source: vis_dev/glu-2.3/src/cuBdd/doc/cudd.ps @ 23

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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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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
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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
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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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cleartomark

%%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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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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cleartomark

%%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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(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p Black 1669 w(28) p
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(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p
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(.) g(.) h(.) f(.) g(.) p Black 1669 w(30) p Black 7796
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814 b(.) 606 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g
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3 2 bop Black Black Fp 7796 7638 a(Refer) -22 b(ences) 31189
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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
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(functions) 5978 19431 y(of) 395 b(cube) i(sets,) 418
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(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
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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
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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
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y(be) 280 b(written) h(in) f(this) g(w) -12 b(ay) -79
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5 4 bop Black Black Fq 5978 7638 a(2) 1594 b(Ho) -16
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a(The) 474 b(CUDD) h(package) h(is) e(a) -24 b(v) -30
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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
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eop
%%Page: 6 6
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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
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(\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
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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
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(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
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(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
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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
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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
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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
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b(wn,) 279 b(it) 272 b(can) h(be) g(set) g(to) g(0,) 278
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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
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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
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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
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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
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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
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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
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-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
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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
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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
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y(depends) 378 b(on) h(the) g(number) g(of) f(v) -30
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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
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10 9 bop Black Black Fo 7859 7638 a(The) 379 b(constant) f(0) g(is) g
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19262 y(are) 303 b(created) g(at) g(initialization) h(time.) p
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%%Page: 11 11
11 10 bop Black Black Fo 5978 7638 a(that) 427 b(read) h(sparse) f
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dyy eop
%%Page: 12 12
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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
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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
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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
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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
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b(that) 273 b(after) f(v) -30 b(ariable) 273 b(reordering,) 278
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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
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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
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Fn 305 w(Cudd) p 33632 44399 V 437 w(addApply) p Fo(.) 383
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Fo 15987 51926 a(.) p Black Black Fh 11796 54307 a(DdManag) r(er) 727
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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)
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10649 y(tmp) h(=) f(Cudd) r(_addAppl) r(y\(manag) r(er,Cudd) r
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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
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35381 28293 364 45 v 437 w(addApply) p Fo 230 w(with) p
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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
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39928 y(e) g(v) -18 b(er) -48 b(,) 246 b(it) 233 b(is) f(also) h
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(boolean) h(operators) e(to) h(other) g(ZDDs,) 5978 41434
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42939 y(illustrates) 406 b(ho) -30 b(w) 408 b(to) g(b) -24
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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
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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
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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
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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\(manage) r(r,tmp\);)
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14705 13660 y(tmp) g(=) f(f;) 11796 15165 y(}) 11796
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26191 y(the) 303 b(manager) -67 b(.) p Black Fm 7796
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Fo 303 w(does) h(not) g(require) g(referencing.) 5978
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38212 a(U) p Fo 132 w(.) p Fn 594 w(Cudd) p 10534 38212
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44234 y(is) 400 b(safe) h(e) -30 b(v) -18 b(en) 401 b(without) h
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b(\(see) h(Section) g(3.15\)) g(groups) g(will) g(be) g(k) -12
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b(ice) 332 b(V) -133 b(ersa) p Fo 5978 51386 a(Se) -30
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(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)
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(logical) g(0) g(and) g(1) f(on) h(the) g(arithmetic) g(0) g(and) g(1.)
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58913 V 437 w(addIthBit) p Fo(.) p Fi 5978 62236 a(3.11) 1329
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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
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12154 y(v) -30 b(ariables) 302 b(changes) h(while) h(ZDDs) e(are) h
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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
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b(ar) -12 b(s) n(F) -67 b(r) -55 b(omBddV) -135 b(ar) -12
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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
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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
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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
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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
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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
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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
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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
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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
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(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
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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
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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
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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
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b(v) -18 b(e.) 5978 64072 y(Instead,) 418 b(when) 396
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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
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29 28 bop Black Black Fo 7859 7638 a(The) 302 b(cache) g(is) f(also) g
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(tak) -12 b(es) 302 b(place.) 5978 9143 y(In) g(both) h(cases,) g(the) g
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(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
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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
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413 w(and) p Fn 391 w(cuddCac) i(heLookup) p Fo(.) 641
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29800 y(can) 344 b(be) g(lossless) e(\(no) i(results) f(are) h(e) -30
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32811 y(when) 380 b(using) g(a) h(local) f(cache) h(is) f(that) g
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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
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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
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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
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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
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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
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b(is) 9008 25658 y(set.) 355 b(If) 240 b(the) h(datasize) g(limit) g
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b(ault) 240 b(which) i(is) e(rather) h(small.) 9008 27164
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(\(say) f(64MB) g(or) g(more\)) g(you) h(should) f(seriously) f(con-)
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b(set) g(the) h(datasize) g(limit,) 380 b(or) 364 b(o) -18
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Black 606 w(If) 265 b(a) g(process) g(seems) g(to) g(be) h(going) g(no)
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b(for) e(this) h(parameter) h(may) 9008 34182 y(be) 381
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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
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b(\002ciently) 5978 48373 y(f) -12 b(ast.) 365 b(In) 273
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Black Fh 8887 52712 a(Garbage) 729 b(collect) r(ion) f(enabled) r(:) f
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b(good) g(reasons) g(for) f(doing) h(so.) 787 b(It) 440
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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
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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
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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
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(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
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(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
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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
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(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
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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
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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
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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
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b(to) g(use) f(it) h(without) f(reading) h(the) g(code.) 375
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42 41 bop Black Black Black Fo 6584 7638 a([5]) p Black
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43 42 bop Black Black Black Fo 5978 7638 a([16]) p Black
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90 rotate dyy eop
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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