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vis_user.ps @ 54

Last change on this file since 54 was 14, checked in by cecile, 13 years ago
vis2.3
File size: 240.3 KB

Rev	Line
[14]	1	%!PS-Adobe-2.0
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	3	%%Title: vis_user.dvi
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	953	(processed)d(by)j(VIS.)22 2409 y Fg(2)36 2424 y Fe(VL)p
	954	Ff(2)p Fe(MV)e Ff(can)f(also)h(e)o(xtract)h(quantitati)o(v)o(e)f
	955	(timing)h(information)g(from)g(a)g(timed)f(V)l(erilog)h(program,)g
	956	(producing)e(BLIF-MVT)m(,)i(based)e(on)h(timed)-31 2470
	957	y(automata,)i(that)h(is)g(an)f(e)o(xtension)f(of)i(BLIF-MV)g(with)g
	958	(timing)g(constructs)e([3)q(].)15 b(Since)9 b(v)o(eri\256cation)g(with)
	959	h(quantitati)o(v)o(e)g(timing)g(is)f(not)h(handled)-31
	960	2516 y(in)g(the)f(current)g(v)o(ersion)f(of)i(VIS,)g(this)f(feature)g
	961	(is)g(of)h(no)f(further)h(interest)f(here.)918 2835 y
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	966	(er)g(an)o(y)f(input)f(changes,)i(the)e(output)g(is)g(updated)h
	967	(instan-)-31 155 y(taneously)m(.)17 b(Only)11 b Fm(wire)i
	968	Fq(v)o(ariables)e(can)h(be)g(used)g(at)f(the)h(left)f(hand)h(side)f(of)
	969	h(continuous)e(assignments.)16 b(Continuous)-31 212 y(assignments)10
	970	b(describe)h(the)h(combinational)d(beha)o(vior)j(of)f(a)h(circuit.)40
	971	268 y Fi(Pr)n(ocedur)o(al)18 b(assignments)g Fq(\()p
	972	Fm(=)i Fq(within)e(a)i(procedural)g(block\),)h(also)e(referred)i(to)e
	973	(as)h Fi(bloc)o(king)e(assignments)p Fq(,)-31 324 y(e)o(x)o(ecute)12
	974	b(sequentially)d(within)g(a)h(procedural)h(block,)g(changing)e(the)i
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	976	-31 381 y(is)h(blocked)g(by)h(a)g(pause.)17 b Fo(VL)p
	977	Fq(2)p Fo(MV)d Fq(compiles)c(procedural)i(blocks)f(based)h(on)f(the)h
	978	(assumption)e(that)h(each)h(basic)g(block)-31 437 y(will)g(be)i(e)o(x)o
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	980	(the)g(block)g(is)f(satis\256ed.)22 b Fo(VL)p Fq(2)p
	981	Fo(MV)15 b Fq(assumes)d(also)h(that)-31 494 y(e)o(x)o(ecution)i(of)f
	982	(procedural)g(assignments)f(takes)g(zero)i(hardware)g(time.)24
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	985	b(Notice)10 b(that)g(a)g(V)-5 b(erilog)10 b(simulator)f(does)h(not)g
	986	(treat)g(simple)f(blocks)h(as)g(atomic.)-31 607 y(If)16
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	988	(same)g Fm(reg)h Fq(v)o(ariables,)g(caution)f(should)f(be)h(taken)g(to)
	989	-31 663 y(make)c(sure)h(that)e(the)i(desired)f(beha)o(vior)g(does)g
	990	(not)g(depend)g(on)g(a)h(speci\256c)g(interlea)o(ving)f(among)f
	991	(processes.)40 720 y(Procedural)i(assignments)d(update)i(v)o(ariables)g
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	993	(left-hand)g(side)-31 776 y(v)o(ariable)i(so)f(that)g(the)h(statement)f
	994	(follo)o(wing)f(the)i(assignment)e(\(in)h(the)h(same)f(process,)i(or)f
	995	Fm(always)i Fq(statement\))d(can)-31 833 y(observ)o(e)h(the)f(v)o(alue)
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	997	h(instance,)f(other)g Fm(always)j Fq(statements)c(or)-31
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	1000	(race)h(conditions)-31 945 y(might)g(arise)h(among)f(multiple)f
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	1003	-31 1002 y(a)k(mechanism)f(that)g(defers)h(the)f(assignment)f(without)g
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	1015	1284 y(might)e(introduce)h(unwanted)g(nondeterminism.)-31
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	1017	b(assignments)f(also)i(pro)o(vide)g(a)g(way)g(to)f(introduce)h
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	1020	(in)g(the)i(current)f(time)f(slot)h(assigning)e(to)i(the)g(same)g(re)o
	1021	(gister)h(v)o(ariable,)-31 1609 y(then)f(the)g(v)o(alue)g(of)h(that)f
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	1023	(will)f(be)g(nondeterministically)e(chosen)i(from)-31
	1024	1666 y(those)d(assigned)g(v)o(alues.)16 b Fi(Even)c(though)e
	1025	Fo(VL)p Fq(2)p Fo(MV)i Fi(accepts)g(this)e(way)i(of)f(specifying)f
	1026	(nondeterminism,)g(in)h(VIS,)h(unlike)-31 1722 y(in)f(HSIS,)h(multiple)
	1027	e(assignments)g(ar)n(e)h(not)g(consider)n(ed)g(le)n(gal)g
	1028	(nondeterminism)p Fq(.)40 1779 y(Instead,)i(a)h(nondeterministic)d
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	1030	b(erilog)12 b(to)h(specify)g(nondeterminism)d(on)-31
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	1037	b(fragment.)-31 2037 y Fd(assign)20 b(r=$ND{GO,NOGO};)-31
	1038	2077 y(.)-31 2116 y(.)-31 2156 y(always@$posedge)f(clk$)h(begin)-31
	1039	2195 y(.)-31 2234 y(.)-31 2274 y(state)g(=)g(r;)-31 2313
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	1053	Fq(:)-31 148 y Fd(typedef)20 b(enum)f({OPEN,OPENING,CLOSED,CLOSING})f
	1054	(door;)-31 293 y Fl(2.4)58 b(Implicit)15 b(vs.)21 b(Explicit)15
	1055	b(Clocking)-31 397 y Fq(The)9 b(clocking)f(discipline)f(is)h
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	1613	n 4215.00 920.00 m 4335.00 950.00 l 4215.00 980.00 l gs col-1 s gr
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	1619	n 4894 2808 m 5049 3038 l gs col-1 s gr
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	1623	gs 1 -1 sc (Y) col-1 show gr
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	1625	n 4994 3158 m 4669 3158 l gs col-1 s gr
	1626	n 4789.00 3188.00 m 4669.00 3158.00 l 4789.00 3128.00 l gs col-1 s gr
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	1629	n 4639.79 2881.88 m 4739.00 2808.00 l 4686.23 2919.87 l gs col-1 s gr
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	1632	4656.37 2652.35 4623.87 2649.85 4599 2623 curveto
	1633	4577.38 2599.66 4593.38 2558.30 4599 2538 curveto
	1634	4606.71 2510.15 4632.16 2456.28 4659 2438 curveto
	1635	4680.00 2423.70 4726.31 2420.18 4749 2423 curveto
	1636	4770.71 2425.70 4814.19 2433.34 4829 2458 curveto
	1637	4840.06 2476.41 4825.31 2508.20 4824 2523 curveto
	1638	4823.24 2531.55 4821.99 2544.05 4819 2573 curveto
	1639	gs col-1 s gr
	1640
	1641	n 4857.06 2496.51 m 4819.00 2573.00 l 4797.38 2490.34 l gs col-1 s gr
	1642	% Interp Spline
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	1644	5169.65 2985.00 5172.15 2952.00 5199 2928 curveto
	1645	5222.34 2907.00 5263.70 2923.00 5284 2928 curveto
	1646	5311.85 2935.00 5365.72 2961.00 5384 2988 curveto
	1647	5398.30 3009.00 5401.82 3055.00 5399 3078 curveto
	1648	5396.30 3099.00 5388.66 3143.00 5364 3158 curveto
	1649	5345.59 3169.00 5313.80 3154.00 5299 3153 curveto
	1650	5290.45 3152.00 5277.95 3150.00 5249 3148 curveto
	1651	gs col-1 s gr
	1652
	1653	n 5326.74 3183.44 m 5249.00 3148.00 l 5330.88 3123.58 l gs col-1 s gr
	1654	% Interp Spline
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	1656	4488.00 3331.00 4485.00 3364.00 4459 3388 curveto
	1657	4435.00 3409.00 4394.00 3393.00 4374 3388 curveto
	1658	4346.00 3381.00 4293.00 3355.00 4274 3328 curveto
	1659	4260.00 3307.00 4257.00 3261.00 4259 3238 curveto
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	1661	4313.00 3147.00 4344.00 3162.00 4359 3163 curveto
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	1664
	1665	n 4331.25 3132.57 m 4409.00 3168.00 l 4327.13 3192.42 l gs col-1 s gr
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	1668	gs 1 -1 sc (controller) col-1 show gr
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	1676	4510 1110 m
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	1682	4520 1538 m
	1683	gs 1 -1 sc (light) col-1 show gr
	1684	/Times-Roman findfont 180.00 scalefont setfont
	1685	2140 1065 m
	1686	gs 1 -1 sc (sensor) col-1 show gr
	1687	/Times-Roman findfont 180.00 scalefont setfont
	1688	2165 1856 m
	1689	gs 1 -1 sc (timer) col-1 show gr
	1690	/Times-Roman findfont 180.00 scalefont setfont
	1691	3210 1578 m
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	1694	3180 1739 m
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	1696	/Times-Roman findfont 180.00 scalefont setfont
	1697	4779 2758 m
	1698	gs 1 -1 sc (R) col-1 show gr
	1699	/Times-Roman findfont 180.00 scalefont setfont
	1700	5059 3188 m
	1701	gs 1 -1 sc (G) col-1 show gr
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	1893	% Arc
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	1900
	1901	% Arc
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	1904	gs col-1 s gr
	1905
	1906	% Ellipse
	1907	n 2100 7088 302 302 0 360 DrawEllipse gs col-1 s gr
	1908
	1909	% Arc
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	1912	gs col-1 s gr
	1913
	1914	% Polyline
	1915	n 7575 7275 m 7800 7350 l 7575 7425 l gs col-1 s gr
	1916	% Polyline
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	1918	% Polyline
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	1920	% Polyline
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	1924	8812.50 2362.50 9375.00 2250.00 9937.50 2400.00 DrawSplineSection
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	1926
	1927	n 10391.78 2490.09 m 10500.00 2550.00 l 10376.32 2548.07 l gs col-1 s gr
	1928	% Open spline
	1929	n 10650.00 2625.00 m 10012.50 2850.00 l
	1930	10012.50 2850.00 9375.00 3075.00 8737.50 2850.00 DrawSplineSection
	1931	8100.00 2625.00 l gs col-1 s gr
	1932
	1933	n 8203.17 2693.23 m 8100.00 2625.00 l 8223.14 2636.65 l gs col-1 s gr
	1934	% Open spline
	1935	n 2400.00 7125.00 m 3187.50 7012.50 l
	1936	3187.50 7012.50 3975.00 6900.00 4575.00 7087.50 DrawSplineSection
	1937	5175.00 7275.00 l gs col-1 s gr
	1938
	1939	n 5069.41 7210.57 m 5175.00 7275.00 l 5051.51 7267.84 l gs col-1 s gr
	1940	% Open spline
	1941	n 3300.00 8925.00 m 2587.50 8737.50 l
	1942	2587.50 8737.50 1875.00 8550.00 1950.00 7987.50 DrawSplineSection
	1943	2025.00 7425.00 l gs col-1 s gr
	1944
	1945	n 1979.40 7539.98 m 2025.00 7425.00 l 2038.88 7547.91 l gs col-1 s gr
	1946	% Open spline
	1947	n 9150.00 9150.00 m 8475.00 8775.00 l
	1948	8475.00 8775.00 7800.00 8400.00 7875.00 7950.00 DrawSplineSection
	1949	7875.00 7950.00 7950.00 7500.00 7950.00 7462.50 DrawSplineSection
	1950	7950.00 7425.00 l gs col-1 s gr
	1951
	1952	n 7920.00 7545.00 m 7950.00 7425.00 l 7980.00 7545.00 l gs col-1 s gr
	1953	% Open spline
	1954	n 10950.00 7500.00 m 10800.00 8175.00 l
	1955	10800.00 8175.00 10650.00 8850.00 10125.00 8962.50 DrawSplineSection
	1956	9600.00 9075.00 l gs col-1 s gr
	1957
	1958	n 9723.62 9079.19 m 9600.00 9075.00 l 9711.05 9020.52 l gs col-1 s gr
	1959	% Open spline
	1960	n 5400.00 7500.00 m 5025.00 8175.00 l
	1961	5025.00 8175.00 4650.00 8850.00 4200.00 8850.00 DrawSplineSection
	1962	3750.00 8850.00 l gs col-1 s gr
	1963
	1964	n 3870.00 8880.00 m 3750.00 8850.00 l 3870.00 8820.00 l gs col-1 s gr
	1965	% Open spline
	1966	n 5175.00 2700.00 m 4912.50 3637.50 l
	1967	4912.50 3637.50 4650.00 4575.00 4125.00 4650.00 DrawSplineSection
	1968	3600.00 4725.00 l gs col-1 s gr
	1969
	1970	n 3723.04 4737.73 m 3600.00 4725.00 l 3714.55 4678.33 l gs col-1 s gr
	1971	% Open spline
	1972	n 2175.00 2625.00 m 2925.00 2887.50 l
	1973	2925.00 2887.50 3675.00 3150.00 4275.00 2925.00 DrawSplineSection
	1974	4875.00 2700.00 l gs col-1 s gr
	1975
	1976	n 4752.11 2714.04 m 4875.00 2700.00 l 4773.17 2770.22 l gs col-1 s gr
	1977	% Open spline
	1978	n 3150.00 4725.00 m 2475.00 4350.00 l
	1979	2475.00 4350.00 1800.00 3975.00 1875.00 3300.00 DrawSplineSection
	1980	1950.00 2625.00 l gs col-1 s gr
	1981
	1982	n 1906.93 2740.95 m 1950.00 2625.00 l 1966.56 2747.58 l gs col-1 s gr
	1983	% Open spline
	1984	n 4800.00 2550.00 m 4200.00 2437.50 l
	1985	4200.00 2437.50 3600.00 2325.00 3000.00 2400.00 DrawSplineSection
	1986	3000.00 2400.00 2400.00 2475.00 2400.00 2475.00 DrawSplineSection
	1987	2400.00 2475.00 2400.00 2475.00 2362.50 2475.00 DrawSplineSection
	1988	2325.00 2475.00 l gs col-1 s gr
	1989
	1990	n 2445.00 2505.00 m 2325.00 2475.00 l 2445.00 2445.00 l gs col-1 s gr
	1991	/Times-Roman findfont 180.00 scalefont setfont
	1992	3150 4725 m
	1993	gs 1 -1 sc (LONG) col-1 show gr
	1994	/Times-Roman findfont 180.00 scalefont setfont
	1995	4800 2625 m
	1996	gs 1 -1 sc (SHORT) col-1 show gr
	1997	/Times-Roman findfont 180.00 scalefont setfont
	1998	1800 2550 m
	1999	gs 1 -1 sc (START) col-1 show gr
	2000	/Times-Roman findfont 180.00 scalefont setfont
	2001	7725 2475 m
	2002	gs 1 -1 sc (NO) col-1 show gr
	2003	/Times-Roman findfont 180.00 scalefont setfont
	2004	10500 2550 m
	2005	gs 1 -1 sc (YES) col-1 show gr
	2006	/Times-Roman findfont 180.00 scalefont setfont
	2007	1950 7200 m
	2008	gs 1 -1 sc (GREEN) col-1 show gr
	2009	/Times-Roman findfont 180.00 scalefont setfont
	2010	5250 7350 m
	2011	gs 1 -1 sc (YELLOW) col-1 show gr
	2012	/Times-Roman findfont 180.00 scalefont setfont
	2013	3300 8925 m
	2014	gs 1 -1 sc (RED) col-1 show gr
	2015	/Times-Roman findfont 180.00 scalefont setfont
	2016	9225 9075 m
	2017	gs 1 -1 sc (RED) col-1 show gr
	2018	/Times-Roman findfont 180.00 scalefont setfont
	2019	7875 7350 m
	2020	gs 1 -1 sc (GREEN) col-1 show gr
	2021	/Times-Roman findfont 180.00 scalefont setfont
	2022	10800 7350 m
	2023	gs 1 -1 sc (YELLOW) col-1 show gr
	2024	/Times-Roman findfont 180.00 scalefont setfont
	2025	1125 1725 m
	2026	gs 1 -1 sc (start or $!start and !rand_choice$) col-1 show gr
	2027	/Times-Roman findfont 180.00 scalefont setfont
	2028	4425 1800 m
	2029	gs 1 -1 sc (!start and !rand_choice/short) col-1 show gr
	2030	/Times-Roman findfont 180.00 scalefont setfont
	2031	2925 1125 m
	2032	gs 1 -1 sc (T I M E R) col-1 show gr
	2033	/Times-Roman findfont 180.00 scalefont setfont
	2034	8775 1275 m
	2035	gs 1 -1 sc (S E N S O R) col-1 show gr
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	2037	2700 7350 m
	2038	gs 1 -1 sc (car_present and long_timer /) col-1 show gr
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	2636	(future.)906 2835 y Fq(19)p eop
	2637	%%Page: 20 21
	2638	20 20 bop -31 11 a Fq(for)15 b(automatic)f(model)g(checking)h(used)f
	2639	(also)g(in)h(VIS)g(has)g(been)g(described)f(by)h(Clarke)g(et)g(al.)g
	2640	([7].)27 b(The)15 b(follo)o(wing)-31 68 y(table)c(sho)o(ws)g(e)o
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	2642	(computation)f(tree)i(of)f(Fig.)h(3.1:)677 203 y(formula)p
	2643	1070 220 2 57 v 274 w(T/F)p 652 221 555 2 v 677 261 a(EG)f($RED$)p
	2644	1070 278 2 57 v 226 w(true)677 317 y(E)g($RED)h(U)f(GREEN$)p
	2645	1070 334 V 51 w(true)677 374 y(AF)h($GREEN$)p 1070
	2646	391 V 167 w(false)-31 495 y Fk(3.1.2)51 b(Speci\256cation)10
	2647	b(of)i(Pr)o(operties)h(in)f(CTL)-31 582 y Fq(T)m(emporal)c(logic)f
	2648	(formulas)g(can)i(be)f(dif)o(\256cult)g(to)f(interpret,)i(so)f(that)f
	2649	(a)i(designer)e(may)h(fail)g(to)f(understand)h(what)f(property)-31
	2650	639 y(has)14 b(been)g(actually)g(v)o(eri\256ed.)25 b(Therefore)15
	2651	b(it)e(is)h(important)e(to)i(be)g(familiar)f(with)g(the)h(most)e
	2652	(common)h(constructs)g(of)-31 695 y(CTL)f(used)f(in)g(hardware)h(v)o
	2653	(eri\256cation.)26 786 y(1.)23 b Fp(AG)p Fb(\()p Fp(r)q(eq)14
	2654	b Fj(!)f Fp(AF)18 b(ack)q Fb(\))83 843 y Fq(F)o(or)c(all)f(reachable)i
	2655	(states)e($)p Fp(AG)p Fq($,)h(if)g Fp(r)q(eq)h Fq(is)e(asserted)h(in)
	2656	f(the)g(state,)h(then)f(always)g(at)g(some)g(later)h(point)e(\()p
	2657	Fp(AF)6 b Fq(\))83 899 y(we)14 b(must)f(reach)i(a)g(state)f(where)g
	2658	Fp(ack)h Fq(is)f(asserted.)25 b Fp(AG)14 b Fq(is)g(interpreted)g
	2659	(relati)o(v)o(e)g(to)g(the)g(initial)f(states)g(of)h(the)83
	2660	956 y(system.)h Fp(AF)j Fq(is)10 b(interpreted)g(relati)o(v)o(e)h(to)f
	2661	(the)g(state)h(where)g Fp(r)q(eq)h Fq(is)f(asserted.)16
	2662	b(In)11 b(other)f(words,)h(it)f(is)g(always)f(the)83
	2663	1012 y(case)j(that)f(if)h(the)f(signal)g Fp(r)q(eq)i
	2664	Fq(is)e(high,)g(then)h(e)o(v)o(entually)f Fp(ack)h Fq(will)f(also)g(be)
	2665	h(high.)k(A)c(common)e(mistake)g(would)83 1068 y(be)j(to)f(write)g
	2666	Fp(r)q(eq)k Fj(!)f Fp(AF)20 b(ack)q Fq(,)13 b(instead)f(of)g
	2667	Fp(AG)p Fb($)p Fp(r)q(eq)k Fj(!)f Fp(AF)k(ack)q Fb($)p
	2668	Fq(.)h(The)13 b(meaning)f(of)h(the)f(former)h(is)f(that)g(if)83
	2669	1125 y Fp(r)q(eq)j Fq(is)e(asserted)g(in)g(the)g(initial)e(state,)j
	2670	(then)f(it)g(is)f(always)g(the)h(case)h(that)f(e)o(v)o(entually)g(we)g
	2671	(reach)h(a)g(state)f(where)83 1181 y Fp(ack)f Fq(is)f(asserted,)i
	2672	(while)e(the)g(latter)h(requires)g(that)f(the)g(condition)f(is)i(true)f
	2673	(for)h(an)o(y)g(reachable)h(state)e(where)h Fp(r)q(eq)83
	2674	1238 y Fq(holds.)k(If)11 b Fp(r)q(eq)j Fq(is)d(identically)f(true,)i
	2675	Fp(AG)p Fb($)p Fp(r)q(eq)i Fj(!)f Fp(AF)18 b(ack)q Fb($)11
	2676	b Fq(reduces)h(to)e Fp(AG)i(AF)18 b(ack)q Fq(.)26 1331
	2677	y(2.)23 b Fp(AG)11 b(AF)18 b(enabl)q(ed)83 1387 y Fq(From)d(e)o(v)o
	2678	(ery)h(reachable)g(state,)h(for)f(all)f(paths)f(starting)h(at)g(that)g
	2679	(state)g(we)h(must)e(reach)i(another)g(state)f(where)83
	2680	1444 y Fp(enabl)q(ed)10 b Fq(is)h(asserted.)17 b(In)12
	2681	b(other)f(words,)g Fp(enabl)q(ed)g Fq(must)f(be)h(asserted)h
	2682	(in\256nitely)e(often.)26 1536 y(3.)23 b Fp(AG)11 b(E)s(F)17
	2683	b(r)q(estar)q(t)83 1593 y Fq(From)e(an)o(y)h(reachable)g(state,)h
	2684	(there)f(must)e(e)o(xist)h(a)h(path)f(starting)g(at)g(that)g(state)g
	2685	(that)g(reaches)i(a)e(state)h(where)83 1649 y Fp(r)q(estar)q(t)c
	2686	Fq(is)f(asserted.)17 b(In)11 b(other)h(words,)f(it)f(must)h(always)f
	2687	(be)h(possible)g(to)f(reach)j(the)e(restart)h(state.)26
	2688	1742 y(4.)23 b Fp(E)s(F)6 b Fb(\()p Fp(star)q(ted)k Fj(^)22
	2689	b(:)p Fp(r)q(eady)r Fb(\))83 1798 y Fq(It)11 b(is)g(possible)f(to)h
	2690	(get)g(to)g(a)h(state)f(where)h Fp(star)q(ted)g Fq(holds,)f(b)o(ut)g
	2691	Fp(r)q(eady)i Fq(does)e(not)g(hold.)26 1891 y(5.)23 b
	2692	Fp(AG)p Fb(\()p Fp(send)12 b Fj(!)h Fp(A)p Fb(\()p Fp(send)f(U)k(r)q
	2693	(eceiv)r(e)p Fb(\)\))83 1948 y Fq(It)d(is)g(always)f(the)h(case)g(that)
	2694	g(if)g Fp(send)h Fq(occurs,)g(then)f(e)o(v)o(entually)g
	2695	Fp(r)q(eceiv)r(e)f Fq(is)h(true,)h(and)f(until)f(that)g(time,)i
	2696	Fp(send)83 2004 y Fq(must)c(continue)h(to)g(be)g(true.)26
	2697	2097 y(6.)23 b Fp(AG)p Fb(\()p Fp(inp)12 b Fj(!)h Fp(AX)i(AX)f(out)p
	2698	Fb(\))83 2153 y Fq(Whene)o(v)o(er)e Fp(inp)f Fq(goes)g(high,)g
	2699	Fp(out)h Fq(will)f(go)g(high)f(within)h(two)f(clock)h(c)o(ycles.)26
	2700	2246 y(7.)23 b Fp(E)s(F)6 b Fb(\()p Fp(a)j Fj(^)i Fp(E)s(X)t
	2701	Fb($)p Fp(a)d Fj(^)i Fp(E)s(X)k(a)p Fb($\))e Fj(!)h
	2702	Fp(E)s(F)6 b Fb(\()p Fp(b)j Fj(^)i Fp(E)s(X)i(E)s(X)h(c)p
	2703	Fb(\))83 2302 y Fq(If)d(it)e(is)h(possible)f(for)i Fp(a)f
	2704	Fq(to)g(be)h(asserted)f(in)g(three)h(consecuti)o(v)o(e)f(states,)g
	2705	(then)g(it)g(is)g(also)g(possible)f(to)h(reach)h(a)f(state)83
	2706	2359 y(where)i Fp(b)f Fq(is)g(asserted)g(and)g(from)h(there)f(to)g
	2707	(reach)h(in)f(two)g(more)g(steps)g(a)h(state)f(where)h
	2708	Fp(c)f Fq(is)g(asserted.)40 2450 y(W)l(e)h(summarize)f(the)g(most)f
	2709	(common)g(CTL)i(templates)e(with)h(the)g(corresponding)g(English)f
	2710	(language)h(meaning:)26 2541 y(1.)23 b Fp(AGp)16 b Fq(is)g(\252nothing)
	2711	g(bad)g(e)o(v)o(er)i(happens\272)e(\()p Fj(:)p Fp(p)h
	2712	Fq(is)f(bad\).)33 b(Used)16 b(to)h(specify)f(an)h(in)n(v)o(ariant,)h
	2713	(i.e.,)h(a)e(condition)83 2598 y(that)e(must)g(be)g(true)h(in)f(all)h
	2714	(states.)29 b(Helpful)15 b(for)h(partial)f(correctness)h(\(no)g(wrong)f
	2715	(answers)h(are)h(produced\),)83 2654 y(mutual)9 b(e)o(xclusion)h(\(no)g
	2716	(two)f(processors)h(are)i(in)d(a)i(critical)f(section)g
	2717	(simultaneously\),)f(deadlock)h(freedom)g(\(no)83 2711
	2718	y(deadlock)h(state)g(is)g(reached\).)906 2835 y(20)p
	2719	eop
	2720	%%Page: 21 22
	2721	21 21 bop 26 11 a Fq(2.)23 b Fp(AF)16 b(AG)10 b(p)f Fq(is)g(\252e)o(v)o
	2722	(entually)g(the)h(system)e(is)i(con\256ned)f(to)h(states)f(where)h
	2723	Fp(p)f Fq(is)g(always)g(true\272)h(or)g(\252the)f(system)g(stays)83
	2724	68 y(out)h(of)h(states)f(where)i Fp(p)f Fq(is)f(true)h(only)f(a)h
	2725	(\256nite)g(number)g(of)g(times\272.)16 b(It)10 b(can)i(be)f(used)f(to)
	2726	h(specify)g(the)f(property)h(of)83 124 y(\256nite)g(number)g(of)g
	2727	(failures)g(in)g(the)h(system.)26 218 y(3.)23 b Fp(AG)p
	2728	Fb($)p Fp(p)e Fj(!)40 b Fp(AF)25 b(q)r Fb($)17 b Fq(is)h(\252from)g
	2729	(all)f(reachable)i(states)e(where)i Fp(p)f Fq(is)f(true,)j(something)c
	2730	(good,)k Fp(q)r Fq(,)g(e)o(v)o(entually)83 275 y(happens\272.)c
	2731	(Helpful)9 b(to)g(e)o(xpress)h(total)f(correctness)h(\(termination)e(e)
	2732	o(v)o(entually)h(occurs)h(with)f(correct)h(answers\),)83
	2733	331 y(accessibility)17 b(\(e)o(v)o(entually)i(a)g(requesting)f(process)
	2734	h(will)f(enter)h(its)g(critical)f(section\),)j(starv)o(ation)d(freedom)
	2735	83 387 y(\(e)o(v)o(entually)h(service)h(will)e(be)i(granted)g(to)f(a)g
	2736	(waiting)f(processor\).)42 b(If)20 b Fp(p)f Fq(is)g(always)g(true,)j
	2737	(it)d(reduces)h(to)83 444 y Fp(AG)11 b(AF)18 b(q)r Fq(.)26
	2738	538 y(4.)23 b Fp(AG)14 b(AF)22 b(q)16 b Fq(is)e(\252in\256nitely)g
	2739	(often)h Fp(q)r Fq(\272,)h(i.e.,)h(from)d(an)o(y)h(reachable)h(state)e
	2740	(one)h(must)e(reach)j(a)e(state)h(where)g Fp(q)i Fq(is)83
	2741	594 y(asserted.)g(It)11 b(can)h(be)f(used,)h(for)g(instance,)f(to)g
	2742	(enforce)h(a)g(reset)g(condition)e(from)h(an)o(y)g(state.)26
	2743	688 y(5.)23 b Fp(AF)18 b(q)13 b Fq(is)e(\252something)f(good,)h
	2744	Fp(q)r Fq(,)h(e)o(v)o(entually)f($or)g(\256nally$)h(happens\272)f
	2745	(\(less)g(restricti)o(v)o(e)g(than)g Fp(AG)h(AF)18 b(q)r
	2746	Fq(\).)26 782 y(6.)23 b Fp(AG)10 b(E)s(F)17 b(p)11 b
	2747	Fq(is)f(\252always)g Fp(p)h Fq(possible\272.)k(It)c(can)g(detect,)h
	2748	(for)f(instance,)g(the)f(absence)h(of)g(deadlocks,)g(by)g(requiring)83
	2749	838 y(that)h(is)h(it)g(always)f(possible)f(to)i(reach)h(deadlock-free)g
	2750	(states.)22 b(This)12 b(is)h(an)g(e)o(xample)g(of)g(a)g(CTL)h(property)
	2751	f(that)83 895 y(cannot)e(be)g(represented)h(by)f(an)h
	2752	Fp(!)r Fq(-automaton)853 878 y Ft(3)872 895 y Fq(.)26
	2753	989 y(7.)23 b Fp(AG)11 b(tr)q(ue)h Fq(forces)g(a)f(complete)g(tra)o(v)o
	2754	(ersal)h(of)g(the)f(states)g(of)g(the)h(system.)26 1082
	2755	y(8.)23 b Fp(E)s(F)18 b(p)13 b Fq(is)f(\252)p Fp(p)h
	2756	Fq(is)f(possible\272.)19 b(This)12 b(is)g(another)h(e)o(xample)f(of)h
	2757	(a)g(CTL)g(property)f(that)g(cannot)h(be)f(represented)h(by)83
	2758	1139 y(an)e Fp(!)r Fq(-automaton.)40 1233 y Fr(Ca)o(veats)26
	2759	1326 y Fq(1.)23 b(The)14 b(v)o(ariables)g(appearing)h(in)f(a)g(CTL)h
	2760	(formula)f(must)f(be)h(a)h(function)f(of)g(re)o(gister)h(v)o(ariables)f
	2761	($e.g.,)i(states)e(or)83 1383 y(outputs)c(attached)i(to)f(states$.)18
	2762	b(V)-5 b(ariables)12 b(that)f(depend)h(on)f(inputs)g(or)h
	2763	(pseudo-inputs)e(are)i(not)g(allo)o(wed,)f(since)83 1439
	2764	y(this)f(could)h(lead)h(to)e(a)i(state)f(where)h(both)f
	2765	Fp(p)g Fq(and)h Fj(:)p Fp(p)f Fq(are)h(true,)g(depending)f(on)g(the)g
	2766	(input.)26 1533 y(2.)23 b(The)11 b(propositional)f(logic)g(operator)i
	2767	Fj(!)p Fq(,)g(as)f(in)g Fp(a)i Fj(!)g Fp(b)e Fq(is)g(equi)o(v)o(alent)f
	2768	(to)h Fj(:)p Fp(a)f Fb(+)h Fp(b)p Fq(,)g(and)g(is)g(satis\256ed)g(by)g
	2769	Fj(:)p Fp(a)p Fq(.)17 b(Do)83 1590 y(not)11 b(use)g(it)g(in)g(place)g
	2770	(of)h Fp(a)e(?)g(b)p Fq(,)h(which)g(is)g(true)g(if)h(and)f(only)g(if)g
	2771	Fp(a)g Fq(and)h Fp(b)f Fq(are)h(both)e(true.)26 1683
	2772	y(3.)23 b(The)11 b(syntax)g(of)g(CTL)h(and)f(of)h(V)-5
	2773	b(erilog)11 b(are)h(dif)o(ferent.)17 b(F)o(or)12 b(instance,)f(we)h(ha)
	2774	o(v)o(e:)242 1791 y Fd(Verilog)20 b(CTL)119 b(meaning)242
	2775	1870 y(&&)h(*)159 b(AND)242 1910 y(\|\|)120 b(+)159 b(OR)242
	2776	1949 y(==)120 b(=)159 b(equal)242 1989 y(a!=NO)60 b(!$a=NO$)39
	2777	b(not)20 b(equal)402 2028 y(->)139 b(implies)402 2067
	2778	y(\303)159 b(xor)-31 2194 y Fk(3.1.3)51 b(F)o(air)o(ness)13
	2779	b(Constraints)-31 2281 y Fq(It)h(is)f(often)g(necessary)h(to)f
	2780	(introduce)g(some)g(notion)f(of)i(fairness.)23 b(F)o(or)14
	2781	b(e)o(xample,)h(if)e(the)g(system)g(allocates)g(a)h(shared)-31
	2782	2338 y(resource)f(among)e(se)o(v)o(eral)h(users,)h(only)e(those)g
	2783	(paths)g(along)h(which)f(no)h(user)g(keeps)f(the)h(resource)g(fore)o(v)
	2784	o(er)h(should)e(be)-31 2394 y(considered.)17 b(CTL)12
	2785	b(by)f(itself)f(cannot)i(e)o(xpress)f(assertions)g(about)g(correctness)
	2786	g(along)g(fair)h(paths.)40 2451 y(F)o(air)f(CTL)f(is)g(a)g
	2787	(modi\256cation)f(of)h(CTL)h(to)e(handle)h(fairness.)16
	2788	b(F)o(air)11 b(CTL)g(is)e(characterized)j(by)e(the)g(introduction)e(of)
	2789	-31 2507 y Fi(fairness)i(constr)o(aints)p Fq(,)h(which)g(are)h(sets)f
	2790	(of)h(states)f(e)o(xpressed)h(by)f(means)g(of)h(CTL)g(formulas,)f(each)
	2791	i(gi)o(ving)d(a)i(fairness)-31 2564 y(condition;)d(a)h
	2792	Fi(fair)e(path)h Fq(is)g(a)h(path)g(along)f(which)g(each)h(fairness)g
	2793	(condition)e(is)h(satis\256ed)g(in\256nitely)g(often.)16
	2794	b(These)10 b(types)p -31 2604 768 2 v 22 2632 a Fg(3)36
	2795	2648 y Ff(It)j(is)f(possible)e(to)i(sho)o(w)f(two)g(transition)i
	2796	(systems)d(that)i(recognize)e(the)h(same)g(language,)g(of)h(which)f
	2797	(one)g(satis\256es)f Fc(AG)h(E)r(F)18 b(p)p Ff(,)13 b(and)e(the)-31
	2798	2693 y(other)e(does)f(not.)906 2835 y Fq(21)p eop
	2799	%%Page: 22 23
	2800	22 22 bop -31 11 a Fq(of)14 b(fairness)g(constraints)e(are)j(called)f
	2801	(B)t(\310)-19 b(uchi)14 b(type.)24 b(More)14 b(general)g(fairness)g
	2802	(constraints,)g(such)f(as)h(Street)h(type,)f(are)-31
	2803	68 y(not)c(allo)o(wed)f(currently)m(.)17 b(F)o(air)11
	2804	b(CTL)g(has)f(the)g(same)g(syntax)f(as)i(CTL,)g(b)o(ut)e(the)h
	2805	(semantics)g(is)f(modi\256ed)h(so)g(that)g(all)g(path)-31
	2806	124 y(quanti\256ers)j(only)f(range)i(o)o(v)o(er)g(fair)e(paths.)22
	2807	b(VIS)13 b(supports)f(F)o(air)i(CTL;)f(in)g(the)f(documentation)g(we)h
	2808	(may)g(sometimes)-31 181 y(refer)g(to)e(CTL,)h(where)g(we)f(really)h
	2809	(mean)f(F)o(air)h(CTL.)40 237 y(An)d(e)o(xample)h(of)g(a)g(fairness)f
	2810	(condition)f(is)i Fp(p)p Fq(,)g(that)f(restricts)g(the)h(system)f(to)g
	2811	(only)g(those)g(paths)g(where)h Fp(p)g Fq(is)f(asserted)-31
	2812	294 y(in\256nitely)i(often.)-31 440 y Fl(3.2)58 b(Pr)o(operties)14
	2813	b(and)h(F)o(air)o(ness)e(Conditions)j(of)f(T)l(raf\256c)f(Light)h
	2814	(Contr)o(oller)g(in)g(CTL)-31 544 y Fq(Not)e(all)h(beha)o(vior)f(e)o
	2815	(xhibited)g(by)h(the)f(description)g(of)g(the)h(T)n(raf)o(\256c)h
	2816	(Light)e(Controller)g(is)g(v)o(alid.)23 b(In)14 b(order)g(to)f
	2817	(restrict)-31 600 y(the)e(beha)o(vior)h(we)f(impose)g(the)g(follo)o
	2818	(wing)f(two)g(fairness)h(constraints.)16 b(The)11 b(\256rst)h(is:)-31
	2819	692 y Fm(!$timer.s)q(ta)q(te=)q(ST)q(ART)q($;)-31 784
	2820	y Fq(The)k(timer)g(must)f(e)o(v)o(entually)h(lea)o(v)o(e)h(the)f(ST)l
	2821	(AR)m(T)h(state.)31 b(This)15 b(constraint)h(pre)o(v)o(ents)g(it)g
	2822	(from)g(staying)f(in)h(ST)l(AR)m(T)-31 841 y(fore)o(v)o(er)m(.)j(The)11
	2823	b(second)g(fairness)g(constraint:)-31 933 y Fm(!\(timer.s)q(ta)q(te=)q
	2824	(SH)q(ORT)q(\);)-31 1025 y Fq(ensures)g(that)g(the)g(timer)f(must)g(e)o
	2825	(v)o(entually)g(lea)o(v)o(e)i(the)f(SHOR)m(T)h(state.)k(Li)o(v)o(eness)
	2826	11 b(properties)g(\(e.g,)h(cars)f(on)g(farm)g(road)-31
	2827	1082 y(and)f(highway)g(will)f(e)o(v)o(entually)h(cross\))g(would)g(not)
	2828	f(pass)h(if)h(these)f(fairness)g(constraints)f(are)i(not)f(placed)h(on)
	2829	f(the)g(timer)m(.)40 1138 y(One)f(ob)o(vious)f(property)h(to)g(check)g
	2830	(is)g(that)g(the)g(light)e(is)i(not)g(green)g(in)g(both)f(directions)h
	2831	(at)g(the)g(same)g(time,)g(ensuring)-31 1195 y(that)j(collisions)e(do)h
	2832	(not)h(occur)g(between)g(traf)o(\256c)h(on)f(the)f(farm)h(road)g(and)g
	2833	(highway)m(.)18 b(This)11 b(property)h(is)f(written)g(as)h(the)-31
	2834	1251 y(CTL)g(formula:)-31 1343 y Fm(AG)28 b(\()g(!\(\(farm_l)q(ig)q(ht)
	2835	j(=)c(GREEN\))j(*)e($hwy_ligh)q(t)i(=)e(GREEN$\))i(\);)40
	2836	1435 y Fq(T)l(o)15 b(ensure)g(that)f(a)h(car)h(on)f(the)f(farm)h(road)g
	2837	(e)o(v)o(entually)f(crosses)h(the)g(intersection,)g(we)g(require)h
	2838	(that)e(if)h(a)g(car)h(is)-31 1492 y(present)11 b(on)g(the)g(farm)g
	2839	(road,)g(and)g(the)g(timer)g(is)f(long,)h(then)g(e)o(v)o(entually)f
	2840	(the)h(farm)g(light)f(will)g(turn)h(green.)17 b(In)11
	2841	b(CTL)g(this)-31 1548 y(is)g(written)g(as:)-31 1640 y
	2842	Fm(AG$\(\(car_)q(pr)q(ese)q(nt)31 b(=)d(YES$)h(*)e(\(timer.s)q(tat)q
	2843	(e)k(=)c(LONG\)\))j(->)e(AF$farm_)q(lig)q(ht)j(=)d(GREEN$\);)40
	2844	1733 y Fq(In)12 b(addition,)g(re)o(gardless)h(of)g(what)f(happens)g(on)
	2845	g(the)h(farm)f(road,)h(the)g(highway)e(should)g(always)h(be)g(green)h
	2846	(in)f(the)-31 1789 y(future:)-31 1881 y Fm(AG\(AF\(hwy)q(_l)q(igh)q(t)
	2847	31 b(=)c(GREEN\)\);)40 1973 y Fq(The)9 b(presence)h(of)f(a)h(car)g(on)f
	2848	(the)g(farm)g(road)h(does)f(not)f(guarantee)i(that)f(e)o(v)o(entually)g
	2849	(the)g(farm)g(light)f(will)g(turn)h(green.)-31 2030 y(A)k(car)h(may)f
	2850	(approach,)h(and)f(then)g(back)h(a)o(way)m(,)g(all)f(before)h(the)f
	2851	(timer)f(goes)h(long.)21 b(This)13 b(property)g(is)f(not)h(necessary)
	2852	-31 2086 y(for)g(safety)m(,)g(it)e(just)h(maximizes)f(the)h(time)f
	2853	(that)h(the)g(highway)f(light)g(is)h(green.)20 b(Thus,)12
	2854	b(it)g(is)f(desirable)h(that)g(the)g(system)-31 2143
	2855	y(satis\256es)f(the)g(follo)o(wing)f(property:)-31 2235
	2856	y Fm(!$AG\(\(car)q(_p)q(res)q(en)q(t)30 b(=)e(YES$)h(->)f(AF\(farm_l)
	2857	q(ig)q(ht)j(=)d(GREEN\)\)\);)-31 2381 y Fl(3.3)58 b(Language)15
	2858	b(Containment)-31 2485 y Fq(There)i(are)h(properties)e(of)g(practical)h
	2859	(interest)f(that)g(cannot)h(be)g(described)f(in)g(CTL.)i(An)e(e)o
	2860	(xample)h(is)f(the)g(\252almost)-31 2541 y(always\272)f(property:)26
	2861	b(a)16 b(condition,)g Fp(q)r Fq(,)i(always)d(holds)g(after)i(a)f
	2862	(\256nite)g(number)g(of)g(transitions)e(\(note)i(that)g(formulas)-31
	2863	2598 y Fp(F)6 b(G)14 b(q)h Fq(and)e Fp(AF)20 b(G)13 b(q)i
	2864	Fq(would)d(e)o(xpress)i(this,)f(b)o(ut)f(these)i(are)g(not)e(le)o(gal)h
	2865	(CTL)h(formulas\).)22 b(This)12 b(property)h(looks)f(a)i(lot)-31
	2866	2654 y(like)f Fp(AF)20 b(AG)13 b(q)r Fq(,)i(b)o(ut)e(it)g(is)g(not)f
	2867	(the)i(same.)23 b(One)13 b(can)h(e)o(xhibit)f(a)h(transition)e(system)g
	2868	(where)i Fp(AF)21 b(G)13 b(q)i Fq(is)e(true,)i(while)-31
	2869	2711 y Fp(AF)j(AG)11 b(q)j Fq(is)d(false.)906 2835 y(22)p
	2870	eop
	2871	%%Page: 23 24
	2872	23 23 bop 40 11 a Fq(A)8 b(solution)f(would)g(be)i(to)f(use)g(a)h(more)
	2873	f(e)o(xpressi)o(v)o(e)h(type)f(of)h(temporal)f(logic)f(\(for)i
	2874	(instance,)h(the)e(pre)o(vious)f(property)-31 68 y(could)12
	2875	b(be)h(e)o(xpressed)g(in)g(PL)l(TL)f(or)h(CTL*\).)21
	2876	b(But)13 b(there)g(would)e(be)i(dra)o(wbacks,)h(such)f(as)g(the)f
	2877	(higher)h(comple)o(xity)e(of)-31 124 y(algorithms)i(for)i(model)f
	2878	(checking.)27 b(An)15 b(alternati)o(v)o(e)g(is)f(to)g(use)h(another)g
	2879	(v)o(eri\256cation)g(paradigm,)g(called)g(language)-31
	2880	181 y(containment,)d(based)h(on)f(the)g(theory)g(of)h
	2881	Fp(!)r Fq(-automata.)19 b(F)o(or)14 b(e)o(xample,)f(it)f(is)g(easy)g
	2882	(to)g(e)o(xpress)h(the)f(pre)o(vious)g(\252almost)-31
	2883	237 y(always\272)f(property)g(using)f(an)i(automaton.)40
	2884	294 y(Currently)17 b(VIS)h(supports)d(a)j(restricted)f(form)g(of)g
	2885	(language)g(containment.)33 b(W)l(e)18 b(re)o(vie)o(w)f(brie\257y)g
	2886	(the)g(idea)g(of)-31 350 y(language)e(containment:)22
	2887	b(for)16 b(a)f(system)f(to)h(satisfy)f(a)i(property)f(it)f(must)g(be)h
	2888	(that)g Fp(L)p Fb($)p Fp(S)s Fb($)h Fj(\022)j Fp(L)p
	2889	Fb($)p Fp(T)6 b Fb($)p Fq(,)15 b(where)h Fp(S)h Fq(is)e(an)-31
	2890	407 y Fp(!)r Fq(-automaton)8 b(representing)h(the)f(system,)h
	2891	Fp(T)15 b Fq(is)8 b(an)h Fp(!)r Fq(-automaton)f(representing)g(the)h
	2892	(property)g(and)f Fp(L)h Fq(is)g(the)f(language)-31 463
	2893	y(accepted)k(by)f(the)h(automaton.)j(It)d(is)e(a)i(fact)g(that)e
	2894	Fp(L)p Fb($)p Fp(S)s Fb($)i Fj(\022)h Fp(L)p Fb(\()p
	2895	Fp(T)6 b Fb(\))k Fq(is)h(equi)o(v)o(alent)g(to)g Fp(L)p
	2896	Fb($)p Fp(S)s Fb($)d Fj(\\)p 1461 424 100 2 v 11 w
	2897	Fp(L)p Fb($)p Fp(T)e Fb($)12 b(=)h Fj(;)p Fq(.)40 519
	2898	y(T)l(o)g(achie)o(v)o(e)h(language)f(containment)f(checking)h(we)h
	2899	(represent)f(the)g(composition)e(of)i(the)g(gi)o(v)o(en)g(system)f
	2900	(with)h(a)-31 576 y(model)d(representing)h(the)g(ne)o(gation)f(of)h
	2901	(the)f(property)h(and)g(check)g(it)g(for)g(language)f(emptiness.)16
	2902	b(The)11 b(language)f(of)h(the)-31 632 y(composed)g(system)f(is)h
	2903	(empty)f(if)i(and)f(only)g(if)g(the)g(system)g(satis\256es)g(the)g
	2904	(property)g Fp(T)6 b Fq(.)40 689 y(Language)14 b(emptiness)f(is)h(used)
	2905	g(not)g(only)f(to)h(v)o(erify)h(properties)f(that)g(cannot)g(be)h(e)o
	2906	(xpressed)f(in)g(F)o(air)i(CTL,)f(b)o(ut)-31 745 y(also)g(to)g(check)h
	2907	(whether)g(the)f(abstraction)g(of)h(a)g(system)e(still)g(contains)h
	2908	(the)g(original)g(system.)28 b(In)16 b(both)e(cases)i(one)-31
	2909	802 y(must)c(complement)g(an)h Fp(!)r Fq(\261automaton)e(\()p
	2910	Fp(T)6 b Fq(\),)14 b(and)f(this)f(is)g(hard)h(to)g(do)f(if)h(the)g
	2911	(automaton)e(is)i(nondeterministic)e(\(as)i(is)-31 858
	2912	y(usually)7 b(the)g(case)i(for)f(an)g(abstraction\).)15
	2913	b(The)8 b(fact)g(that)f(complementation)f(of)i(a)g(deterministic)e
	2914	(property)h(is)h(easy)m(,)h(while)-31 915 y(complementation)e(of)h(a)h
	2915	(nondeterministic)d(property)i(may)g(be)h(hard,)g(is)f(a)h(ke)o(y)f
	2916	(problem)f(with)h(language)g(containment.)-31 971 y(This)k(has)h
	2917	(prompted)f(a)h(lot)f(of)h(research)h(on)f(dif)o(ferent)f(classes)h(of)
	2918	g Fp(!)r Fq(-automata)f(with)h(dif)o(ferent)f(e)o(xpressi)o(v)o(eness)h
	2919	(and)-31 1028 y(dif)o(\256culty)j(of)h(complementation.)31
	2920	b(Currently)16 b(VIS)i(supports)d(language)h(emptiness)g(of)g
	2921	(nondeterministic)f(B)t(\310)-19 b(uchi)-31 1084 y(automata;)15
	2922	b(only)f(it)g(is)g(the)g(responsibility)f(of)h(the)g(user)h(to)f(deri)o
	2923	(v)o(e)h(the)f(complement)g(of)g(a)h(gi)o(v)o(en)f(nondeterministic)-31
	2924	1140 y(property)m(.)21 b(B)t(\310)-19 b(uchi)13 b(automata)f
	2925	(acceptance)i(conditions)d(are)j(states)e(that)h(must)e(be)i(reached)h
	2926	(in\256nitely)e(often)g(and)h(the)o(y)-31 1197 y(are)g(speci\256ed)g
	2927	(by)f(means)g(of)g(fairness)g(constraints.)18 b(Thus)12
	2928	b(to)f(use)i(language)f(containment,)f(the)h(user)h(must)e(insert)h(in)
	2929	-31 1253 y(the)g(V)-5 b(erilog)12 b(hierarchy)g(a)h(monitor)n(,)f
	2930	(which)f(represents)i(the)f(complement)f(automaton)g(structure,)i(and)f
	2931	(impose)f(a)h(set)-31 1310 y(of)j(fairness)g(conditions)e(to)i(specify)
	2932	g(the)g(complement)f(automaton)g(acceptance)i(conditions,)f(i.e.,)i
	2933	(the)e(acceptance)-31 1366 y(conditions)10 b(are)i(speci\256ed)g(in)f
	2934	(terms)g(of)g(fair)g(paths.)40 1423 y(As)d(a)g(\256nal)h(note,)g
	2935	(inside)e(VIS,)j(language)e(emptiness)f($language)h(containment$)g
	2936	(is)g(reduced)g(to)g(CTL,)h(by)f(checking)-31 1479 y(the)k(CTL)g
	2937	(formula)f Fp(E)j(G)d(tr)q(ue)h Fq(on)f(the)h(system)e(\(system)h
	2938	(composed)g(with)g(complemented)f(property\),)i(i.e.,)h(whether)-31
	2939	1536 y(there)f(is)f(an)g(in\256nite)g(path)g(\(notice)g(that)g
	2940	Fp(tr)q(ue)h Fq(is)f(always)f(satis\256ed\),)i(satisfying)e
	2941	(appropriate)h(fairness)g(constraints.)906 2835 y(23)p
	2942	eop
	2943	%%Page: 24 25
	2944	24 24 bop -31 323 a Fn(Chapter)20 b(4)-31 530 y Fs(F)m(ormal)27
	2945	b(V)-10 b(eri\256cation)24 b(in)i(VIS)-31 753 y Fq(In)15
	2946	b(this)f(chapter)h(we)g(describe)g(the)g(usage)g(and)g(the)g(relation)f
	2947	(between)h(the)g(VIS)g(commands)f(that)g(perform)h(formal)-31
	2948	809 y(v)o(eri\256cation.)i(The)12 b(main)f(sections)f(are:)26
	2949	903 y(1.)23 b(b)o(uilding)10 b(an)h(internal)g(representation)g(of)h
	2950	(the)f(\256nite-state)g(system,)26 997 y(2.)23 b(FSM)12
	2951	b(tra)o(v)o(ersal,)26 1091 y(3.)23 b(speci\256cation)11
	2952	b(of)g(fairness)g(constraints,)26 1184 y(4.)23 b(language)11
	2953	b(emptiness,)26 1278 y(5.)23 b(model)10 b(checking,)26
	2954	1372 y(6.)23 b(equi)o(v)o(alence)11 b(checking,)h(and)26
	2955	1466 y(7.)23 b(simulation.)-31 1613 y Fl(4.1)58 b(Repr)o(esenting)15
	2956	b(the)g(System)g(f)o(or)f(V)-6 b(eri\256cation)-31 1716
	2957	y Fq(In)12 b(this)e(section,)h(we)h(describe)f(the)g(steps)g(in)n(v)o
	2958	(olv)o(ed)g(in)g(con)n(v)o(erting)g(a)h(BLIF-MV)g(description)e(into)g
	2959	(an)i(internal)f(FSM)-31 1773 y(representation.)-31 1898
	2960	y Fk(4.1.1)51 b(Building)11 b(the)h(Flattened)f(Network)-31
	2961	1985 y Fq(The)i(compound)e Fi(init)p 323 1985 14 2 v
	2962	15 w(verify)i Fq(command)e(e)o(x)o(ecutes)i(the)g(entire)f(set)g(of)h
	2963	(required)f(initialization)f(commands.)18 b(When)13 b(a)-31
	2964	2041 y(BLIF-MV)e(description)d(is)h(read)i(into)d(VIS,)j(it)e(is)g
	2965	(stored)h(as)f(a)h(\252hierarchy\272)h(tree,)g(which)e(is)g(a)h
	2966	(hierarchical)g(description)-31 2098 y(of)h(the)f(design;)g(it)g
	2967	(consists)f(of)i(modules)e(\(also)h(called)h Fi(hnodes)p
	2968	Fq(\))f(that)g(in)g(turn)g(consist)g(of)g(sub-modules)f(\(also)i
	2969	(hnodes\))-31 2154 y(that)16 b(are)h(related)g(in)e(some)h(fashion.)31
	2970	b(This)15 b(relation)h(is)g(represented)g(as)h(a)f(table,)i(which)e
	2971	(implements)e(the)i(output)-31 2211 y(function)d(in)g(terms)f(of)i(the)
	2972	f(sub-module)f(inputs.)21 b(The)13 b Fi(print)p 970 2211
	2973	V 16 w(hier)o(ar)n(c)o(hy)p 1160 2211 V 16 w(stats)f
	2974	Fq(command)h(in)g(VIS)h(prints)e(hierarchy)-31 2267 y(information,)e
	2975	(and)g(the)g Fi(print)p 442 2267 V 15 w(models)g Fq(command)f(lists)g
	2976	(statistics)f(on)i(all)g(the)g(models)f(in)h(the)g(hierarchy)m(.)16
	2977	b(Other)11 b(useful)-31 2324 y(print)g(commands)f(are)i
	2978	Fi(print)p 436 2324 V 16 w(io)e Fq(and)i Fi(print)p 666
	2979	2324 V 15 w(latc)o(hes)p Fq(.)40 2380 y(The)j(hierarchy)h(can)g(be)g
	2980	(described)g(by)f(a)h(tree.)30 b(The)16 b(root)f(of)g(the)h(tree)g(is)f
	2981	(the)h(main)f(module,)h(and)f(the)h(lea)o(v)o(es)-31
	2982	2436 y(are)f(lo)o(wer)f(le)o(v)o(el)f(instantiations)f(of)i(modules.)23
	2983	b(The)14 b(hierarchy)g(in)g(VIS)g(can)h(be)f(tra)o(v)o(ersed)g(in)g(a)g
	2984	(manner)g(similar)f(to)-31 2493 y(tra)o(v)o(ersing)g(directories)f(in)g
	2985	(UNIX.)h(It)f(is)g(possible)g(to)g(reach)h(a)g(desired)f(node)h(in)f
	2986	(the)g(tree)h(by)f(walking)f(up)h(and)h(do)o(wn)-31 2549
	2987	y(with)g(the)h Fi(cd)g Fq(command.)23 b(At)14 b(an)o(y)g(node)g
	2988	(simulation,)f(v)o(eri\256cation)h(and)g(synthesis)e(operations)h(can)i
	2989	(be)f(performed.)-31 2606 y(The)e(command)e Fi(pwd)i
	2990	Fq(prints)e(the)h(name)h(of)f(the)g(current)h(node.)17
	2991	b(The)11 b(command)f Fi(ls)h Fq(lists)f(all)h(the)h(nodes)f
	2992	($submodules$)-31 2662 y(in)g(the)g(current)h(node;)f
	2993	Fi(ls)g(-R)g Fq(lists)f(all)h(the)h(nodes)f(in)g(the)g(current)g
	2994	(subtree.)906 2835 y(24)p eop
	2995	%%Page: 25 26
	2996	25 25 bop 40 11 a Fq(The)15 b(\256rst)h(step)f(to)o(wards)g(v)o
	2997	(eri\256cation)h(consists)e(of)i(\252\257attening\272)f(this)g
	2998	(hierarchical)h(description)f(into)f(a)i(single)-31 68
	2999	y(network)10 b($netlist)g(of)h(multi-v)o(alued)f(logic)g(gates$.)17
	3000	b(The)11 b(output)e(is)i(computed)f(from)h(the)g(inputs)e(of)j(the)e
	3001	(design)h(by)f(the)-31 124 y(network)g(circuit,)g(which)g(consists)f
	3002	(of)h(logic)g(gates,)g(interconnections)f(between)i(them,)f(and)g
	3003	(latches)g(to)g(represent)g(the)-31 181 y(sequential)d(elements.)16
	3004	b(The)8 b Fi(\257atten)p 549 181 14 2 v 15 w(hier)o(ar)n(c)o(hy)h
	3005	Fq(command)e(creates)i(this)e(network,)i(and)f(the)g
	3006	Fi(print)p 1542 181 V 15 w(network)g Fq(command)-31 237
	3007	y(can)16 b(be)f(used)g(to)g(print)g(it.)28 b(Other)15
	3008	b(related)g(commands)f(are)j Fi(print)p 1059 237 V 15
	3009	w(network)p 1221 237 V 16 w(stats)d Fq(command)h(that)g(prints)f
	3010	(statistics)-31 294 y(about)e(the)g(network,)g(and)g
	3011	Fi(test)p 469 294 V 16 w(network)p 632 294 V 16 w(acyclic)h
	3012	Fq(command)e(that)h(checks)g(the)g(network)f(for)i(combinational)d(c)o
	3013	(ycles.)-31 350 y(On)h(the)h(T)n(raf)o(\256c)h(Light)d(Controller)h(e)o
	3014	(xample)g(these)h(commands)e(work)h(as)g(follo)o(ws)f(:)-31
	3015	430 y Fd(UC)20 b(Berkeley,)f(VIS)h(Release)f(1.0)h(\(compiled)f
	3016	(11-Dec-95)g(at)h(10:36)g(AM\))-31 470 y(VIS>)g(read_blif_mv)f(tlc.mv)
	3017	-31 509 y(Warning:)g(Some)h(variables)f(are)h(unused)g(in)f(model)h
	3018	(main.)-31 548 y(vis>)g(print_hierarchy_stats)-31 588
	3019	y(Model)g(name)f(=)h(main,)g(Instance)f(name)h(=)g(main)-31
	3020	627 y(inputs)g(=)f(0,)h(outputs)g(=)g(0,)f(variables)h(=)f(12,)h
	3021	(tables)g(=)f(3,)h(latches)g(=)f(0,)h(children)g(=)f(4)-31
	3022	667 y(vis>)h(print_models)-31 706 y(Model)g(name)f(=)h(hwy_control)-31
	3023	746 y(inputs)g(=)f(4,)h(outputs)g(=)g(3,)f(variables)h(=)f(49,)h
	3024	(tables)g(=)f(44,)h(latches)g(=)f(1)-31 785 y(subckts)h(=)f(0)-31
	3025	824 y(Model)h(name)f(=)h(sensor)-31 864 y(inputs)g(=)f(0,)h(outputs)g
	3026	(=)g(1,)f(variables)h(=)f(12,)h(tables)g(=)f(11,)h(latches)g(=)f(1)-31
	3027	903 y(subckts)h(=)f(0)-31 943 y(Model)h(name)f(=)h(main)-31
	3028	982 y(inputs)g(=)f(0,)h(outputs)g(=)g(0,)f(variables)h(=)f(12,)h
	3029	(tables)g(=)f(3,)h(latches)g(=)f(0)-31 1022 y(subckts)h(=)f(4)-31
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	3489	%%Page: 32 33
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	3517	%%Page: 33 34
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	3573	%%Page: 34 35
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	3643	%%Page: 35 36
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	4207	i 1 sub dup i dup i 1 add dup i 2 add dup false subspline
	4208	} for
	4209	n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline
	4210	n 2 sub dup n 1 sub dup 0 0 1 1 false subspline
	4211	patternNone not { ifill } if
	4212	brushNone not { istroke } if
	4213	} {
	4214	Poly
	4215	} ifelse
	4216	end
	4217	} dup 0 4 dict put def
	4218
	4219	/Elli {
	4220	0 begin
	4221	newpath
	4222	4 2 roll
	4223	translate
	4224	scale
	4225	0 0 1 0 360 arc
	4226	patternNone not { ifill } if
	4227	brushNone not { istroke } if
	4228	end
	4229	} dup 0 1 dict put def
	4230
	4231	/Line {
	4232	0 begin
	4233	2 storexyn
	4234	newpath
	4235	x 0 get y 0 get moveto
	4236	x 1 get y 1 get lineto
	4237	brushNone not { istroke } if
	4238	0 0 1 1 leftarrow
	4239	0 0 1 1 rightarrow
	4240	end
	4241	} dup 0 4 dict put def
	4242
	4243	/MLine {
	4244	0 begin
	4245	storexyn
	4246	newpath
	4247	n 1 gt {
	4248	x 0 get y 0 get moveto
	4249	1 1 n 1 sub {
	4250	/i exch def
	4251	x i get y i get lineto
	4252	} for
	4253	patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if
	4254	brushNone not { istroke } if
	4255	0 0 1 1 leftarrow
	4256	n 2 sub dup n 1 sub dup rightarrow
	4257	} if
	4258	end
	4259	} dup 0 4 dict put def
	4260
	4261	/Poly {
	4262	3 1 roll
	4263	newpath
	4264	moveto
	4265	-1 add
	4266	{ lineto } repeat
	4267	closepath
	4268	patternNone not { ifill } if
	4269	brushNone not { istroke } if
	4270	} def
	4271
	4272	/Rect {
	4273	0 begin
	4274	/t exch def
	4275	/r exch def
	4276	/b exch def
	4277	/l exch def
	4278	newpath
	4279	l b moveto
	4280	l t lineto
	4281	r t lineto
	4282	r b lineto
	4283	closepath
	4284	patternNone not { ifill } if
	4285	brushNone not { istroke } if
	4286	end
	4287	} dup 0 4 dict put def
	4288
	4289	/Text {
	4290	ishow
	4291	} def
	4292
	4293	/idef {
	4294	dup where { pop pop pop } { exch def } ifelse
	4295	} def
	4296
	4297	/ifill {
	4298	0 begin
	4299	gsave
	4300	patternGrayLevel -1 ne {
	4301	fgred bgred fgred sub patternGrayLevel mul add
	4302	fggreen bggreen fggreen sub patternGrayLevel mul add
	4303	fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor
	4304	eofill
	4305	} {
	4306	eoclip
	4307	originalCTM setmatrix
	4308	pathbbox /t exch def /r exch def /b exch def /l exch def
	4309	/w r l sub ceiling cvi def
	4310	/h t b sub ceiling cvi def
	4311	/imageByteWidth w 8 div ceiling cvi def
	4312	/imageHeight h def
	4313	bgred bggreen bgblue setrgbcolor
	4314	eofill
	4315	fgred fggreen fgblue setrgbcolor
	4316	w 0 gt h 0 gt and {
	4317	l b translate w h scale
	4318	w h true [w 0 0 h neg 0 h] { patternproc } imagemask
	4319	} if
	4320	} ifelse
	4321	grestore
	4322	end
	4323	} dup 0 8 dict put def
	4324
	4325	/istroke {
	4326	gsave
	4327	brushDashOffset -1 eq {
	4328	[] 0 setdash
	4329	1 setgray
	4330	} {
	4331	brushDashArray brushDashOffset setdash
	4332	fgred fggreen fgblue setrgbcolor
	4333	} ifelse
	4334	brushWidth setlinewidth
	4335	originalCTM setmatrix
	4336	stroke
	4337	grestore
	4338	} def
	4339
	4340	/ishow {
	4341	0 begin
	4342	gsave
	4343	fgred fggreen fgblue setrgbcolor
	4344	/fontDict printFont printSize scalefont dup setfont def
	4345	/descender fontDict begin 0 [FontBBox] 1 get FontMatrix end
	4346	transform exch pop def
	4347	/vertoffset 1 printSize sub descender sub def {
	4348	0 vertoffset moveto show
	4349	/vertoffset vertoffset printSize sub def
	4350	} forall
	4351	grestore
	4352	end
	4353	} dup 0 3 dict put def
	4354	/patternproc {
	4355	0 begin
	4356	/patternByteLength patternString length def
	4357	/patternHeight patternByteLength 8 mul sqrt cvi def
	4358	/patternWidth patternHeight def
	4359	/patternByteWidth patternWidth 8 idiv def
	4360	/imageByteMaxLength imageByteWidth imageHeight mul
	4361	stringLimit patternByteWidth sub min def
	4362	/imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv
	4363	patternHeight mul patternHeight max def
	4364	/imageHeight imageHeight imageMaxHeight sub store
	4365	/imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def
	4366	0 1 imageMaxHeight 1 sub {
	4367	/y exch def
	4368	/patternRow y patternByteWidth mul patternByteLength mod def
	4369	/patternRowString patternString patternRow patternByteWidth getinterval def
	4370	/imageRow y imageByteWidth mul def
	4371	0 patternByteWidth imageByteWidth 1 sub {
	4372	/x exch def
	4373	imageString imageRow x add patternRowString putinterval
	4374	} for
	4375	} for
	4376	imageString
	4377	end
	4378	} dup 0 12 dict put def
	4379
	4380	/min {
	4381	dup 3 2 roll dup 4 3 roll lt { exch } if pop
	4382	} def
	4383
	4384	/max {
	4385	dup 3 2 roll dup 4 3 roll gt { exch } if pop
	4386	} def
	4387
	4388	/midpoint {
	4389	0 begin
	4390	/y1 exch def
	4391	/x1 exch def
	4392	/y0 exch def
	4393	/x0 exch def
	4394	x0 x1 add 2 div
	4395	y0 y1 add 2 div
	4396	end
	4397	} dup 0 4 dict put def
	4398
	4399	/thirdpoint {
	4400	0 begin
	4401	/y1 exch def
	4402	/x1 exch def
	4403	/y0 exch def
	4404	/x0 exch def
	4405	x0 2 mul x1 add 3 div
	4406	y0 2 mul y1 add 3 div
	4407	end
	4408	} dup 0 4 dict put def
	4409
	4410	/subspline {
	4411	0 begin
	4412	/movetoNeeded exch def
	4413	y exch get /y3 exch def
	4414	x exch get /x3 exch def
	4415	y exch get /y2 exch def
	4416	x exch get /x2 exch def
	4417	y exch get /y1 exch def
	4418	x exch get /x1 exch def
	4419	y exch get /y0 exch def
	4420	x exch get /x0 exch def
	4421	x1 y1 x2 y2 thirdpoint
	4422	/p1y exch def
	4423	/p1x exch def
	4424	x2 y2 x1 y1 thirdpoint
	4425	/p2y exch def
	4426	/p2x exch def
	4427	x1 y1 x0 y0 thirdpoint
	4428	p1x p1y midpoint
	4429	/p0y exch def
	4430	/p0x exch def
	4431	x2 y2 x3 y3 thirdpoint
	4432	p2x p2y midpoint
	4433	/p3y exch def
	4434	/p3x exch def
	4435	movetoNeeded { p0x p0y moveto } if
	4436	p1x p1y p2x p2y p3x p3y curveto
	4437	end
	4438	} dup 0 17 dict put def
	4439
	4440	/storexyn {
	4441	/n exch def
	4442	/y n array def
	4443	/x n array def
	4444	n 1 sub -1 0 {
	4445	/i exch def
	4446	y i 3 2 roll put
	4447	x i 3 2 roll put
	4448	} for
	4449	} def
	4450
	4451	/SSten {
	4452	fgred fggreen fgblue setrgbcolor
	4453	dup true exch 1 0 0 -1 0 6 -1 roll matrix astore
	4454	} def
	4455
	4456	/FSten {
	4457	dup 3 -1 roll dup 4 1 roll exch
	4458	newpath
	4459	0 0 moveto
	4460	dup 0 exch lineto
	4461	exch dup 3 1 roll exch lineto
	4462	0 lineto
	4463	closepath
	4464	bgred bggreen bgblue setrgbcolor
	4465	eofill
	4466	SSten
	4467	} def
	4468
	4469	/Rast {
	4470	exch dup 3 1 roll 1 0 0 -1 0 6 -1 roll matrix astore
	4471	} def
	4472
	4473
	4474	%I Idraw 10 Grid 8 8
	4475
	4476
	4477	Begin
	4478	%I b u
	4479	%I cfg u
	4480	%I cbg u
	4481	%I f u
	4482	%I p u
	4483	%I t
	4484	[ 0.757382 0 0 0.757382 0 0 ] concat
	4485	/originalCTM matrix currentmatrix def
	4486
	4487	Begin %I Text
	4488	%I cfg Black
	4489	0 0 0 SetCFg
	4490	%I f --helvetica-bold-r-normal--14-------*
	4491	Helvetica-Bold 14 SetF
	4492	%I t
	4493	[ 1 0 0 1 346 706 ] concat
	4494	%I
	4495	[
	4496	(cd)
	4497	] Text
	4498	End
	4499
	4500	Begin %I Text
	4501	%I cfg Black
	4502	0 0 0 SetCFg
	4503	%I f --helvetica-bold-r-normal--14-------*
	4504	Helvetica-Bold 14 SetF
	4505	%I t
	4506	[ 1 0 0 1 306 634 ] concat
	4507	%I
	4508	[
	4509	(flatten_hierarchy)
	4510	] Text
	4511	End
	4512
	4513	Begin %I Text
	4514	%I cfg Black
	4515	0 0 0 SetCFg
	4516	%I f --helvetica-bold-r-normal--14-------*
	4517	Helvetica-Bold 14 SetF
	4518	%I t
	4519	[ 1 0 0 1 478 643 ] concat
	4520	%I
	4521	[
	4522	(print_network_stats)
	4523	(print_network)
	4524	(test_network_acyclic)
	4525	] Text
	4526	End
	4527
	4528	Begin %I Text
	4529	%I cfg Black
	4530	0 0 0 SetCFg
	4531	%I f --helvetica-bold-r-normal--14-------*
	4532	Helvetica-Bold 14 SetF
	4533	%I t
	4534	[ 1 0 0 1 321 573 ] concat
	4535	%I
	4536	[
	4537	(static_order)
	4538	] Text
	4539	End
	4540
	4541	Begin %I Text
	4542	%I cfg Black
	4543	0 0 0 SetCFg
	4544	%I f --helvetica-bold-r-normal--14-------*
	4545	Helvetica-Bold 14 SetF
	4546	%I t
	4547	[ 1 0 0 1 291 498 ] concat
	4548	%I
	4549	[
	4550	(build_partition_mdds)
	4551	] Text
	4552	End
	4553
	4554	Begin %I Text
	4555	%I cfg Black
	4556	0 0 0 SetCFg
	4557	%I f --helvetica-bold-r-normal--14-------*
	4558	Helvetica-Bold 14 SetF
	4559	%I t
	4560	[ 1 0 0 1 495 572 ] concat
	4561	%I
	4562	[
	4563	(write_order)
	4564	] Text
	4565	End
	4566
	4567	Begin %I Text
	4568	%I cfg Black
	4569	0 0 0 SetCFg
	4570	%I f --helvetica-bold-r-normal--14-------*
	4571	Helvetica-Bold 14 SetF
	4572	%I t
	4573	[ 1 0 0 1 188 580 ] concat
	4574	%I
	4575	[
	4576	(init_verify)
	4577	] Text
	4578	End
	4579
	4580	Begin %I Rect
	4581	%I b 65535
	4582	2 0 0 [] 0 SetB
	4583	%I cfg Black
	4584	0 0 0 SetCFg
	4585	%I cbg White
	4586	1 1 1 SetCBg
	4587	none SetP %I p n
	4588	%I t
	4589	[ 1 0 0 1 210 258 ] concat
	4590	%I
	4591	264 289 410 322 Rect
	4592	End
	4593
	4594	Begin %I Rect
	4595	%I b 65535
	4596	2 0 0 [] 0 SetB
	4597	%I cfg Black
	4598	0 0 0 SetCFg
	4599	%I cbg White
	4600	1 1 1 SetCBg
	4601	none SetP %I p n
	4602	%I t
	4603	[ 1 0 0 1 209 260 ] concat
	4604	%I
	4605	264 182 409 271 Rect
	4606	End
	4607
	4608	Begin %I Rect
	4609	%I b 65535
	4610	2 0 0 [] 0 SetB
	4611	%I cfg Black
	4612	0 0 0 SetCFg
	4613	%I cbg White
	4614	1 1 1 SetCBg
	4615	none SetP %I p n
	4616	%I t
	4617	[ 0.986667 0 0 1.3125 214.48 201.271 ] concat
	4618	%I
	4619	262 148 408 176 Rect
	4620	End
	4621
	4622	Begin %I Rect
	4623	%I b 65535
	4624	2 0 0 [] 0 SetB
	4625	%I cfg Black
	4626	0 0 0 SetCFg
	4627	%I cbg White
	4628	1 1 1 SetCBg
	4629	none SetP %I p n
	4630	%I t
	4631	[ 1 0 0 1 216 255 ] concat
	4632	%I
	4633	258 84 407 115 Rect
	4634	End
	4635
	4636	Begin %I Rect
	4637	%I b 65535
	4638	2 0 0 [] 0 SetB
	4639	%I cfg Black
	4640	0 0 0 SetCFg
	4641	%I cbg White
	4642	1 1 1 SetCBg
	4643	none SetP %I p n
	4644	%I t
	4645	[ 1 0 0 1 211 261 ] concat
	4646	%I
	4647	262 397 409 464 Rect
	4648	End
	4649
	4650	Begin %I Rect
	4651	%I b 65535
	4652	2 0 0 [] 0 SetB
	4653	%I cfg Black
	4654	0 0 0 SetCFg
	4655	%I cbg White
	4656	1 1 1 SetCBg
	4657	none SetP %I p n
	4658	%I t
	4659	[ 1 0 0 1 213 260 ] concat
	4660	%I
	4661	260 335 410 389 Rect
	4662	End
	4663
	4664	Begin %I Elli
	4665	%I b 65535
	4666	2 0 0 [] 0 SetB
	4667	%I cfg Black
	4668	0 0 0 SetCFg
	4669	%I cbg White
	4670	1 1 1 SetCBg
	4671	none SetP %I p n
	4672	%I t
	4673	[ 1 0 0 1 196 265 ] concat
	4674	%I
	4675	158 435 46 16 Elli
	4676	End
	4677
	4678	Begin %I Elli
	4679	%I b 65535
	4680	2 0 0 [] 0 SetB
	4681	%I cfg Black
	4682	0 0 0 SetCFg
	4683	%I cbg White
	4684	1 1 1 SetCBg
	4685	none SetP %I p n
	4686	%I t
	4687	[ 1 0 0 1 201 256 ] concat
	4688	%I
	4689	160 373 80 20 Elli
	4690	End
	4691
	4692	Begin %I Elli
	4693	%I b 65535
	4694	2 0 0 [] 0 SetB
	4695	%I cfg Black
	4696	0 0 0 SetCFg
	4697	%I cbg White
	4698	1 1 1 SetCBg
	4699	none SetP %I p n
	4700	%I t
	4701	[ 1 0 0 1 193 258 ] concat
	4702	%I
	4703	167 305 56 20 Elli
	4704	End
	4705
	4706	Begin %I Elli
	4707	%I b 65535
	4708	2 0 0 [] 0 SetB
	4709	%I cfg Black
	4710	0 0 0 SetCFg
	4711	%I cbg White
	4712	1 1 1 SetCBg
	4713	none SetP %I p n
	4714	%I t
	4715	[ 1 0 0 1 198 249 ] concat
	4716	%I
	4717	166 241 80 27 Elli
	4718	End
	4719
	4720	Begin %I Elli
	4721	%I b 65535
	4722	2 0 0 [] 0 SetB
	4723	%I cfg Black
	4724	0 0 0 SetCFg
	4725	%I cbg White
	4726	1 1 1 SetCBg
	4727	none SetP %I p n
	4728	%I t
	4729	[ 0.915692 0 0 2.55203 203.748 12.0202 ] concat
	4730	%I
	4731	168 143 76 14 Elli
	4732	End
	4733
	4734	Begin %I Rect
	4735	%I b 65535
	4736	2 0 0 [] 0 SetB
	4737	%I cfg Black
	4738	0 0 0 SetCFg
	4739	%I cbg White
	4740	1 1 1 SetCBg
	4741	none SetP %I p n
	4742	%I t
	4743	[ 1 0 0 1 176 257 ] concat
	4744	%I
	4745	6 298 86 333 Rect
	4746	End
	4747
	4748	Begin %I Line
	4749	%I b 65535
	4750	2 0 1 [] 0 SetB
	4751	%I cfg Black
	4752	0 0 0 SetCFg
	4753	%I cbg White
	4754	1 1 1 SetCBg
	4755	none SetP %I p n
	4756	%I t
	4757	[ 1 0 0 1 130 258 ] concat
	4758	%I
	4759	225 352 225 324 Line
	4760	%I 1
	4761	End
	4762
	4763	Begin %I Line
	4764	%I b 65535
	4765	2 0 1 [] 0 SetB
	4766	%I cfg Black
	4767	0 0 0 SetCFg
	4768	%I cbg White
	4769	1 1 1 SetCBg
	4770	none SetP %I p n
	4771	%I t
	4772	[ 1 0 0 1 130 258 ] concat
	4773	%I
	4774	226 205 226 156 Line
	4775	%I 1
	4776	End
	4777
	4778	Begin %I MLine
	4779	%I b 65535
	4780	2 0 1 [] 0 SetB
	4781	%I cfg Black
	4782	0 0 0 SetCFg
	4783	%I cbg White
	4784	1 1 1 SetCBg
	4785	none SetP %I p n
	4786	%I t
	4787	[ 1 0 0 1 130 258 ] concat
	4788	%I 3
	4789	223 402
	4790	88 402
	4791	88 332
	4792	3 MLine
	4793	%I 1
	4794	End
	4795
	4796	Begin %I Line
	4797	%I b 65535
	4798	2 0 1 [] 0 SetB
	4799	%I cfg Black
	4800	0 0 0 SetCFg
	4801	%I cbg White
	4802	1 1 1 SetCBg
	4803	none SetP %I p n
	4804	%I t
	4805	[ 1 0 0 1 130 258 ] concat
	4806	%I
	4807	225 425 225 389 Line
	4808	%I 1
	4809	End
	4810
	4811	Begin %I Elli
	4812	%I b 65535
	4813	2 0 0 [] 0 SetB
	4814	%I cfg Black
	4815	0 0 0 SetCFg
	4816	%I cbg White
	4817	1 1 1 SetCBg
	4818	none SetP %I p n
	4819	%I t
	4820	[ 1.34209 0 0 0.932851 48.0848 294.187 ] concat
	4821	%I
	4822	227 503 48 20 Elli
	4823	End
	4824
	4825	Begin %I Line
	4826	%I b 65535
	4827	2 0 1 [] 0 SetB
	4828	%I cfg Black
	4829	0 0 0 SetCFg
	4830	%I cbg White
	4831	1 1 1 SetCBg
	4832	none SetP %I p n
	4833	%I t
	4834	[ 1 0 0 1 127 258 ] concat
	4835	%I
	4836	228 482 228 457 Line
	4837	%I 1
	4838	End
	4839
	4840	Begin %I Line
	4841	%I b 65535
	4842	2 1 1 [] 0 SetB
	4843	%I cfg Black
	4844	0 0 0 SetCFg
	4845	%I cbg White
	4846	1 1 1 SetCBg
	4847	none SetP %I p n
	4848	%I t
	4849	[ 1 0 0 1 130 258 ] concat
	4850	%I
	4851	271 441 342 441 Line
	4852	%I 1
	4853	End
	4854
	4855	Begin %I Line
	4856	%I b 65535
	4857	2 0 1 [] 0 SetB
	4858	%I cfg Black
	4859	0 0 0 SetCFg
	4860	%I cbg White
	4861	1 1 1 SetCBg
	4862	none SetP %I p n
	4863	%I t
	4864	[ 1 0 0 1 130 258 ] concat
	4865	%I
	4866	311 371 340 371 Line
	4867	%I 1
	4868	End
	4869
	4870	Begin %I Line
	4871	%I b 65535
	4872	2 0 1 [] 0 SetB
	4873	%I cfg Black
	4874	0 0 0 SetCFg
	4875	%I cbg White
	4876	1 1 1 SetCBg
	4877	none SetP %I p n
	4878	%I t
	4879	[ 1 0 0 1 130 258 ] concat
	4880	%I
	4881	286 306 342 306 Line
	4882	%I 1
	4883	End
	4884
	4885	Begin %I Line
	4886	%I b 65535
	4887	2 0 1 [] 0 SetB
	4888	%I cfg Black
	4889	0 0 0 SetCFg
	4890	%I cbg White
	4891	1 1 1 SetCBg
	4892	none SetP %I p n
	4893	%I t
	4894	[ 1 0 0 1 130 258 ] concat
	4895	%I
	4896	314 232 340 232 Line
	4897	%I 1
	4898	End
	4899
	4900	Begin %I Text
	4901	%I cfg Black
	4902	0 0 0 SetCFg
	4903	%I f --helvetica-bold-r-normal--14-------*
	4904	Helvetica-Bold 14 SetF
	4905	%I t
	4906	[ 1 0 0 1 484 718 ] concat
	4907	%I
	4908	[
	4909	(ls)
	4910	(pwd)
	4911	(write_blif$ _mv$)
	4912	(read_blif$ _mv$ -i)
	4913	] Text
	4914	End
	4915
	4916	Begin %I Text
	4917	%I cfg Black
	4918	0 0 0 SetCFg
	4919	%I f --helvetica-bold-r-normal--14-------*
	4920	Helvetica-Bold 14 SetF
	4921	%I t
	4922	[ 1 0 0 1 487 521 ] concat
	4923	%I
	4924	[
	4925	(simulate)
	4926	(compute_reach)
	4927	(comb_verify)
	4928	(seq_verify)
	4929	(print_img_info)
	4930	] Text
	4931	End
	4932
	4933	Begin %I Text
	4934	%I cfg Black
	4935	0 0 0 SetCFg
	4936	%I f --helvetica-bold-r-normal--14-------*
	4937	Helvetica-Bold 14 SetF
	4938	%I t
	4939	[ 1 0 0 1 304 769 ] concat
	4940	%I
	4941	[
	4942	(read_blif $_mv$)
	4943	] Text
	4944	End
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	5293	%%Trailer
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	5296	%%EOF

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