24
b(ugging) 353 b(procedures) f(can) g(con-) 5978 38877
y(siderably) 366 b(narro) -30 b(w) 367 b(do) -30 b(wn) 367
b(the) g(search) g(for) g(the) g(source) g(of) g(the) g(problem.) 568
b(\(F) -18 b(or) 367 b(instance,) 383 b(a) 5978 40383
y(call) 306 b(to) p Fn 306 w(Cudd) p 11982 40383 V 437
w(Recur) -12 b(siveDer) -45 b(ef) p Fo 483 w(where) 306
b(one) h(to) p Fn 306 w(Cudd) p 29584 40383 V 437 w(Der) -45
b(ef) p Fo 306 w(w) -12 b(as) 306 b(required) g(may) h(be) f(iden-) 5978
41888 y(ti\002ed) d(in) g(this) f(w) -12 b(ay) -79 b(.\)) 7859
43393 y(One) 376 b(of) f(the) g(most) g(common) g(problems) g
(encountered) h(in) f(deb) -24 b(ugging) 375 b(code) h(based) f(on) 5978
44899 y(the) 441 b(CUDD) g(package) h(is) e(a) h(missing) f(call) h(to)
p Fn 441 w(Cudd) p 28901 44899 V 437 w(Recur) -12 b(s) n(iveDer) -45
b(ef) p Fo(.) 790 b(T) -97 b(o) 440 b(help) h(identify) 5978
46404 y(this) 287 b(type) i(of) f(problems,) i(the) f(package) g(pro)
-18 b(vides) 287 b(a) i(function) f(called) p Fn 288
w(Cudd) p 38305 46404 V 437 w(Chec) -24 b(kZer) -55 b(oRef) p
Fo(.) 5978 47910 y(This) 475 b(function) i(should) g(be) g(called) g
(immediately) g(before) f(shutting) h(do) -30 b(wn) 477
b(the) f(manager) -67 b(.) p Fn 5978 49415 a(Cudd) p
8677 49415 V 437 w(Chec) -24 b(kZer) -55 b(oRef) p Fo
420 w(checks) 242 b(that) g(the) h(only) f(nodes) h(left) f(with) g
(non-zero) g(reference) g(counts) 5978 50921 y(are) 340
b(the) h(prede\002ned) g(constants,) 349 b(the) 341 b(BDD) g
(projection) g(functions,) 349 b(and) 341 b(nodes) g(whose) f(ref-) 5978
52426 y(erence) 303 b(counts) g(are) g(saturated.) 7859
53932 y(F) -18 b(or) 385 b(this) f(function) h(to) g(be) g(ef) -30
b(fecti) g(v) -18 b(e) 384 b(the) h(application) h(must) e(e) -18
b(xplicitly) 385 b(dispose) f(of) h(all) 5978 55437 y(diagrams) 302
b(to) h(which) h(it) f(has) f(pointers) h(before) g(calling) g(it.) p
Fi 5978 58760 a(4.8) 1328 b(Gathering) 333 b(and) e(Inter) -13
b(p) n(r) -24 b(eting) 332 b(Statistics) p Fo 5978 61083
a(Function) p Fn 409 w(Cudd) p 13396 61083 V 437 w(PrintI) n(nfo) p
Fo 409 w(can) 409 b(be) g(called) g(to) g(print) f(out) h(the) g(v) -30
b(alues) 408 b(of) h(parameters) f(and) 5978 62589 y(statistics) 354
b(for) g(a) i(manager) -67 b(.) 533 b(The) 355 b(output) h(of) p
Fn 355 w(Cudd) p 27871 62589 V 437 w(PrintI) n(nfo) p
Fo 356 w(is) f(di) -30 b(vided) 355 b(in) g(tw) -12 b(o) 356
b(sections.) 5978 64094 y(The) 244 b(\002rst) g(reports) f(the) i(v) -30
b(alues) 244 b(of) g(parameters) g(that) h(are) g(under) f(the) h
(application) g(control.) 356 b(The) 5978 65600 y(second) 325
b(reports) g(the) h(v) -30 b(alues) 325 b(of) g(statistical) g
(counters) g(and) h(other) f(non-modi\002able) h(parame-) p
Black 25297 69672 a(33) p Black 90 rotate dyy eop
%%Page: 34 34
34 33 bop Black Black Fo 5978 7638 a(ters.) 391 b(A) 308
b(quick) h(guide) f(to) h(the) f(interpretation) h(of) f(all) g(these) g
(quantities) g(follo) -30 b(ws.) 391 b(F) -18 b(or) 308
b(ease) g(of) 5978 9143 y(e) -18 b(xposition,) 351 b(we) 342
b(re) -30 b(v) -18 b(erse) 341 b(the) h(order) f(and) h(describe) g
(the) g(non-modi\002able) g(parameters) f(\002rst.) 5978
10649 y(W) -97 b(e') -12 b(ll) 302 b(use) h(a) g(sample) g(run) g(as) g
(e) -18 b(xample.) 376 b(There) 303 b(is) f(nothing) h(special) h
(about) f(this) f(run.) p Fp 5978 13927 a(4.8.1) 1212
b(Non) 303 b(Modi\002able) g(P) -12 b(arameters) p Fo
5978 16251 a(The) 302 b(list) h(of) g(non-modi\002able) g(parameters) f
(starts) g(with:) p Black Black Fh 8887 18753 a(****) 728
b(CUDD) g(non-m) r(odifiab) r(le) f(para) r(meters) h(****) 8887
20258 y(Memory) h(in) e(use:) i(3254422) r(0) p Fo 5978
22760 a(This) 317 b(is) i(the) f(memory) h(used) g(by) f(CUDD) i(for) e
(three) h(things) f(mainly:) 407 b(Unique) 320 b(table) f(\(includ-)
5978 24265 y(ing) 341 b(all) f(DD) i(nodes) e(in) h(use\),) 350
b(node) 341 b(free) g(list,) 349 b(and) 342 b(computed) f(table.) 490
b(This) 340 b(number) g(almost) 5978 25771 y(ne) -30
b(v) -18 b(er) 350 b(decreases) g(in) h(the) g(lifetime) g(of) f(a) h
(CUDD) h(manager) -48 b(,) 362 b(because) 352 b(CUDD) f(does) g(not) g
(re-) 5978 27276 y(lease) 384 b(memory) h(when) g(it) g(frees) f
(nodes.) 621 b(Rather) -48 b(,) 405 b(it) 385 b(puts) g(the) g(nodes) f
(on) h(its) g(o) -30 b(wn) 384 b(free) h(list.) 5978
28782 y(This) 396 b(number) h(is) f(in) h(bytes.) 658
b(It) 397 b(does) g(not) g(represent) f(the) h(peak) h(memory) f
(occupation,) 421 b(be-) 5978 30287 y(cause) 393 b(it) g(does) g(not) g
(include) h(the) f(size) g(of) g(data) h(structures) e(created) h
(temporarily) g(by) g(some) 5978 31793 y(functions) 302
b(\(e.g.,) h(local) g(look-up) g(tables\).) p Black Black
Fh 8887 34626 a(Peak) 728 b(number) h(of) f(nodes:) h(837018) p
Fo 5978 37460 a(This) 400 b(number) h(is) f(the) h(number) g(of) g
(nodes) g(that) g(the) g(manager) g(has) g(allocated.) 670
b(This) 401 b(is) f(not) 5978 38966 y(the) 353 b(lar) -22
b(gest) 353 b(size) g(of) g(the) g(BDDs,) 366 b(because) 353
b(the) h(manager) f(will) g(normally) h(ha) -24 b(v) -18
b(e) 353 b(some) g(dead) 5978 40471 y(nodes) 302 b(and) i(some) f
(nodes) f(on) i(the) f(free) f(list.) p Black Black Fh
8887 43305 a(Peak) 728 b(number) h(of) f(live) g(nodes:) h(836894) p
Fo 5978 46139 a(This) 256 b(is) i(the) g(lar) -22 b(gest) 257
b(number) h(of) f(li) -30 b(v) -18 b(e) 258 b(nodes) g(that) f(the) h
(manager) h(has) e(held) h(since) g(its) f(creation.) p
Black Black Fh 8887 48973 a(Number) 729 b(of) e(BDD) h(vari) r(ables:) g
(198) 8887 50478 y(Number) h(of) e(ZDD) h(vari) r(ables:) g(0) p
Fo 5978 53312 a(These) 302 b(numbers) h(tell) g(us) f(this) h(run) g(w)
-12 b(as) 302 b(not) h(using) g(ZDDs.) p Black Black
Fh 8887 56146 a(Number) 729 b(of) e(cache) i(entrie) r(s:) e(1048) r
(576) p Fo 5978 58979 a(Current) 309 b(number) g(of) f(slots) g(of) h
(the) g(computed) h(table.) 394 b(If) 308 b(one) h(has) g(a) g
(performance) g(problem,) 5978 60485 y(this) 302 b(is) h(one) g(of) g
(the) g(numbers) f(to) h(look) h(at.) 375 b(The) 303
b(cache) h(size) f(is) f(al) -12 b(w) g(ays) 303 b(a) g(po) -30
b(wer) 303 b(of) g(2.) p Black Black Fh 8887 63319 a(Number) 729
b(of) e(cache) i(look-u) r(ps:) f(2996536) 8887 64824
y(Number) h(of) e(cache) i(hits:) g(1187087) p Black
Fo 25297 69672 a(34) p Black 90 rotate dyy eop
%%Page: 35 35
35 34 bop Black Black Fo 5978 7638 a(These) 280 b(numbers) h(gi) -30
b(v) -18 b(e) 281 b(an) g(indication) g(of) g(the) g(hit) g(rate) g(in)
g(the) h(computed) f(table.) 369 b(It) 281 b(is) f(not) h(un-) 5978
9143 y(lik) -12 b(ely) 303 b(for) f(model) h(checking) h(runs) e(to) h
(get) h(hit) f(rates) f(e) -30 b(v) -18 b(en) 303 b(higher) g(than) g
(this) g(one) g(\(39.62\045\).) p Black Black Fh 8887
11874 a(Number) 729 b(of) e(cache) i(insert) r(ions:) f(18094) r(73)
8887 13380 y(Number) h(of) e(cache) i(collis) r(ions:) f(96120) r(8)
8887 14885 y(Number) h(of) e(cache) i(deleti) r(ons:) f(0) p
Fo 5978 17616 a(A) 399 b(collision) f(occurs) h(when) h(a) f(cache) h
(entry) e(is) h(o) -18 b(v) g(erwritten.) 663 b(A) 399
b(deletion) h(occurs) e(when) i(a) 5978 19122 y(cache) 332
b(entry) g(is) g(in) -48 b(v) -30 b(alidated) 331 b(\(e.g.,) 339
b(during) 332 b(g) -6 b(arbage) 332 b(collection\).) 463
b(If) 331 b(the) i(number) e(of) h(dele-) 5978 20627
y(tions) 265 b(is) g(high) h(compared) g(to) g(the) g(number) g(of) g
(collisions,) 272 b(it) 266 b(means) g(that) g(g) -6
b(arbage) 266 b(collection) 5978 22133 y(occurs) 385
b(too) i(often.) 625 b(In) 386 b(this) g(case) g(there) g(were) g(no) h
(g) -6 b(arbage) 386 b(collections;) 428 b(hence,) 408
b(no) 386 b(dele-) 5978 23638 y(tions.) p Black Black
Fh 8887 26369 a(Cache) 728 b(used) h(slots) f(=) g(80.90\045) h
(\(expect) r(ed) e(82.1) r(9\045\)) p Fo 5978 29100 a(Percentage) 311
b(of) f(cache) h(slots) e(that) i(contain) g(a) g(v) -30
b(alid) 310 b(entry) -79 b(.) 398 b(If) 310 b(this) g(number) h(is) e
(small,) j(it) f(may) 5978 30606 y(signal) 302 b(one) i(of) e(three) h
(conditions:) p Black 7493 33022 a(1.) p Black 606 w(The) g(cache) h
(may) f(ha) -24 b(v) -18 b(e) 303 b(been) g(recently) h(resized) e(and)
i(it) f(is) f(still) g(\002lling) h(up.) p Black 7493
35489 a(2.) p Black 606 w(The) 363 b(cache) g(is) g(too) g(lar) -22
b(ge) 363 b(for) f(the) h(BDDs.) 556 b(This) 362 b(should) h(not) g
(happen) g(if) g(the) g(size) f(of) 9008 36995 y(the) 303
b(cache) h(is) e(determined) i(by) f(CUDD.) p Black 7493
39462 a(3.) p Black 606 w(The) k(hash) g(function) h(is) f(not) g(w) -12
b(orking) 308 b(properly) -79 b(.) 388 b(This) 307 b(is) g(accompanied)
h(by) g(a) g(de) -18 b(gra-) 9008 40968 y(dation) 428
b(in) f(performance.) 748 b(Con) -48 b(v) -18 b(ersely) -79
b(,) 459 b(a) 427 b(de) -18 b(gradation) 428 b(in) f(performance) g
(may) h(be) 9008 42473 y(due) 303 b(to) g(bad) h(hash) e(function) h
(beha) -24 b(vior) -67 b(.) 5978 44889 y(The) 342 b(e) -18
b(xpected) 343 b(v) -30 b(alue) 342 b(is) g(computed) h(assuming) f(a) g
(uniformly) g(random) h(distrib) -24 b(u) n(tion) 343
b(of) f(the) 5978 46394 y(accesses.) 563 b(If) 365 b(the) h(dif) -30
b(fer) n(ence) 367 b(between) f(the) g(measured) g(v) -30
b(alue) 366 b(and) g(the) f(e) -18 b(xpected) 367 b(v) -30
b(alue) 366 b(is) 5978 47900 y(lar) -22 b(ge) 303 b(\(unlik) -12
b(e) 303 b(this) f(case\),) h(the) g(cache) h(is) e(not) h(w) -12
b(orking) 303 b(properly) -79 b(.) p Black Black Fh 8887
50631 a(Soft) 728 b(limit) h(for) f(cache) g(size:) h(131891) r(2) p
Fo 5978 53362 a(This) 319 b(number) i(says) f(ho) -30
b(w) 320 b(lar) -22 b(ge) 321 b(the) g(cache) g(can) g(gro) -30
b(w) -79 b(.) 429 b(This) 319 b(limit) i(is) f(based) h(on) f(the) h
(size) f(of) 5978 54867 y(the) 362 b(unique) h(table.) 555
b(CUDD) 363 b(uses) f(a) g(re) -30 b(w) -12 b(ard-based) 362
b(polic) -18 b(y) 363 b(for) e(gro) -30 b(wing) 363 b(the) f(cache.) 555
b(\(See) 5978 56373 y(Section) 394 b(4.4.1.\)) 647 b(The) 394
b(def) -12 b(ault) 394 b(hit) f(rate) h(for) f(resizing) g(is) g
(30\045) h(and) g(the) g(v) -30 b(alue) 394 b(in) g(ef) -30
b(fect) 393 b(is) 5978 57878 y(reported) 302 b(among) i(the) f
(modi\002able) g(parameters.) p Black Black Fh 8887 60609
a(Number) 729 b(of) e(bucke) r(ts) h(in) f(uniqu) r(e) g(table) r(:) g
(32972) r(8) p Fo 5978 63340 a(This) 357 b(number) i(is) f(e) -18
b(xactly) 359 b(one) g(quarter) g(of) f(the) h(one) g(abo) -18
b(v) g(e.) 543 b(This) 358 b(is) g(indeed) h(ho) -30
b(w) 359 b(the) g(soft) 5978 64846 y(limit) 482 b(is) g(determined) h
(currently) -79 b(,) 528 b(unless) 482 b(the) g(computed) i(table) f
(hits) f(the) h(speci\002ed) f(hard) 5978 66351 y(limit.) 375
b(\(See) 303 b(belo) -30 b(w) -79 b(.\)) p Black 25297
69672 a(35) p Black 90 rotate dyy eop
%%Page: 36 36
36 35 bop Black Black Black Black Fh 8887 7638 a(Used) 728
b(bucket) r(s) f(in) h(unique) h(table:) g(87.96\045) g(\(expect) r(ed)
e(87.9) r(3\045\)) p Fo 5978 10302 a(Percentage) 322
b(of) f(unique) h(table) g(b) -24 b(uck) -12 b(ets) 321
b(that) h(contain) g(at) g(least) f(one) h(node.) 432
b(Remarks) 322 b(analo-) 5978 11807 y(gous) 302 b(to) h(those) g(made) h
(about) f(the) g(used) g(cache) h(slots) e(apply) -79
b(.) p Black Black Fh 8887 14471 a(Number) 729 b(of) e(BDD) h(and) h
(ADD) f(nodes:) h(836894) 8887 15976 y(Number) g(of) e(ZDD) h(node) r
(s:) f(0) p Fo 5978 18640 a(Ho) -30 b(w) 303 b(man) -18
b(y) 303 b(nodes) g(are) g(currently) f(in) h(the) h(unique) f(table,) g
(either) g(ali) -30 b(v) -18 b(e) 303 b(or) g(dead.) p
Black Black Fh 8887 21303 a(Number) 729 b(of) e(dead) i(BDD) f(and) g
(ADD) g(nodes:) h(0) 8887 22808 y(Number) g(of) e(dead) i(ZDD) f
(nodes:) h(0) p Fo 5978 25472 a(Subtract) 351 b(these) h(numbers) f
(from) g(those) g(abo) -18 b(v) g(e) 352 b(to) f(get) h(the) g(number) g
(of) f(li) -30 b(v) -18 b(e) 351 b(nodes.) 521 b(In) 352
b(this) 5978 26977 y(case) 391 b(there) h(are) g(no) g(dead) g(nodes) f
(because) i(the) e(application) i(uses) e(delayed) h(dereferencing) p
Fn 5978 28483 a(Cudd) p 8677 28483 364 45 v 437 w(DelayedDer) -45
b(efBdd) p Fo(.) p Black Black Fh 8887 31146 a(Total) 728
b(numbe) r(r) f(of) h(nodes) h(allocat) r(ed:) f(836894) p
Fo 5978 33810 a(This) 373 b(is) i(the) g(total) f(number) h(of) f
(nodes) h(that) g(were) g(requested) f(and) h(obtained) h(from) e(the) h
(free) 5978 35315 y(list.) 680 b(It) 404 b(ne) -30 b(v) -18
b(er) 405 b(decreases,) 430 b(and) 405 b(is) f(not) h(an) g(indication)
g(of) f(memory) h(occupation) h(after) e(the) 5978 36821
y(\002rst) 302 b(g) -6 b(arbage) 303 b(collection.) 376
b(Rather) -48 b(,) 303 b(it) g(is) g(a) g(measure) g(of) f(the) i
(package) g(acti) -30 b(vity) -79 b(.) p Black Black
Fh 8887 39484 a(Total) 728 b(numbe) r(r) f(of) h(nodes) h(reclaim) r
(ed:) f(0) p Fo 5978 42148 a(These) 365 b(are) h(the) g(nodes) f(that) h
(were) g(resuscitated) g(from) f(the) h(dead.) 564 b(If) 366
b(the) -18 b(y) 365 b(are) h(man) -18 b(y) 366 b(more) 5978
43653 y(than) 276 b(the) g(allocated) g(nodes,) 281 b(and) c(the) f
(total) g(number) f(of) h(slots) f(is) g(lo) -30 b(w) 276
b(relati) -30 b(v) -18 b(e) 275 b(to) h(the) g(number) 5978
45159 y(of) 338 b(nodes,) 347 b(then) 339 b(one) g(may) g(w) -12
b(ant) 339 b(to) f(increase) h(the) f(limit) h(for) f(f) -12
b(ast) 337 b(unique) i(table) g(gro) -30 b(wth.) 482
b(In) 5978 46664 y(this) 302 b(case,) h(the) g(number) g(is) g(0) g
(because) g(of) g(delayed) h(dereferencing.) p Black
Black Fh 8887 49328 a(Garbage) 729 b(collect) r(ions) f(so) g(far:) g
(0) 8887 50833 y(Time) g(for) g(garbag) r(e) f(colle) r(ctions:) i
(0.00) f(sec) 8887 52339 y(Reorder) r(ings) g(so) g(far:) g(0) 8887
53844 y(Time) g(for) g(reorde) r(ring:) g(0.00) h(sec) p
Fo 5978 56508 a(There) 327 b(is) h(a) g(GC) h(for) f(each) g
(reordering.) 451 b(Hence) 329 b(the) f(\002rst) f(count) i(will) f(al)
-12 b(w) g(ays) 328 b(be) g(at) h(least) e(as) 5978 58013
y(lar) -22 b(ge) 303 b(as) g(the) g(second.) p Black
Black Fh 8887 60677 a(Node) 728 b(swaps) h(in) e(reor) r(dering:) i(0) p
Fo 5978 63340 a(This) 400 b(is) g(the) h(number) g(of) g(elementary) g
(reordering) g(steps.) 669 b(Each) 401 b(step) f(consists) g(of) h(the)
g(re-) 5978 64846 y(e) -18 b(xpressi) n(on) 363 b(of) f(one) h(node) g
(while) g(sw) -12 b(apping) 363 b(tw) -12 b(o) 362 b(adjacent) i(v) -30
b(ariables.) 554 b(This) 361 b(number) i(is) f(a) 5978
66351 y(good) 303 b(measure) g(of) f(the) i(amount) f(of) g(w) -12
b(ork) 302 b(done) i(in) f(reordering.) p Black 25297
69672 a(36) p Black 90 rotate dyy eop
%%Page: 37 37
37 36 bop Black Black Fp 5978 7638 a(4.8.2) 1212 b(Modi\002able) 303
b(P) -12 b(arameters) p Fo 5978 9962 a(Let) 296 b(us) g(no) -30
b(w) 297 b(consider) f(the) h(modi\002able) g(parameters,) g(that) g
(is,) g(those) f(settings) g(on) h(which) g(the) 5978
11467 y(application) 303 b(or) g(the) g(user) g(has) f(control.) p
Black Black Fh 8887 14301 a(****) 728 b(CUDD) g(modif) r(iable) g
(param) r(eters) g(****) 8887 15806 y(Hard) g(limit) h(for) f(cache) g
(size:) h(838860) r(8) p Fo 5978 18640 a(This) 391 b(number) i(counts) f
(entries.) 644 b(Each) 392 b(entry) h(is) f(16) g(bytes) h(if) f(CUDD) h
(is) f(compiled) h(to) f(use) 5978 20146 y(32-bit) 302
b(pointers.) 376 b(T) -97 b(w) -12 b(o) 302 b(important) h(observ) -30
b(ations) 302 b(are) h(in) g(order:) p Black 7493 22647
a(1.) p Black 606 w(If) 323 b(the) g(datasize) h(limit) f(is) g(set,)
328 b(CUDD) d(will) e(use) g(it) h(to) f(determine) h(this) f(number) g
(auto-) 9008 24153 y(matically) -79 b(.) 571 b(On) 368
b(a) g(Unix) g(system,) 383 b(one) 368 b(can) h(type) f(\223limit\224) g
(to) g(v) -18 b(erify) 367 b(if) g(this) h(v) -30 b(alue) 368
b(is) 9008 25658 y(set.) 355 b(If) 240 b(the) h(datasize) g(limit) g
(is) f(not) h(set,) 253 b(CUDD) 242 b(uses) e(a) h(def) -12
b(ault) 240 b(which) i(is) e(rather) h(small.) 9008 27164
y(If) 311 b(you) g(ha) -24 b(v) -18 b(e) 312 b(enough) f(memory) h
(\(say) f(64MB) g(or) g(more\)) g(you) h(should) f(seriously) f(con-)
9008 28669 y(sider) p Fn 364 w(not) p Fo 386 w(using) 364
b(the) h(def) -12 b(ault.) 561 b(So,) 380 b(either) 364
b(set) g(the) h(datasize) g(limit,) 380 b(or) 364 b(o) -18
b(v) g(erride) 364 b(the) 9008 30175 y(def) -12 b(ault) 303
b(with) p Fn 303 w(Cudd) p 17822 30175 364 45 v 437 w(SetMaxCac) -18
b(heHar) -45 b(d) p Fo(.) p Black 7493 32676 a(2.) p
Black 606 w(If) 265 b(a) g(process) g(seems) g(to) g(be) h(going) g(no)
-30 b(where,) 273 b(a) 266 b(small) f(v) -30 b(alue) 266
b(for) e(this) h(parameter) h(may) 9008 34182 y(be) 381
b(the) g(culprit.) 609 b(One) 381 b(cannot) g(o) -18
b(v) g(eremphasize) 381 b(the) g(importance) g(of) g(the) g(computed)
9008 35687 y(table) 303 b(in) g(BDD) h(algorithms.) 5978
38189 y(In) e(this) g(case) g(the) h(limit) f(w) -12
b(as) 302 b(automatically) h(set) f(for) g(a) g(tar) -22
b(get) 303 b(maximum) f(memory) h(occupa-) 5978 39695
y(tion) g(of) f(104) i(MB.) p Black Black Fh 8887 42528
a(Cache) 728 b(hit) g(thres) r(hold) g(for) g(resiz) r(ing:) g(15\045) p
Fo 5978 45362 a(This) 314 b(number) i(can) g(be) f(changed) i(if) e
(one) h(suspects) e(performance) h(is) g(hindered) h(by) g(the) g
(small) 5978 46868 y(size) 373 b(of) g(the) h(cache,) 392
b(and) 373 b(the) h(cache) g(is) f(not) h(gro) -30 b(wing) 373
b(to) -30 b(w) -12 b(ards) 372 b(the) i(soft) f(limit) g(suf) -30
b(\002ciently) 5978 48373 y(f) -12 b(ast.) 365 b(In) 273
b(such) h(a) g(case) f(one) h(can) h(change) f(the) g(def) -12
b(ault) 274 b(30\045) f(to) h(15\045) f(\(as) g(in) h(this) f(case\)) h
(or) f(e) -30 b(v) -18 b(en) 5978 49879 y(1\045.) p Black
Black Fh 8887 52712 a(Garbage) 729 b(collect) r(ion) f(enabled) r(:) f
(yes) p Fo 5978 55546 a(One) 440 b(can) h(disable) f(it,) 474
b(b) -24 b(ut) 440 b(there) g(are) g(fe) -30 b(w) 440
b(good) g(reasons) g(for) f(doing) h(so.) 787 b(It) 440
b(is) f(normally) 5978 57052 y(preferable) 302 b(to) h(raise) g(the) g
(limit) g(for) f(f) -12 b(ast) 302 b(unique) i(table) f(gro) -30
b(wth.) 376 b(\(See) 302 b(belo) -30 b(w) -79 b(.\)) p
Black Black Fh 8887 59886 a(Limit) 728 b(for) g(fast) h(unique) g
(table) f(growt) r(h:) f(1363) r(148) p Fo 5978 62719
a(See) 305 b(Section) h(4.5) f(and) g(the) h(comments) f(abo) -18
b(v) g(e) 305 b(about) h(reclaimed) f(nodes) g(and) h(hard) f(limit) g
(for) 5978 64225 y(the) g(cache) h(size.) 381 b(This) 305
b(v) -30 b(alue) 305 b(w) -12 b(as) 304 b(chosen) i(automatically) f
(by) g(CUDD) h(for) f(a) g(datasize) g(limit) 5978 65730
y(of) d(1) h(GB.) p Black 25297 69672 a(37) p Black 90 rotate
dyy eop
%%Page: 38 38
38 37 bop Black Black Black Black Fh 8887 7638 a(Maximum) 729
b(number) g(of) f(variable) r(s) f(sifte) r(d) g(per) h(reord) r
(ering:) h(1000) 8887 9143 y(Maximum) g(number) g(of) f(variable) h
(swaps) g(per) f(reorder) r(ing:) g(200000) r(0) 8887
10649 y(Maximum) h(growth) g(while) f(sifti) r(ng) g(a) f(variab) r
(le:) h(1.2) p Fo 5978 13445 a(Lo) -30 b(wering) 360
b(these) g(numbers) g(will) h(cause) g(reordering) f(to) h(be) g(less) f
(accurate) h(and) g(f) -12 b(aster) -67 b(.) 548 b(Re-) 5978
14950 y(sults) 262 b(are) i(some) -30 b(what) 264 b(unpredictable,) 272
b(because) 264 b(lar) -22 b(ger) 264 b(BDDs) g(after) g(one) g
(reordering) f(do) h(not) 5978 16456 y(necessarily) 302
b(mean) h(the) h(process) e(will) h(go) g(f) -12 b(aster) 302
b(or) h(slo) -30 b(wer) -67 b(.) p Black Black Fh 8887
19252 a(Dynamic) 729 b(reorder) r(ing) f(of) g(BDDs) g(enable) r(d:) f
(yes) 8887 20757 y(Default) i(BDD) f(reorde) r(ring) g(method) r(:) f
(4) 8887 22263 y(Dynamic) i(reorder) r(ing) f(of) g(ZDDs) g(enable) r
(d:) f(no) 8887 23768 y(Default) i(ZDD) f(reorde) r(ring) g(method) r
(:) f(4) p Fo 5978 26564 a(These) 489 b(lines) h(tell) h(whether) f
(automatic) h(reordering) f(can) h(tak) -12 b(e) 491
b(place) f(and) h(what) g(method) 5978 28069 y(w) -12
b(ould) 352 b(be) h(used.) 525 b(The) 353 b(mapping) g(from) f(numbers)
g(to) h(methods) f(is) h(in) p Fh 352 w(cudd.) r(h) p
Fo(.) 525 b(One) 353 b(may) 5978 29575 y(w) -12 b(ant) 366
b(to) g(try) g(dif) -30 b(ferent) 365 b(BDD) i(reordering) f(methods.)
565 b(If) 366 b(v) -30 b(ariable) 366 b(groups) f(are) i(used,) 382
b(ho) -30 b(w-) 5978 31080 y(e) g(v) -18 b(er) -48 b(,) 262
b(one) 253 b(should) f(not) h(e) -18 b(xpect) 253 b(to) g(see) g(big) g
(dif) -30 b(ferences,) 262 b(because) 253 b(CUDD) g(uses) f(the) h
(reported) 5978 32586 y(method) 380 b(only) f(to) h(reorder) f(each) h
(leaf) g(v) -30 b(ariable) 379 b(group) h(\(typically) f(corresponding)
h(present) 5978 34091 y(and) 394 b(ne) -18 b(xt) 393
b(state) h(v) -30 b(ariables\).) 647 b(F) -18 b(or) 393
b(the) h(relati) -30 b(v) -18 b(e) 393 b(order) h(of) f(the) h(groups,)
416 b(it) 393 b(al) -12 b(w) g(ays) 394 b(uses) f(the) 5978
35597 y(same) 302 b(algorithm,) h(which) h(is) e(ef) -30
b(fecti) g(v) -18 b(ely) 303 b(sifting.) 7859 37102 y(As) 369
b(for) e(enabling) i(dynamic) g(reordering) f(or) g(not,) 385
b(a) 369 b(sensible) f(recommendation) h(is) f(the) 5978
38608 y(follo) -30 b(wing:) 440 b(Unless) 335 b(the) h(circuit) f(is) g
(rather) h(small) f(or) g(one) h(has) f(a) h(pretty) g(good) g(idea) g
(of) f(what) 5978 40113 y(the) 303 b(order) f(should) h(be,) g
(reordering) g(should) g(be) g(enabled.) p Black Black
Fh 8887 42909 a(Realign) r(ment) 728 b(of) g(ZDDs) g(to) g(BDDs) g
(enabl) r(ed:) g(no) 8887 44414 y(Realign) r(ment) g(of) g(BDDs) g(to) g
(ZDDs) g(enabl) r(ed:) g(no) 8887 45920 y(Dead) g(nodes) h(counted) g
(in) f(trigger) r(ing) g(reorder) r(ing:) g(no) 8887
47425 y(Group) g(check) r(ing) g(criteri) r(on:) g(7) 8887
48931 y(Recombi) r(nation) g(thre) r(shold:) g(0) 8887
50436 y(Symmetr) r(y) f(violat) r(ion) h(thresho) r(ld:) g(0) 8887
51942 y(Arc) g(violati) r(on) f(thre) r(shold:) h(0) 8887
53447 y(GA) f(popu) r(lation) h(size) r(:) f(0) 8887
54953 y(Number) i(of) e(cross) r(overs) h(for) g(GA:) h(0) p
Fo 5978 57749 a(P) -18 b(arameters) 323 b(for) h(reordering.) 438
b(See) 325 b(the) f(documentation) h(of) f(the) g(functions) g(used) g
(to) g(control) 5978 59254 y(these) 302 b(parameters) h(for) f(the) i
(details.) p Black Black Fh 8887 62050 a(Next) 728 b(reorde) r(ring) g
(thresh) r(old:) g(100000) p Fo 5978 64846 a(When) 317
b(the) f(number) g(of) h(nodes) f(crosses) f(this) h(threshold,) j
(reordering) d(will) g(be) h(triggered.) 415 b(\(If) 5978
66351 y(enabled;) 300 b(in) e(this) g(case) g(it) g(is) f(not.\)) 374
b(This) 297 b(parameter) h(is) g(updated) h(by) f(the) g(package) h
(whene) -30 b(v) -18 b(er) p Black 25297 69672 a(38) p
Black 90 rotate dyy eop
%%Page: 39 39
39 38 bop Black Black Fo 5978 7638 a(reordering) 312
b(tak) -12 b(es) 313 b(place.) 407 b(The) 313 b(application) h(can) g
(change) g(it,) i(for) c(instance) h(at) h(start-up.) 405
b(An-) 5978 9143 y(other) 288 b(possibility) g(is) h(to) g(use) f(a) h
(hook) h(function) e(\(see) h(Section) g(3.16\)) g(to) g(o) -18
b(v) g(erride) 288 b(the) h(def) -12 b(ault) 5978 10649
y(updating) 303 b(polic) -18 b(y) -79 b(.) p Fp 5978
13927 a(4.8.3) 1212 b(Extended) 303 b(Statistics) e(and) i(Reporting) p
Fo 5978 16251 a(The) 350 b(follo) -30 b(wing) 351 b(symbols) e(can) j
(be) f(de\002ned) g(during) f(compilation) i(to) e(increase) h(the) g
(amount) 5978 17756 y(of) 302 b(statistics) g(g) -6 b(athered) 303
b(and) h(the) f(number) g(of) g(messages) f(produced) h(by) g(the) g
(package:) p Black Fm 7796 20258 a(\262) p Black Fo 606
w(DD) p 10831 20258 364 45 v 437 w(ST) -113 b(A) -135
b(TS;) p Black Fm 7796 22760 a(\262) p Black Fo 606 w(DD) p
10831 22760 V 437 w(CA) -48 b(CHE) p 15327 22760 V 436
w(PR) g(OFILE;) p Black Fm 7796 25261 a(\262) p Black
Fo 606 w(DD) p 10831 25261 V 437 w(UNIQ) -12 b(UE) p
15901 25261 V 436 w(PR) -48 b(OFILE) n(.) p Black Fm
7796 27763 a(\262) p Black Fo 606 w(DD) p 10831 27763
V 437 w(VERBOSE;) 5978 30265 y(De\002ning) 345 b(DD) p
12388 30265 V 437 w(CA) -48 b(CHE) p 16884 30265 V 437
w(PR) g(OFILE) 344 b(causes) g(each) i(entry) f(of) g(the) h(cache) g
(to) f(include) h(an) f(ac-) 5978 31770 y(cess) 357 b(counter) -48
b(,) 372 b(which) 359 b(is) f(used) g(to) g(compute) h(simple) f
(statistics) f(on) i(the) g(distrib) -24 b(u) n(tion) 359
b(of) f(the) 5978 33276 y(k) -12 b(e) -18 b(ys.) p Fi
5978 36598 a(4.9) 1328 b(Guidelines) 332 b(f) -33 b(or) 332
b(Documen) n(tatio) r(n) p Fo 5978 38922 a(The) 465 b(documentation) h
(of) g(the) f(CUDD) i(functions) e(is) g(e) -18 b(xtracted) 466
b(automatically) g(from) f(the) 5978 40427 y(sources) 265
b(by) h(Stephen) g(Edw) -12 b(ards') -67 b(s) 265 b(e) -18
b(xtdoc.) 363 b(\(The) 266 b(Ext) f(system) h(is) f(a) -24
b(v) -30 b(ailable) 266 b(via) g(anon) -18 b(ymous) 5978
41933 y(FTP) 374 b(from) p Fh 375 w(ic.eecs) r(.berkel) r(ey.edu) p
Fo(.\)) 593 b(The) 375 b(follo) -30 b(wing) 375 b(guidelines) g(are) g
(follo) -30 b(wed) 5978 43438 y(in) 358 b(CUDD) h(to) f(insure) f
(consistent) h(and) g(ef) -30 b(fecti) g(v) -18 b(e) 357
b(use) h(of) g(automatic) g(e) -18 b(xtraction.) 541
b(It) 358 b(is) g(rec-) 5978 44944 y(ommended) 303 b(that) g(e) -18
b(xtensions) 303 b(to) g(CUDD) h(follo) -30 b(w) 302
b(the) i(same) e(documentation) i(guidelines.) p Black
Fm 7796 47446 a(\262) p Black Fo 606 w(The) 404 b(documentation) h(of) f
(an) h(e) -18 b(xported) 404 b(procedure) h(should) f(be) g(suf) -30
b(\002cient) 404 b(to) g(allo) -30 b(w) 9008 48951 y(one) 301
b(to) g(use) f(it) h(without) f(reading) h(the) g(code.) 375
b(It) 301 b(is) f(not) h(necessary) f(to) g(e) -18 b(xplain) 301
b(ho) -30 b(w) 301 b(the) 9008 50456 y(procedure) i(w) -12
b(orks;) 302 b(only) h(what) h(it) f(does.) p Black Fm
7796 52958 a(\262) p Black Fo 606 w(The) p Fn 389 w(SeeAlso) p
Fo 388 w(\002elds) 389 b(should) f(be) h(space-separated) g(lists) f
(of) g(function) h(names.) 633 b(The) p Fn 9008 54464
a(SeeAlso) p Fo 299 w(\002eld) 300 b(of) f(an) h(e) -18
b(xported) 299 b(procedure) h(should) f(only) g(reference) h(other) f
(e) -18 b(xported) 9008 55969 y(procedures.) 483 b(The) p
Fn 339 w(SeeAlso) p Fo 338 w(\002eld) 339 b(of) g(an) g(internal) g
(procedure) f(may) i(reference) e(other) 9008 57475 y(internal) 293
b(procedures) g(as) f(well) i(as) f(e) -18 b(xported) 293
b(procedures,) h(b) -24 b(ut) 293 b(no) h(static) f(procedures.) p
Black Fm 7796 59976 a(\262) p Black Fo 606 w(The) 401
b(return) f(v) -30 b(alues) 401 b(are) f(detailed) i(in) f(the) p
Fn 401 w(Description) p Fo 400 w(\002eld,) 426 b(not) 401
b(in) g(the) p Fn 401 w(Synopsis) p Fo 9008 61482 a(\002eld.) p
Black Fm 7796 63984 a(\262) p Black Fo 606 w(The) 366
b(parameters) f(are) h(documented) h(alongside) f(their) f
(declarations.) 565 b(Further) 365 b(com-) 9008 65489
y(ments) 303 b(may) g(appear) g(in) g(the) p Fn 303 w(Description) p
Fo 303 w(\002eld.) p Black 25297 69672 a(39) p Black
90 rotate dyy eop
%%Page: 40 40
40 39 bop Black Black Black Fm 7796 7638 a(\262) p Black
Fo 606 w(If) 376 b(the) p Fn 377 w(Description) p Fo
376 w(\002eld) h(is) f(non-empty\227which) i(is) e(the) h(normal) g
(case) f(for) g(an) h(e) -18 b(x-) 9008 9143 y(ported) 230
b(procedure\227then) h(the) f(synopsis) f(is) h(repeated\227possibly) g
(slightly) g(changed\227) 9008 10649 y(at) 331 b(the) h(be) -18
b(ginning) 331 b(of) g(the) p Fn 332 w(Description) p
Fo 330 w(\002eld.) 461 b(This) 330 b(is) h(so) g(because) g(e) -18
b(xtdoc) 332 b(will) f(not) 9008 12154 y(put) 303 b(the) g(synopsis) f
(in) h(the) g(same) g(HTML) f(\002le) h(as) g(the) g(description.) p
Black Fm 7796 14656 a(\262) p Black Fo 606 w(The) p Fn
303 w(Synopsis) p Fo 302 w(\002eld) g(should) g(be) g(about) h(one) f
(line) g(long.) p Fq 5978 18558 a(5) 1594 b(The) 398
b(C++) g(Interface) p Fi 5978 21362 a(5.1) 1328 b(Compiling) 332
b(and) g(Linking) p Fo 5978 23686 a(T) -97 b(o) 302 b(b) -24
b(uild) 303 b(an) g(application) h(that) f(uses) g(the) g(CUDD) h(C++) e
(interf) -12 b(ace,) 303 b(you) h(should) e(add) p Black
Black Fh 5978 26187 a(#include) 729 b("cuddO) r(bj.hh") p
Fo 5978 28689 a(to) 398 b(your) h(source) f(\002les.) 662
b(In) 398 b(addition) h(to) f(the) h(normal) f(CUDD) i(libraries) d
(\(see) h(Section) h(3.1\)) 5978 30195 y(you) 267 b(should) g(link) p
Fh 268 w(libobj.) r(a) p Fo 267 w(to) h(your) f(e) -18
b(x) g(ecutable.) 365 b(Refer) 267 b(to) h(the) p Fh
267 w(Makef) r(ile) p Fo 268 w(in) f(the) h(top) 5978
31700 y(le) -30 b(v) -18 b(el) 302 b(directory) h(of) g(the) g(distrib)
-24 b(ution) 302 b(for) g(further) h(details.) p Fi 5978
35023 a(5.2) 1328 b(Basic) 332 b(Manipulation) p Fo 5978
37346 a(The) 289 b(follo) -30 b(wing) 289 b(fragment) g(of) g(code) h
(illustrates) f(some) g(simple) g(operations) g(on) h(BDDs) f(using)
5978 38852 y(the) 303 b(C++) g(interf) -12 b(ace.) p
Black Black Fh 11796 41353 a(Cudd) 728 b(mgr\(0,) r(0\);) 11796
42859 y(BDD) g(x) f(=) h(mgr.bd) r(dVar\(\);) 11796 44364
y(BDD) g(y) f(=) h(mgr.bd) r(dVar\(\);) 11796 45870 y(BDD) g(f) f(=) h
(x) f(*) h(y;) 11796 47375 y(BDD) g(g) f(=) h(y) f(+) h(!x;) 11796
48881 y(cout) g(<<) g("f) g(is") g(<<) g(\(f) f(<=) h(g) g(?) f("") h
(:) g(") f(not"\)) 15432 50386 y(<<) h(") f(less) i(than) f(or) g
(equal) h(to) e(g\\n") r(;) p Fo 5978 52888 a(This) 284
b(code) i(creates) f(a) h(manager) f(called) p Fh 286
w(mgr) p Fo 286 w(and) h(tw) -12 b(o) 285 b(v) -30 b(ariables) 285
b(in) g(it.) 370 b(It) 285 b(then) h(de\002nes) f(tw) -12
b(o) 5978 54393 y(functions) p Fh 362 w(f) p Fo 363 w(and) p
Fh 363 w(g) p Fo 363 w(in) 362 b(terms) g(of) h(the) g(v) -30
b(ariables.) 554 b(Finally) -79 b(,) 378 b(it) 362 b(prints) g(a) h
(message) f(based) h(on) 5978 55899 y(the) 387 b(comparison) g(of) g
(the) h(tw) -12 b(o) 387 b(functions.) 629 b(No) 388
b(e) -18 b(xplicit) 387 b(referencing) g(or) g(dereferencing) h(is) 5978
57404 y(required.) 418 b(The) 317 b(operators) g(are) g(o) -18
b(v) g(erloaded) 318 b(in) f(the) h(intuiti) -30 b(v) -18
b(e) 317 b(w) -12 b(ay) -79 b(.) 419 b(BDDs) 317 b(are) h(freed) f
(when) 5978 58910 y(e) -18 b(x) g(ecution) 248 b(lea) -24
b(v) -18 b(es) 247 b(the) h(scope) g(in) g(which) g(the) -18
b(y) 248 b(are) g(de\002ned) g(or) g(when) g(the) g(v) -30
b(ariables) 247 b(referring) 5978 60415 y(to) 303 b(them) g(are) g(o)
-18 b(v) g(erwritten.) p Black 25297 69672 a(40) p Black
90 rotate dyy eop
%%Page: 41 41
41 40 bop Black Black Fq 5978 7638 a(6) 1594 b(Ackno) -16
b(wledgments) p Fo 5978 10398 a(The) 348 b(contrib) -24
b(utors) n(:) 466 b(Iris) 347 b(Bahar) -48 b(,) 360 b(Hyunw) -12
b(oo) 349 b(Cho,) 360 b(Erica) 347 b(Frohm,) 360 b(Charlie) 348
b(Gaona,) 360 b(Cheng) 5978 11904 y(Hua,) 413 b(Jae-Y) -133
b(oung) 391 b(Jang,) 414 b(Seh-W) -97 b(oong) 391 b(Jeong,) 414
b(Balakrishna) 391 b(K) -18 b(umthekar) -48 b(,) 413
b(Enrico) 391 b(Macii,) 5978 13409 y(Bobbie) 231 b(Manne,) 245
b(In-Ho) 229 b(Moon,) 245 b(Curt) 230 b(Musfeldt,) 244
b(Shipra) 230 b(P) -18 b(anda,) 245 b(Abelardo) 231 b(P) -18
b(ardo,) 245 b(Bernard) 5978 14914 y(Plessier) -50 b(,) 348
b(Ka) -24 b(vita) 339 b(Ra) -24 b(vi,) 349 b(Hyongk) -18
b(yoon) 340 b(Shin,) 348 b(Alan) 339 b(Shuler) -48 b(,) 348
b(Arun) 339 b(Si) -30 b(v) g(akumaran,) 347 b(Jor) -22
b(gen) 5978 16420 y(Si) -30 b(v) -18 b(esind.) 5978 17925
y(The) 419 b(early) g(adopters:) 607 b(Gianpiero) 420
b(Cabodi,) 449 b(Jordi) 418 b(Cortadella,) 449 b(Mario) 419
b(Escobar) -48 b(,) 447 b(Gayani) 5978 19431 y(Gamage,) 364
b(Gary) 352 b(Hachtel,) 365 b(Mariano) 352 b(Hermida,) 364
b(W) -97 b(ooh) -6 b(yuk) 352 b(Lee,) 364 b(Enric) 352
b(P) -18 b(astor) -48 b(,) 362 b(Massimo) 5978 20936
y(Poncino,) 303 b(Ellen) g(Sento) -18 b(vich,) 303 b(the) g(students) g
(of) f(ECEN5139.) 7859 22442 y(I) 467 b(am) h(also) f(particularly) h
(indebted) g(to) f(the) h(follo) -30 b(wing) 467 b(people) h(for) f
(in-depth) g(discus-) 5978 23947 y(sions) 380 b(on) h(BDDs:) 532
b(Armin) 381 b(Biere,) 402 b(Oli) -30 b(vier) 380 b(Coudert,) 401
b(Geert) 382 b(Janss) n(en,) 401 b(Da) -24 b(vid) 382
b(Long,) 400 b(Jean) 5978 25453 y(Christophe) 373 b(Madre,) 392
b(K) -30 b(en) 374 b(McMillan,) 391 b(Shin-Ichi) 373
b(Minato,) 392 b(Jaehong) 374 b(P) -18 b(ark,) 391 b(Rajee) -30
b(v) 375 b(Ran-) 5978 26958 y(jan,) 303 b(Rick) h(Rudell,) f(Ellen) g
(Sento) -18 b(vich,) 303 b(T) -97 b(om) 303 b(Shiple,) g(and) h(Bw) -12
b(olen) 303 b(Y) -121 b(ang.) 7859 28464 y(Special) 352
b(thanks) g(to) f(Norris) f(Ip) i(for) e(guiding) i(my) g(f) -12
b(altering) 351 b(steps) f(in) i(the) f(design) h(of) f(the) 5978
29969 y(C++) 367 b(interf) -12 b(ace.) 571 b(Gianpiero) 368
b(Cabodi) g(and) h(Stef) -12 b(ano) 367 b(Quer) h(ha) -24
b(v) -18 b(e) 368 b(graciously) g(agreed) g(to) g(let) 5978
31475 y(me) 303 b(distrib) -24 b(ute) 302 b(their) h(dddmp) g(library) g
(with) g(CUDD.) 7859 32980 y(Masahiro) 321 b(Fujita,) 326
b(Gary) c(Hachtel,) 327 b(and) 322 b(Carl) g(Pixle) -18
b(y) 321 b(ha) -24 b(v) -18 b(e) 322 b(pro) -18 b(vided) 321
b(encouragement) 5978 34485 y(and) 303 b(advice.) 7859
35991 y(The) 473 b(National) h(Science) f(F) -18 b(oundation) 473
b(and) h(the) f(Semiconductor) g(Research) g(Council) 5978
37496 y(ha) -24 b(v) -18 b(e) 303 b(supported) f(in) h(part) g(the) g
(de) -30 b(v) -18 b(elopment) 304 b(of) e(this) h(package.) p
Fq 5978 41398 a(Refer) -31 b(ences) p Black Fo 6584 44158
a([1]) p Black 605 w(R.) 371 b(I.) g(Bahar) -48 b(,) 388
b(E.) 370 b(A.) h(Frohm,) 388 b(C.) 371 b(M.) f(Gaona,) 389
b(G.) 371 b(D.) g(Hachtel,) 388 b(E.) 371 b(Macii,) 387
b(A.) 371 b(P) -18 b(ardo,) 8603 45664 y(and) 316 b(F) -97
b(.) 315 b(Somenzi.) 477 b(Algebraic) 316 b(decision) f(diagrams) g
(and) h(their) f(applications.) 477 b(In) p Fn 315 w(Pr) -55
b(o-) 8603 47169 y(ceedings) 355 b(of) h(the) f(International) g
(Confer) -45 b(ence) 356 b(on) f(Computer) -24 b(-Aided) 355
b(Design) p Fo(,) 368 b(pages) 8603 48674 y(188\226191,) 304
b(Santa) f(Clara,) g(CA,) h(No) -18 b(v) g(ember) 303
b(1993.) p Black 6584 51176 a([2]) p Black 605 w(B.) 484
b(Bollig,) 530 b(M.) 483 b(L) 16768 51170 y(\250) 16667
51176 y(obbing,) 529 b(and) 484 b(I.) g(W) -97 b(e) -18
b(gener) -67 b(.) 1015 b(Simulated) 484 b(annealing) h(to) f(impro) -18
b(v) g(e) 8603 52682 y(v) -30 b(ariable) 380 b(orderings) f(for) h
(OBDDs.) 683 b(Presented) 380 b(at) g(the) g(International) g(W) -97
b(orkshop) 380 b(on) 8603 54187 y(Logic) 303 b(Synthesis,) f
(Granlibakk) -12 b(en,) 304 b(CA,) f(May) g(1995.) p
Black 6584 56689 a([3]) p Black 605 w(K.) 390 b(S.) g(Brace,) 413
b(R.) 391 b(L.) e(Rudell,) 413 b(and) 390 b(R.) h(E.) f(Bryant.) 715
b(Ef) -30 b(\002cient) 389 b(implementation) i(of) f(a) 8603
58194 y(BDD) 395 b(package.) 731 b(In) p Fn 394 w(Pr) -55
b(oceedings) 394 b(of) h(the) g(27th) f(Design) h(A) -24
b(utomation) 394 b(Confer) -45 b(ence) p Fo(,) 8603 59700
y(pages) 303 b(40\22645,) g(Orlando,) h(FL,) e(June) h(1990.) p
Black 6584 62202 a([4]) p Black 605 w(R.) 330 b(K.) g(Brayton) f(et) h
(al.) 521 b(VIS:) 329 b(A) h(system) e(for) h(v) -18
b(eri\002cation) 329 b(and) h(synthesis.) 520 b(T) -85
b(echnical) 8603 63707 y(Report) 386 b(UCB) r(/ERL) f(M95/104,) 407
b(Electronics) 385 b(Research) h(Lab,) 407 b(Uni) -30
b(v) -79 b(.) 386 b(of) g(California,) 8603 65212 y(December) 304
b(1995.) p Black 25297 69672 a(41) p Black 90 rotate
dyy eop
%%Page: 42 42
42 41 bop Black Black Black Fo 6584 7638 a([5]) p Black
605 w(R.) 435 b(E.) f(Bryant.) 856 b(Graph-based) 434
b(algorithms) g(for) f(Boolean) i(function) g(manipulation.) p
Fn 8603 9143 a(IEEE) 301 b(T) -67 b(r) -18 b(ansactions) 303
b(on) g(Computer) -12 b(s) p Fo(,) 303 b(C-35\(8\):677\226691,) g
(August) f(1986.) p Black 6584 11552 a([6]) p Black 605
w(R.) 435 b(Drechsler) -48 b(,) 466 b(B.) 435 b(Beck) -12
b(er) -48 b(,) 467 b(and) 434 b(N.) h(G) 26043 11546
y(\250) 25942 11552 y(ock) -12 b(el.) 856 b(A) 435 b(genetic) g
(algorithm) f(for) f(v) -30 b(ariable) 8603 13058 y(ordering) 318
b(of) h(OBDDs.) 487 b(Presented) 318 b(at) h(the) g(International) g(W)
-97 b(orkshop) 318 b(on) h(Logic) f(Syn-) 8603 14563
y(thesis,) 302 b(Granlibakk) -12 b(en,) 304 b(CA,) f(May) g(1995.) p
Black 6584 16972 a([7]) p Black 605 w(S.) 352 b(J.) f(Friedman) g(and) h
(K.) g(J.) f(Supo) -30 b(wit.) 592 b(Finding) 352 b(the) f(optimal) h
(v) -30 b(ariable) 352 b(ordering) f(for) 8603 18477
y(binary) 289 b(decision) f(diagrams.) p Fn 405 w(IEEE) f(T) -67
b(r) -18 b(ansactions) 287 b(on) i(Computer) -12 b(s) p
Fo(,) 291 b(39\(5\):710\226713,) 8603 19983 y(May) 303
b(1990.) p Black 6584 22392 a([8]) p Black 605 w(M.) 468
b(Fujita,) 509 b(Y) -156 b(.) 468 b(Matsunag) -6 b(a,) 510
b(and) 468 b(T) -90 b(.) 468 b(Kakuda.) 966 b(On) 468
b(v) -30 b(ariable) 468 b(ordering) g(of) g(binary) 8603
23897 y(decision) 358 b(diagrams) f(for) g(the) h(application) g(of) f
(multi-le) -30 b(v) -18 b(el) 358 b(logic) f(synthesis.) 611
b(In) p Fn 357 w(Pr) -55 b(o-) 8603 25403 y(ceedings) 399
b(of) g(the) h(Eur) -55 b(opean) 399 b(Confer) -45 b(ence) 400
b(on) f(Design) g(A) -24 b(utomation) p Fo(,) 423 b(pages) 399
b(50\22654,) 8603 26908 y(Amsterdam,) 303 b(February) g(1991.) p
Black 6584 29317 a([9]) p Black 605 w(M.) 346 b(Held) g(and) g(R.) g
(M.) g(Karp.) 574 b(A) 346 b(dynamic) g(programming) g(approach) g(to) g
(sequencing) 8603 30822 y(problems.) p Fn 436 w(J) -30
b(.) 303 b(SIAM) p Fo(,) f(10\(1\):196\226210,) h(1962.) p
Black 5978 33231 a([10]) p Black 605 w(N.) 346 b(Ishiura,) 355
b(H.) 346 b(Sa) -18 b(w) -12 b(ada,) 356 b(and) 346 b(S.) f(Y) -121
b(ajima.) 573 b(Minimization) 345 b(of) g(binary) h(decision) f(dia-)
8603 34736 y(grams) 352 b(based) g(on) h(e) -18 b(xchanges) 352
b(of) h(v) -30 b(ariables.) 593 b(In) p Fn 352 w(Pr) -55
b(oceedings) 353 b(of) f(the) h(International) 8603 36242
y(Confer) -45 b(ence) 457 b(on) f(Computer) -24 b(-Aided) 456
b(Design) p Fo(,) 494 b(pages) 456 b(472\226475,) 495
b(Santa) 457 b(Clara,) 494 b(CA,) 8603 37747 y(No) -18
b(v) g(ember) 303 b(1991.) p Black 5978 40156 a([11]) p
Black 605 w(S.-W) -112 b(.) 432 b(Jeong,) 464 b(T) -90
b(.-S.) 432 b(Kim,) 464 b(and) 432 b(F) -97 b(.) 432
b(Somenzi.) 850 b(An) 432 b(ef) -30 b(\002cient) 431
b(method) i(for) e(optimal) 8603 41662 y(BDD) 349 b(ordering) f
(computation.) 582 b(In) p Fn 348 w(International) 347
b(Confer) -45 b(ence) 350 b(on) e(VLSI) f(and) i(CAD) 8603
43167 y(\(ICVC'93\)) p Fo(,) 302 b(T) -97 b(aejon,) 303
b(K) -42 b(orea,) 303 b(No) -18 b(v) g(ember) 303 b(1993.) p
Black 5978 45576 a([12]) p Black 605 w(S.-I.) 391 b(Minato.) 718
b(Zero-suppres) n(sed) 392 b(BDDs) f(for) g(set) g(manipulation) h(in) f
(combinatorial) 8603 47081 y(problems.) 440 b(In) p Fn
304 w(Pr) -55 b(oceedings) 304 b(of) g(the) h(Design) f(A) -24
b(utomation) 304 b(Confer) -45 b(ence) p Fo(,) 306 b(pages) e(272\226)
8603 48587 y(277,) f(Dallas,) g(TX,) g(June) g(1993.) p
Black 5978 50995 a([13]) p Black 605 w(S.) 515 b(P) -18
b(anda) 515 b(and) g(F) -97 b(.) 515 b(Somenzi.) 1115
b(Who) 516 b(are) f(the) g(v) -30 b(ariables) 514 b(in) h(your) g
(neighborhood.) 8603 52501 y(In) p Fn 355 w(Pr) -55 b(oceedings) 355
b(of) g(the) g(International) g(Confer) -45 b(ence) 356
b(on) f(Computer) -24 b(-Aided) 355 b(Design) p Fo(,) 8603
54006 y(pages) 303 b(74\22677,) g(San) h(Jose,) e(CA,) i(No) -18
b(v) g(ember) 303 b(1995.) p Black 5978 56415 a([14]) p
Black 605 w(S.) 558 b(P) -18 b(anda,) 623 b(F) -97 b(.) 558
b(Somenzi,) 623 b(and) 559 b(B.) g(F) -97 b(.) 558 b(Plessier) -67
b(.) 1253 b(Symmetry) 559 b(detection) g(and) f(dy-) 8603
57921 y(namic) 398 b(v) -30 b(ariable) 397 b(ordering) f(of) h
(decision) g(diagrams.) 737 b(In) p Fn 397 w(Pr) -55
b(oceedings) 397 b(of) g(the) g(Inter) -24 b(-) 8603
59426 y(national) 385 b(Confer) -45 b(ence) 386 b(on) g(Computer) -24
b(-Aided) 385 b(Design) p Fo(,) 405 b(pages) 385 b(628\226631,) 407
b(San) 385 b(Jose,) 8603 60932 y(CA,) 304 b(No) -18 b(v) g(ember) 303
b(1994.) p Black 5978 63340 a([15]) p Black 605 w(B.) 352
b(F) -97 b(.) 351 b(Plessier) -67 b(.) p Fn 589 w(A) 351
b(Gener) -18 b(al) 351 b(F) -67 b(r) -18 b(ame) g(work) 351
b(for) f(V) -135 b(eri\002cation) 352 b(of) f(Sequential) g(Cir) -45
b(cuits) p Fo(.) 8603 64846 y(PhD) 322 b(thesis,) 327
b(Uni) -30 b(v) -18 b(ersity) 321 b(of) h(Colorado) h(at) f(Boulder) -48
b(,) 328 b(Dept.) 322 b(of) g(Electrical) g(and) h(Com-) 8603
66351 y(puter) 303 b(Engineering,) g(1993.) p Black 25297
69672 a(42) p Black 90 rotate dyy eop
%%Page: 43 43
43 42 bop Black Black Black Fo 5978 7638 a([16]) p Black
605 w(R.) 330 b(Rudell.) 521 b(Dynamic) 330 b(v) -30
b(ariable) 329 b(ordering) g(for) g(ordered) g(binary) g(decision) h
(diagrams.) 8603 9143 y(In) p Fn 355 w(Pr) -55 b(oceedings) 355
b(of) g(the) g(International) g(Confer) -45 b(ence) 356
b(on) f(Computer) -24 b(-Aided) 355 b(Design) p Fo(,) 8603
10649 y(pages) 303 b(42\22647,) g(Santa) h(Clara,) f(CA,) h(No) -18
b(v) g(ember) 303 b(1993.) p Black 5978 13151 a([17]) p
Black 605 w(E.) 576 b(M.) f(Sento) -18 b(vich,) 645 b(K.) 576
b(J.) g(Singh,) 644 b(C.) 577 b(Moon,) 644 b(H.) 576
b(Sa) -24 b(v) g(oj,) 644 b(R.) 577 b(K.) f(Brayton,) 645
b(and) 8603 14656 y(A.) 473 b(Sangio) -18 b(v) -30 b(anni-V) -73
b(incentelli.) 979 b(Sequential) 473 b(circuit) f(design) g(using) h
(synthesis) e(and) 8603 16162 y(optimization.) 687 b(In) p
Fn 380 w(Pr) -55 b(oceedings) 381 b(of) h(the) f(International) f
(Confer) -45 b(ence) 382 b(on) g(Computer) 8603 17667
y(Design) p Fo(,) 303 b(pages) g(328\226333,) g(Cambridge,) h(MA,) f
(October) g(1992.) p Black 25297 69672 a(43) p Black
90 rotate dyy eop
%%Page: 44 44
44 43 bop Black Black Black Fq 5978 9401 a(Index) p Black
Fo 5978 11896 a(ADD,) 303 b(4,) g(7,) g(11,) g(13) 5978
13401 y(aggre) -18 b(g) -6 b(ation,) 303 b(18) 5978 14907
y(Algebraic) 230 b(Decision) h(Diagram,) p Fn 245 w(see) p
Fo 230 w(ADD) 5978 16412 y(arc) 8192 17918 y(complement,) 303
b(11,) g(24,) h(28) 8192 19423 y(re) -18 b(gular) -48
b(,) 302 b(24,) h(28) 5978 22036 y(background) g(v) -30
b(alue,) 303 b(10) 5978 23541 y(BDD,) g(4,) h(7,) f(10,) g(12) 5978
25047 y(Binary) g(Decision) g(Diagram,) p Fn 303 w(see) p
Fo 303 w(BDD) 5978 26552 y(box) 8192 28058 y(black,) g(4) 8192
29563 y(clear) -48 b(,) 302 b(4,) h(25) 5978 32175 y(cache,) g(8,) h
(28) 8192 33681 y(collision,) e(35) 8192 35186 y(collision) g(list,) h
(31) 8192 36692 y(deletion,) g(35) 8192 38197 y(local,) g(29,) g(30)
8192 39703 y(lossl) n(ess,) g(30) 8192 41208 y(re) -30
b(w) -12 b(ard-bas) n(ed) 304 b(resizing,) e(29) 8192
42714 y(sizing,) g(29) 5978 44219 y(cacheSize,) i(8) 5978
45725 y(canonical,) f(7,) h(30) 5978 47230 y(compiling,) f(6,) g(10,) g
(25) 5978 48736 y(con\002guration,) g(5) 5978 50241 y(con) -48
b(v) -18 b(ersion) 8192 51747 y(of) 302 b(ADDs) h(to) g(BDDs,) h(15)
8192 53252 y(of) e(BDDs) i(to) f(ADDs,) g(15) 8192 54757
y(of) f(BDDs) i(to) f(ZDDs,) f(14,) h(15) 8192 56263
y(of) f(ZDDs) h(to) g(BDDs,) g(15) 5978 57768 y(cube) g(sets,) f(4) 5978
59274 y(cudd.h,) h(6,) g(17,) g(28) p Fn 5978 60779 a(Cudd) p
8677 60779 364 45 v 437 w(addApply) p Fo(,) g(13,) g(14) p
Fn 5978 62285 a(Cudd) p 8677 62285 V 437 w(addBddInterval) p
Fo(,) f(15) p Fn 5978 63790 a(Cudd) p 8677 63790 V 437
w(addBddP) -97 b(attern) p Fo(,) 302 b(15) p Fn 5978
65296 a(Cudd) p 8677 65296 V 437 w(addBddThr) -45 b(eshold) p
Fo(,) 302 b(15) p Fn 27840 11896 a(Cudd) p 30539 11896
V 437 w(addConst) p Fo(,) h(11) p Fn 27840 13401 a(Cudd) p
30539 13401 V 437 w(addHarwell) p Fo(,) h(11) p Fn 27840
14907 a(Cudd) p 30539 14907 V 437 w(AddHook) p Fo(,) f(22) p
Fn 27840 16412 a(Cudd) p 30539 16412 V 437 w(addIthBit) p
Fo(,) f(15) p Fn 27840 17918 a(Cudd) p 30539 17918 V
437 w(addIthV) -135 b(ar) p Fo(,) 303 b(11) p Fn 27840
19423 a(Cudd) p 30539 19423 V 437 w(addNe) -18 b(wV) -135
b(ar) p Fo(,) 304 b(11) p Fn 27840 20929 a(Cudd) p 30539
20929 V 437 w(addNe) -18 b(wV) -135 b(arAtLe) -18 b(vel) p
Fo(,) 304 b(11,) f(20) p Fn 27840 22434 a(Cudd) p 30539
22434 V 437 w(addRead) p Fo(,) g(11) p Fn 27840 23940
a(Cudd) p 30539 23940 V 437 w(addT) -67 b(imes) p Fo(,) 303
b(14) p Fn 27840 25445 a(Cudd) p 30539 25445 V 437 w(A) -24
b(utodynDisable) p Fo(,) 303 b(17) p Fn 27840 26951 a(Cudd) p
30539 26951 V 437 w(A) -24 b(utodynDisableZdd) p Fo(,) 303
b(20) p Fn 27840 28456 a(Cudd) p 30539 28456 V 437 w(A) -24
b(utodynEnable) p Fo(,) 303 b(17) p Fn 27840 29962 a(Cudd) p
30539 29962 V 437 w(A) -24 b(utodynEnableZdd) p Fo(,) 303
b(20) p Fn 27840 31467 a(Cudd) p 30539 31467 V 437 w(bddAnd) p
Fo(,) g(12\22614) p Fn 27840 32972 a(Cudd) p 30539 32972
V 437 w(bddConstr) -18 b(ain) p Fo(,) 303 b(7) p Fn 27840
34478 a(Cudd) p 30539 34478 V 437 w(bddIte) p Fo(,) g(12) p
Fn 27840 35983 a(Cudd) p 30539 35983 V 437 w(bddIthV) -135
b(ar) p Fo(,) 303 b(11) p Fn 27840 37489 a(Cudd) p 30539
37489 V 437 w(bddNe) -18 b(wV) -135 b(ar) p Fo(,) 304
b(11) p Fn 27840 38994 a(Cudd) p 30539 38994 V 437 w(bddNe) -18
b(wV) -135 b(arAtLe) -18 b(vel) p Fo(,) 304 b(11,) f(20) p
Fn 27840 40500 a(Cudd) p 30539 40500 V 437 w(BddT) -112
b(oAdd) p Fo(,) 303 b(15) p Fn 27840 42005 a(Cudd) p
30539 42005 V 437 w(bddXor) p Fo(,) f(14) 27840 43511
y(CUDD) p 31346 43511 V 437 w(CA) -48 b(CHE) p 35842
43511 V 437 w(SLO) g(TS,) 302 b(8) p Fn 27840 45016 a(Cudd) p
30539 45016 V 437 w(Chec) -24 b(kK) -42 b(e) -36 b(ys) p
Fo(,) 303 b(33) p Fn 27840 46522 a(Cudd) p 30539 46522
V 437 w(Chec) -24 b(kZer) -55 b(oRef) p Fo(,) 304 b(33) p
Fn 27840 48027 a(Cudd) p 30539 48027 V 437 w(CountMinterm) p
Fo(,) f(11) p Fn 27840 49533 a(Cudd) p 30539 49533 V
437 w(Deb) -24 b(ugChec) g(k) p Fo(,) 304 b(33) p Fn
27840 51038 a(Cudd) p 30539 51038 V 437 w(DelayedDer) -45
b(efBdd) p Fo(,) 304 b(36) p Fn 27840 52544 a(Cudd) p
30539 52544 V 437 w(Der) -45 b(ef) p Fo(,) 303 b(27) p
Fn 27840 54049 a(Cudd) p 30539 54049 V 437 w(DumpBlif) p
Fo(,) g(23) p Fn 27840 55554 a(Cudd) p 30539 55554 V
437 w(DumpDaV) -90 b(inci) p Fo(,) 304 b(23) p Fn 27840
57060 a(Cudd) p 30539 57060 V 437 w(DumpDot) p Fo(,) g(23) p
Fn 27840 58565 a(Cudd) p 30539 58565 V 437 w(F) -127
b(or) -45 b(eac) -18 b(hCube) p Fo(,) 303 b(6,) g(11) p
Fn 27840 60071 a(Cudd) p 30539 60071 V 437 w(F) -127
b(or) -45 b(eac) -18 b(hNode) p Fo(,) 303 b(6) p Fn 27840
61576 a(Cudd) p 30539 61576 V 437 w(HookT) -90 b(ype) p
Fo(,) 304 b(21) p Fn 27840 63082 a(Cudd) p 30539 63082
V 437 w(Init) p Fo(,) f(8,) g(9) p Fn 27840 64587 a(Cudd) p
30539 64587 V 437 w(Mak) -12 b(eT) -67 b(r) -45 b(eeNode) p
Fo(,) 304 b(19,) f(20) p Fn 27840 66093 a(Cudd) p 30539
66093 V 437 w(Mak) -12 b(eZddT) -67 b(r) -45 b(eeNode) p
Fo(,) 304 b(21) p Black 25297 69672 a(44) p Black 90 rotate
dyy eop
%%Page: 45 45
45 44 bop Black Black Fn 5978 7638 a(Cudd) p 8677 7638
364 45 v 437 w(Not) p Fo(,) 303 b(10) p Fn 5978 9143
a(Cudd) p 8677 9143 V 437 w(PrintI) n(nfo) p Fo(,) g(33) p
Fn 5978 10649 a(Cudd) p 8677 10649 V 437 w(PrintM) n(interm) p
Fo(,) g(11) p Fn 5978 12154 a(Cudd) p 8677 12154 V 437
w(Quit) p Fo(,) g(9) p Fn 5978 13660 a(Cudd) p 8677 13660
V 437 w(ReadBac) -24 b(kgr) -55 b(ound) p Fo(,) 303 b(10) p
Fn 5978 15165 a(Cudd) p 8677 15165 V 437 w(ReadEpsilon) p
Fo(,) f(10) p Fn 5978 16671 a(Cudd) p 8677 16671 V 437
w(ReadErr) -57 b(orCode) p Fo(,) 304 b(26) p Fn 5978
18176 a(Cudd) p 8677 18176 V 437 w(ReadIn) -48 b(vP) -99
b(erm) p Fo(,) 303 b(13) p Fn 5978 19682 a(Cudd) p 8677
19682 V 437 w(ReadLo) -12 b(gicZer) -55 b(o) p Fo(,) 303
b(10) p Fn 5978 21187 a(Cudd) p 8677 21187 V 437 w(ReadLooseUpto) p
Fo(,) g(9) p Fn 5978 22693 a(Cudd) p 8677 22693 V 437
w(ReadMaxGr) -55 b(owth) p Fo(,) 303 b(18) p Fn 5978
24198 a(Cudd) p 8677 24198 V 437 w(ReadMinusI) n(n\002nity) p
Fo(,) h(10) p Fn 5978 25704 a(Cudd) p 8677 25704 V 437
w(ReadOne) p Fo(,) f(9) p Fn 5978 27209 a(Cudd) p 8677
27209 V 437 w(ReadPlusI) n(n\002nity) p Fo(,) h(10) p
Fn 5978 28715 a(Cudd) p 8677 28715 V 437 w(ReadReor) -45
b(derings) p Fo -2 w(,) 303 b(32) p Fn 5978 30220 a(Cudd) p
8677 30220 V 437 w(ReadSiftMaxV) -135 b(ar) p Fo(,) 302
b(18) p Fn 5978 31725 a(Cudd) p 8677 31725 V 437 w(ReadT) -67
b(r) -45 b(ee) p Fo(,) 303 b(19) p Fn 5978 33231 a(Cudd) p
8677 33231 V 437 w(ReadZddOne) p Fo(,) g(9,) g(15) p
Fn 5978 34736 a(Cudd) p 8677 34736 V 437 w(ReadZer) -55
b(o) p Fo(,) 303 b(10) p Fn 5978 36242 a(Cudd) p 8677
36242 V 437 w(Recur) -12 b(s) n(iveDer) -45 b(ef) p Fo(,) 462
b(7,) e(25\22627,) i(30,) 10405 37747 y(33) p Fn 5978
39253 a(Cudd) p 8677 39253 V 437 w(Recur) -12 b(s) n(iveDer) -45
b(efZdd) p Fo(,) 304 b(7,) f(26,) g(27) p Fn 5978 40758
a(Cudd) p 8677 40758 V 437 w(ReduceHeap) p Fo(,) g(17) p
Fn 5978 42264 a(Cudd) p 8677 42264 V 437 w(Ref) p Fo(,) f(7,) i(12,) f
(25,) g(27) p Fn 5978 43769 a(Cudd) p 8677 43769 V 437
w(Re) -48 b(gular) p Fo(,) 302 b(28) 5978 45275 y(CUDD) p
9484 45275 V 437 w(REORDER) p 15577 45275 V 437 w(ANNEALING,) 230
b(19) 5978 46780 y(CUDD) p 9484 46780 V 437 w(REORDER) p
15577 46780 V 437 w(EXA) -48 b(CT) -90 b(,) 303 b(19) 5978
48286 y(CUDD) p 9484 48286 V 437 w(REORDER) p 15577 48286
V 437 w(GENETIC,) f(19) 5978 49791 y(CUDD) p 9484 49791
V 437 w(REORDER) p 15577 49791 V 437 w(GR) -48 b(OUP) p
20073 49791 V 437 w(SIFT) -90 b(,) 230 b(18) 5978 51297
y(CUDD) p 9484 51297 V 437 w(REORDER) p 15577 51297 V
437 w(GR) -48 b(OUP) p 20073 51297 V 437 w(SIFT) p 23003
51297 V 435 w(CONV) -156 b(,) 10405 52802 y(18) 5978
54307 y(CUDD) p 9484 54307 V 437 w(REORDER) p 15577 54307
V 437 w(NONE,) 303 b(17,) g(20) 5978 55813 y(CUDD) p
9484 55813 V 437 w(REORDER) p 15577 55813 V 437 w(RANDOM,) 231
b(17,) 245 b(20) 5978 57318 y(CUDD) p 9484 57318 V 437
w(REORDER) p 15577 57318 V 437 w(RANDOM) p 21400 57318
V 437 w(PIV) -48 b(O) g(T) -90 b(,) 10405 58824 y(17,) 304
b(20) 5978 60329 y(CUDD) p 9484 60329 V 437 w(REORDER) p
15577 60329 V 437 w(SAME,) e(17,) i(20) 5978 61835 y(CUDD) p
9484 61835 V 437 w(REORDER) p 15577 61835 V 437 w(SIFT) -90
b(,) 303 b(17,) g(21) 5978 63340 y(CUDD) p 9484 63340
V 437 w(REORDER) p 15577 63340 V 437 w(SIFT) p 18507
63340 V 436 w(CONVERGE,) 10405 64846 y(18,) h(21) 27840
7638 y(CUDD) p 31346 7638 V 437 w(REORDER) p 37439 7638
V 438 w(SYMM) p 41582 7638 V 435 w(SIFT) -90 b(,) 230
b(18,) 32268 9143 y(21) 27840 10649 y(CUDD) p 31346 10649
V 437 w(REORDER) p 37439 10649 V 438 w(SYMM) p 41582
10649 V 435 w(SIFT) p 44510 10649 V 436 w(CONV) -156
b(,) 32268 12154 y(18,) 303 b(21) 27840 13660 y(CUDD) p
31346 13660 V 437 w(REORDER) p 37439 13660 V 438 w(WINDO) -42
b(W2,) 303 b(18) 27840 15165 y(CUDD) p 31346 15165 V
437 w(REORDER) p 37439 15165 V 438 w(WINDO) -42 b(W2) p
43758 15165 V 436 w(CONV) -156 b(,) 32268 16671 y(18) 27840
18176 y(CUDD) p 31346 18176 V 437 w(REORDER) p 37439
18176 V 438 w(WINDO) -42 b(W3,) 303 b(18) 27840 19682
y(CUDD) p 31346 19682 V 437 w(REORDER) p 37439 19682
V 438 w(WINDO) -42 b(W3) p 43758 19682 V 436 w(CONV) -156
b(,) 32268 21187 y(18) 27840 22693 y(CUDD) p 31346 22693
V 437 w(REORDER) p 37439 22693 V 438 w(WINDO) -42 b(W4,) 303
b(18) 27840 24198 y(CUDD) p 31346 24198 V 437 w(REORDER) p
37439 24198 V 438 w(WINDO) -42 b(W4) p 43758 24198 V
436 w(CONV) -156 b(,) 32268 25704 y(19) p Fn 27840 27209
a(Cudd) p 30539 27209 V 437 w(SetEpsilon) p Fo(,) 303
b(10) p Fn 27840 28715 a(Cudd) p 30539 28715 V 437 w(SetLooseUpT) -112
b(o) p Fo(,) 304 b(9) p Fn 27840 30220 a(Cudd) p 30539
30220 V 437 w(SetMaxCac) -18 b(heHar) -45 b(d) p Fo(,) 304
b(37) p Fn 27840 31725 a(Cudd) p 30539 31725 V 437 w(SetMaxGr) -55
b(owth) p Fo(,) 304 b(18) p Fn 27840 33231 a(Cudd) p
30539 33231 V 437 w(SetSiftMaxV) -135 b(ar) p Fo(,) 303
b(18) p Fn 27840 34736 a(Cudd) p 30539 34736 V 437 w(SetT) -67
b(r) -45 b(ee) p Fo(,) 304 b(19) p Fn 27840 36242 a(Cudd) p
30539 36242 V 437 w(Shuf) -22 b(\003eHeap) p Fo(,) 304
b(19) p Fn 27840 37747 a(Cudd) p 30539 37747 V 437 w(StdP) -97
b(ostReor) -45 b(dHook) p Fo(,) 302 b(22) p Fn 27840
39253 a(Cudd) p 30539 39253 V 437 w(StdPr) -45 b(eReor) g(dHook) p
Fo(,) 303 b(22) p Fn 27840 40758 a(Cudd) p 30539 40758
V 437 w(SymmPr) -55 b(o\002le) p Fo(,) 303 b(18) 27840
42264 y(CUDD) p 31346 42264 V 437 w(UNIQ) -12 b(UE) p
36416 42264 V 436 w(SLO) -48 b(TS,) 302 b(8) p Fn 27840
43769 a(Cudd) p 30539 43769 V 437 w(zddDumpDot) p Fo(,) h(23) p
Fn 27840 45275 a(Cudd) p 30539 45275 V 437 w(zddIsop) p
Fo(,) f(15) p Fn 27840 46780 a(Cudd) p 30539 46780 V
437 w(zddIthV) -135 b(ar) p Fo(,) 302 b(12) p Fn 27840
48286 a(Cudd) p 30539 48286 V 437 w(zddP) -97 b(ortF) -69
b(r) -55 b(omBdd) p Fo(,) 304 b(16) p Fn 27840 49791
a(Cudd) p 30539 49791 V 437 w(zddP) -97 b(ortT) -112
b(oBdd) p Fo(,) 302 b(16) p Fn 27840 51297 a(Cudd) p
30539 51297 V 437 w(zddRealignDisable) p Fo(,) g(21) p
Fn 27840 52802 a(Cudd) p 30539 52802 V 437 w(zddRealignEnable) p
Fo(,) h(21) p Fn 27840 54307 a(Cudd) p 30539 54307 V
437 w(zddReduceHeap) p Fo(,) g(20) p Fn 27840 55813 a(Cudd) p
30539 55813 V 437 w(zddShuf) -22 b(\003eHeap) p Fo(,) 304
b(20) p Fn 27840 57318 a(Cudd) p 30539 57318 V 437 w(zddV) -135
b(ar) -12 b(sF) -69 b(r) -55 b(omBddV) -135 b(ar) -12
b(s) p Fo(,) 303 b(16) p Fn 27840 58824 a(Cudd) p 30539
58824 V 437 w(zddW) -112 b(eakDiv) p Fo(,) 304 b(15) p
Fn 27840 60329 a(cuddCac) -18 b(heInsert) p Fo(,) 303
b(29) p Fn 27840 61835 a(cuddCac) -18 b(heInsert1) p
Fo(,) 303 b(29) p Fn 27840 63340 a(cuddCac) -18 b(heInsert2) p
Fo(,) 303 b(29) p Fn 27840 64846 a(cuddCac) -18 b(heLookup) p
Fo 2 w(,) 303 b(29) p Fn 27840 66351 a(cuddCac) -18 b(heLookup) r(1) p
Fo(,) 303 b(29) p Black 25297 69672 a(45) p Black 90 rotate
dyy eop
%%Page: 46 46
46 45 bop Black Black Fn 5978 7638 a(cuddCac) -18 b(heLookup2) p
Fo(,) 304 b(29) 5978 9143 y(CUDDDIR,) g(22) p Fn 5978
10649 a(cuddHeapPr) -55 b(o\002le) p Fo(,) 303 b(33) p
Fn 5978 12154 a(cuddI) p Fo(,) g(30) 5978 13660 y(cuddInt.h,) g(33) p
Fn 5978 15165 a(cuddIZ) p Fo(,) g(30) p Fn 5978 16671
a(cuddSatDec) p Fo(,) h(28) p Fn 5978 18176 a(cuddSatInc) p
Fo(,) f(28) p Fn 5978 19682 a(cuddUniqueConst) p Fo(,) h(25,) f(26) p
Fn 5978 21187 a(cuddUniqueInter) p Fo(,) g(25,) g(26,) g(28,) g(32) p
Fn 5978 22693 a(cuddUniqueInterZdd) p Fo(,) g(25,) g(26,) g(32) 5978
25202 y(DD) p 7801 25202 364 45 v 436 w(CA) -48 b(CHE) p
12296 25202 V 437 w(PR) g(OFILE,) 302 b(39) 5978 26707
y(DD) p 7801 26707 V 436 w(DEB) -12 b(UG,) 304 b(33) 5978
28213 y(DD) p 7801 28213 V 436 w(ST) -113 b(A) -135 b(TS,) 303
b(39) 5978 29718 y(DD) p 7801 29718 V 436 w(UNIQ) -12
b(UE) p 12870 29718 V 436 w(PR) -48 b(OFILE,) 302 b(39) 5978
31224 y(DD) p 7801 31224 V 436 w(VERBOSE,) i(39) 5978
32729 y(DdManager) -48 b(,) 302 b(7,) h(8) 5978 34235
y(DdNode,) g(6,) g(29) 5978 35740 y(deb) -24 b(ugging,) 303
b(33) 5978 37246 y(DEC) g(Alpha,) g(10,) g(23) 5978 38751
y(documentation,) g(39) p Fn 8192 40256 a(Description) p
Fo(,) f(39) 8192 41762 y(HTML) f(\002les,) i(40) p Fn
8192 43267 a(SeeAlso) p Fo(,) f(39) p Fn 8192 44773 a(Synopsis) p
Fo(,) g(39) 5978 46278 y(dot,) p Fn 303 w(see) p Fo 303
w(graph,) h(dra) -18 b(wing) 5978 48787 y(Epsilon,) 302
b(10) 5978 50293 y(e) -18 b(xtdoc,) p Fn 303 w(see) p
Fo 303 w(documentation) 5978 52802 y(\003oating) 303
b(point,) g(10) 8192 54307 y(double) g(\(C) g(type\),) g(7) 8192
55813 y(IEE) n(E) g(Standard) g(754,) g(10) 5978 57318
y(free) f(list,) h(26) 5978 58824 y(FTP) -135 b(,) 303
b(5,) g(23,) g(39) 5978 60329 y(function) 8192 61835
y(characteristic,) f(4,) h(16) 8192 63340 y(co) -18 b(v) g(er) -48
b(,) 302 b(15,) h(16) 9298 64846 y(irredundant,) g(15) 8192
66351 y(minterms,) f(11,) h(32) 30054 7638 y(ON-set,) g(4) 30054
9143 y(sum) g(of) f(products,) h(11) 30054 10649 y(switching,) g(4)
27840 13261 y(g) -6 b(arbage) 452 b(collection,) 490
b(7\2269,) f(25,) g(26,) g(28,) 32268 14767 y(30,) 303
b(31) 30054 16272 y(hooks,) g(21) 27840 17778 y(gcc,) h(10) 27840
19283 y(generator) -48 b(,) 303 b(6) 27840 20789 y(global) g(v) -30
b(ariables,) 303 b(7) 27840 22294 y(graph) 30054 23800
y(arc) g(capacity) -79 b(,) 304 b(10) 30054 25305 y(arc) f(length,) g
(10) 30054 26811 y(dra) -18 b(wing,) 303 b(23) 27840
28316 y(gro) -30 b(wth,) 303 b(9) 27840 29822 y(gzip,) g(5) 27840
32434 y(HA) -164 b(VE) p 31115 32434 V 437 w(IEEE) p
34177 32434 V 435 w(754,) 303 b(10) 27840 33939 y(header) g(\002les,) g
(17,) g(28) 27840 35445 y(hook,) g(21) 27840 38057 y(in\002nities,) g
(10) 27840 39563 y(installation,) g(5) 27840 41068 y(Intel) g
(PentiumPro,) g(5) 27840 42574 y(interf) -12 b(ace) 30054
44079 y(cache,) 304 b(29) 30054 45585 y(SIS,) f(22) 30054
47090 y(VIS,) g(22) 27840 49703 y(libraries,) f(5) 30054
51208 y(cudd,) h(6) 30054 52713 y(dddmp,) g(25) 30054
54219 y(mtr) -48 b(,) 302 b(6,) h(19) 30054 55724 y(obj,) g(40) 30054
57230 y(st,) f(6,) i(29) 30054 58735 y(util,) f(6) 27840
61348 y(Mak) -12 b(e\002le,) 303 b(6,) g(10,) g(40) 27840
62853 y(manager) -48 b(,) 303 b(7,) g(9) 27840 64359
y(matrix) 30054 65864 y(sparse,) f(10) p Black 25297
69672 a(46) p Black 90 rotate dyy eop
%%Page: 47 47
47 46 bop Black Black Fo 5978 7638 a(maxCache,) 304 b(29) 5978
9143 y(maxMemory) -79 b(,) 303 b(8) 5978 10649 y(MinusI) n(n\002nity)
-79 b(,) 304 b(10) 5978 12154 y(MTR) p 8678 12154 364
45 v 436 w(DEF) -90 b(A) -67 b(UL) -112 b(T) -90 b(,) 303
b(20) 5978 13660 y(MTR) p 8678 13660 V 436 w(FIXED,) f(19) 5978
16169 y(nanotra) -24 b(v) -79 b(,) 303 b(5) 5978 17674
y(node,) g(6) 8192 19180 y(constant,) g(6,) g(9\22611,) g(25,) g(27)
9298 20685 y(v) -30 b(alue,) 304 b(7) 8192 22191 y(dead,) f(26,) g(28,)
g(31) 8192 23696 y(dereference,) g(14) 8192 25202 y(reclaimed,) g(31)
8192 26707 y(rec) -18 b(ycling,) 303 b(7) 8192 28213
y(reference,) f(14) 8192 29718 y(reference) 259 b(count,) 269
b(6,) g(7,) g(12,) g(13,) g(25\226) 10405 31224 y(28,) 304
b(30,) f(33) 9298 32729 y(saturated,) g(33) 8192 34235
y(terminal,) p Fn 302 w(see) p Fo 303 w(node,) h(constant) 8192
35740 y(v) -30 b(ariable) 302 b(inde) -18 b(x,) 304 b(6) 5978
37246 y(numSlots,) e(8) 5978 38751 y(numV) -135 b(ars,) 303
b(8) 5978 40256 y(numV) -135 b(arsZ,) 302 b(8) 5978 42766
y(PlusIn\002nity) -79 b(,) 302 b(10) 5978 44271 y(projection) 416
b(functions,) 445 b(11,) h(12,) f(14,) h(15,) 10405 45777
y(33) 5978 48286 y(README) 302 b(\002le,) h(5) 5978 49791
y(reordering,) f(4,) h(6,) g(29) 8192 51297 y(abort) f(and) i(retry) -79
b(,) 302 b(32) 8192 52802 y(asynchronous,) g(17,) h(32) 8192
54307 y(con) -48 b(v) -18 b(er) c(ging,) 302 b(17,) i(18) 8192
55813 y(Cudd) p 10891 55813 V 437 w(ReorderingT) -97
b(ype,) 303 b(17) 8192 57318 y(dynamic,) g(4,) g(16,) g(20) 8192
58824 y(e) -18 b(xact,) 303 b(19) 8192 60329 y(function) f(wrapper) -48
b(,) 303 b(32,) g(33) 8192 61835 y(genetic,) g(19) 8192
63340 y(group,) f(17,) i(18) 8192 64846 y(hooks,) e(21) 8192
66351 y(interruptible) g(procedure,) h(32) 30054 7638
y(of) g(BDDs) g(and) g(ADDs,) g(16) 30054 9143 y(of) g(ZDDs,) f(15,) h
(20) 30054 10649 y(random,) g(17) 30054 12154 y(sifting,) f(17) 30054
13660 y(simulated) h(annealing,) h(19) 30054 15165 y(symmetric,) f(18)
30054 16671 y(threshold,) f(17,) i(32) 30054 18176 y(windo) -30
b(w) -79 b(,) 303 b(18) 27840 20789 y(saturating) 30054
22294 y(decrements,) g(27) 30054 23800 y(increments,) g(27) 27840
25305 y(SISDIR,) g(22) 27840 26811 y(SIZEOF) p 32022
26811 V 435 w(INT) -90 b(,) 303 b(28) 27840 28316 y(SIZEOF) p
32022 28316 V 435 w(V) -48 b(OID) p 35438 28316 V 436
w(P) -135 b(,) 304 b(28) 27840 29822 y(statistical) e(counters,) h(7,) g
(29) 27840 31327 y(statistical) f(counters,) h(26) 27840
32832 y(statistics,) f(33) 27840 34338 y(subtable,) h(8,) g(26) 27840
35843 y(symmetry) -79 b(,) 303 b(18) 27840 38456 y(table) 30054
39961 y(computed,) h(8) 30054 41467 y(gro) -30 b(wth,) 303
b(9) 30054 42972 y(hash,) g(7,) g(30) 30054 44478 y(unique,) g(6\2269,)
h(16,) f(26,) g(29,) g(30) 31161 45983 y(f) -12 b(ast) 302
b(gro) -30 b(wth,) 303 b(31) 31161 47489 y(re) -30 b(w) -12
b(ard-based) 302 b(resizing,) h(31) 31161 48994 y(slo) -30
b(w) 302 b(gro) -30 b(wth,) 303 b(31) 27840 51606 y(v) -30
b(ariable) 30054 53112 y(groups,) 302 b(19) 30054 54617
y(order) -48 b(,) 302 b(6,) h(11) 30054 56123 y(permutation,) g(6,) g
(30) 30054 57628 y(tree,) g(19,) g(20) 27840 60241 y(ZDD,) g(4,) g(7,) g
(12,) g(14,) h(15) 27840 61746 y(zero) 30054 63252 y(arithmetic,) f(9,)
g(11,) g(15) 30054 64757 y(logical,) g(9,) g(15) p Black
25297 69672 a(47) p Black 90 rotate dyy eop
%%Page: 48 48
48 47 bop Black Black Fo 5978 7638 a(Zero-s) n(uppressed) 250
b(Binary) i(Decision) f(Di-) 10405 9143 y(agram,) p Fn
304 w(see) p Fo 302 w(ZDD) p Black 25297 69672 a(48) p
Black 90 rotate dyy eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF