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vis_user.ps @ 86

Last change on this file since 86 was 14, checked in by cecile, 13 years ago
vis2.3
File size: 240.3 KB

Line
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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
975	(content)e(of)i(state)f(v)o(ariables,)h(until)e(the)h(e)o(x)o(ecution)
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
979	(ecuted)g(atomically)e(if)h(the)g(delay/e)o(v)o(ent)f(control)h(of)g
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
983	b(All)13 b(procedural)i(blocks)e(with)h(acti)o(v)o(e)g(e)o(v)o(ent)-31
984	550 y(controls)c(get)g(e)o(x)o(ecuted)h(concurrently)m(.)17
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
987	b(there)f(is)g(more)g(than)f(one)h(procedural)h(block)e(sharing)h(the)g
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
992	(instantaneously)m(,)f(meaning)g(that)h(the)o(y)g(change)h(the)f
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)
996	g(change.)20 b(On)12 b(the)g(other)g(hand,)h(other)f(processes)g(\(for)
997	h(instance,)f(other)g Fm(always)j Fq(statements)c(or)-31
998	889 y(continuous)e(assignments\))f(cannot)i(see)h(the)f(change)g(until)
999	f(the)h(ne)o(xt)g(clock)g(c)o(ycle.)17 b(Because)12 b(of)e(this,)g
1000	(race)h(conditions)-31 945 y(might)g(arise)h(among)f(multiple)f
1001	(procedural)i(assignments.)17 b Fi(Non-bloc)o(king)12
1002	b(pr)n(ocedur)o(al)f(assignments)f Fq($)p Fm(<=)p Fq($)j(pro)o(vide)
1003	-31 1002 y(a)k(mechanism)f(that)g(defers)h(the)f(assignment)f(without)g
1004	(blocking)h(the)g(e)o(x)o(ecution)h(of)f(statements)g(in)g(a)h(block.)
1005	31 b(On)-31 1058 y(encountering)16 b(a)h(non-blocking)e(assignment,)h
1006	(the)h(right)e(hand-side)h(of)h(the)f(assignment)f(is)h(e)o(v)o
1007	(aluated)g(according)-31 1115 y(to)f(the)g(most)e(recent)j(v)o(alues)f
1008	(of)g(the)g(referred)h(v)o(ariables.)28 b(Ho)o(we)o(v)o(er)n(,)17
1009	b(without)c(changing)i(the)g(v)o(ariable)g(on)f(the)h(left)-31
1010	1171 y(hand-side,)c(program)e(e)o(x)o(ecution)i(continues.)k(Then)10
1011	b(v)o(ariables)g(are)h(updated)f(simultaneously)d(at)k(the)f(v)o(ery)g
1012	(be)o(ginning)-31 1228 y(of)i(the)h(ne)o(xt)f(time)f(slot.)19
1013	b(F)o(or)13 b Fo(VL)p Fq(2)p Fo(MV)p Fq(,)h(non-blocking)d(procedural)i
1014	(assignments)d(should)h(ne)o(v)o(er)i(be)f(used,)h(since)f(the)o(y)-31
1015	1284 y(might)e(introduce)h(unwanted)g(nondeterminism.)-31
1016	1409 y Fk(2.3.2)51 b(Nondeterminism)-31 1496 y Fq(Non-blocking)11
1017	b(assignments)f(also)i(pro)o(vide)g(a)g(way)g(to)f(introduce)h
1018	(nondeterminism)e(on)h Fm(reg)i Fq(v)o(ariables.)19 b(If)12
1019	b(there)h(is)-31 1553 y(more)h(than)g(one)g(non-blocking)f(assignment)g
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
1022	(re)o(gister)g(v)o(ariable)h(in)f(the)g(ne)o(xt)g(clock)g(c)o(ycle)h
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
1029	(construct,)i Fm($ND)p Fq(,)i(has)e(been)g(added)g(to)g(V)-5
1030	b(erilog)12 b(to)h(specify)g(nondeterminism)d(on)-31
1031	1835 y(wire)i(v)o(ariables)f(and)g(is)f(the)i(only)e(le)o(gal)h(way)g
1032	(to)g(introduce)f(nondeterminism)g(in)g(VIS.)j(F)o(or)f(e)o(xample,)f
1033	(to)g(require)h(that)-31 1892 y(the)f(output)g(at)g(a)h(particular)f
1034	(state)g(is)g(nondeterministically)e(GO)j(or)f(NOGO,)h(one)f(can)h
1035	(introduce)f(a)h(ne)o(w)f(v)o(ariable,)h Fp(r)q Fq(,)-31
1036	1948 y(and)g(write)f(the)g(follo)o(wing)f(V)-5 b(erilog)11
1037	b(fragment.)-31 2037 y Fd(assign)20 b(r=$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
1040	y(.)-31 2353 y(.)-31 2392 y(end)-31 2517 y Fk(2.3.3)51
1041	b(Symbolic)12 b(V)-5 b(ariables)-31 2604 y Fq(Sometimes)14
1042	b(it)h(is)f(desirable)h(to)g(specify)g(and)g(e)o(xamine)g(the)g(v)o
1043	(alue)g(of)g(some)g(v)o(ariables)f(symbolically)m(,)h(rather)h(than)-31
1044	2661 y(ha)o(ving)f(to)f(e)o(xplicitly)g(encode)i(them.)28
1045	b Fo(VL)p Fq(2)p Fo(MV)16 b Fq(e)o(xtends)f(V)-5 b(erilog)15
1046	b(to)g(allo)o(w)f(users)h(to)g(declare)h(symbolic)d(v)o(ariables)918
1047	2835 y(8)p eop
1048	%%Page: 9 10
1049	9 9 bop -31 11 a Fq(using)11 b(an)g(enumerated)h(type)f(mechanism)g
1050	(similar)f(to)h(the)h(one)f(a)o(v)o(ailable)h(in)f(the)g(C)h
1051	(programming)e(language.)18 b(As)11 b(an)-31 68 y(e)o(xample,)h(we)g
1052	(introduce)f(a)g(symbolic)f(type)h(named)g Fm(door)p
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
1056	(determined)g(by)g(the)h(de\256nition)f(of)g(the)h(V)-5
1057	b(erilog)8 b(simulator)n(,)g(and)h(it)f(can)h(be)f(either)h(implicit)
1058	-31 453 y(or)j(e)o(xplicit.)k(Implicit)10 b(is)h(the)g(default.)16
1059	b(Explicit)10 b(may)h(be)h(required)f(in)g(some)g(cases.)40
1060	510 y(A)e(V)-5 b(erilog)8 b(simulator)f(is)i(an)g(e)o(v)o(ent-dri)o(v)o
1061	(en)g Fi(passive)f(sc)o(heduler)p Fq(.)16 b(A)9 b(simulator)e
1062	(schedules)h(e)o(v)o(ents)h(generated)g(from)-31 566
1063	y(V)-5 b(erilog)15 b(modules)f(and)h(then)g(sends)f(them)h(to)g
1064	(modules)f(which)g(are)i(sensiti)o(v)o(e)f(to)f(these)h(e)o(v)o(ents.)
1065	28 b(Statements)15 b(with)-31 623 y(sensitized)e(e)o(v)o(ents)g(\(acti)
1066	o(v)o(e)h(statements\))f(are)h(e)o(x)o(ecuted)g(and)g(in)f(turn)g(more)
1067	g(e)o(v)o(ents)h(are)g(generated,)h(which)e(are)i(then)-31
1068	679 y(scheduled)e(by)f(the)h(simulator)m(.)21 b(The)13
1069	b(simulator)e(itself)i(does)f(not)h(generate)h(an)o(y)f(e)o(v)o(ent,)h
1070	(b)o(ut)e(it)h(coordinates)f(between)-31 736 y(the)e(producers)h(and)f
1071	(consumers)g(of)g(e)o(v)o(ents.)17 b(Hence,)11 b(to)f(write)h(a)f
1072	(synchronous)g(system,)f(a)i(designer)f(needs)h(to)f(write)g(a)-31
1073	792 y(small)g(clock)i(generator)n(,)g(i.e.,)h(an)e(e)o(v)o(ent)h
1074	(generator)f(which)g(creates)i(e)o(v)o(ents)e(in)g(time.)16
1075	b(The)11 b(produced)g(e)o(v)o(ents)h(pro)o(v)o(oke)-31
1076	849 y(a)j(chain)g(of)g(reactions)f(among)g(modules.)26
1077	b(The)14 b(system)g(reaches)i(a)f(stable)f(state)g(when)h(there)g(are)g
1078	(no)g(more)f(e)o(v)o(ents)-31 905 y(other)h(than)f(the)g(clocking)g(e)o
1079	(v)o(ent.)26 b(The)15 b(ne)o(xt)f(clocking)g(e)o(v)o(ent)g(is)g(then)h
1080	(chosen)f(by)g(the)g(simulator)n(,)h(and)f(simulation)-31
1081	961 y(time)e(is)f(adv)o(anced)i(according)f(to)g(the)g(time)f(stamp)h
1082	(of)g(the)g(ne)o(wly)f(scheduled)h(clocking)g(e)o(v)o(ent.)19
1083	b(W)l(e)13 b(call)f(the)g(system)-31 1018 y Fi(implicitly)i(cloc)o(ked)
1084	i Fq(when)f(all)g(transitions)f(are)i(synchronized)f(by)g(an)h
1085	(implicit)d Fi(time)p Fq(.)29 b(F)o(or)16 b(an)g(implicitly)d(clocked)
1086	-31 1074 y(system)d(hardware)h(resources)g(will)e(not)h(be)h(allocated)
1087	f(for)h(a)g(synchronizing)f(v)o(ariable.)16 b(Also,)11
1088	b(for)f(implicitly)f(clocked)-31 1131 y(designs,)16 b(one)g(symbolic)e
1089	(latch)i($or)g(state)f(v)o(ariable$)h(is)f(allocated)g(for)h(each)h
1090	Fm(reg)g Fq(v)o(ariable,)g(and)e(synchronization)-31
1091	1187 y(v)o(ariables)c(are)h(dropped.)17 b(By)12 b(default,)f(implicit)e
1092	(clocking)i(semantics)g(is)f(assumed.)40 1244 y(On)j(the)g(other)g
1093	(hand,)i(for)e(some)g(designs,)g(the)h(operation)f(of)g(a)h(system)e
1094	(depends)h(e)o(xplicitly)f(on)h(se)o(v)o(eral)h(phases)-31
1095	1300 y(\(rising)e(edge,)h(falling)e(edge,)i(1-le)o(v)o(el,)g(0-le)o(v)o
1096	(el\))g(of)f(one)g(or)h(more)f(synchronizing)f(signals)g(\(generally)h
1097	(referred)i(to)e(as)-31 1357 y Fi(cloc)o(ks)p Fq(\).)20
1098	b(In)12 b(such)g(a)g(case)h(the)f(clock)g(signals)f(should)g(be)h
1099	(interpreted)g(literally)f(and)h(hardware)h(resources)f(should)f(be)-31
1100	1413 y(allocated.)24 b(A)14 b(design)f(is)g(called)h
1101	Fi(e)o(xplicitly)f(cloc)o(ked)h Fq(if)g(synchronizing)e(signals)h(are)h
1102	(to)g(be)g(compiled)e(literally)h(into)-31 1470 y(hardware.)22
1103	b(F)o(or)14 b(e)o(xplicitly)e(clocked)g(systems,)g(each)i
1104	Fm(reg)g Fq(v)o(ariable)f(is)f(modeled)h(by)f(a)h(symbolic)f(latch)h
1105	(along)f(with)-31 1526 y(some)i(e)o(xtra)h(logic)f(to)h(emulate)f(the)g
1106	(clocking)g(mechanism.)26 b(An)14 b(e)o(xample)h(of)g(e)o(xplicit)f
1107	(clocking)g(declared)h(by)f(the)-31 1582 y(user)d(is)g(the)g(follo)o
1108	(wing.)k(Suppose)c(that)g(a)h(system)e(is)g(composed)h(of)g(parallel)g
1109	(components)f(that)h(progress)g(dif)o(ferently)-31 1639
1110	y(according)k(to)e(synchronization)g(signals)h(e)o(xchanged)h(among)e
1111	(them)h(by)g(means)g(of)g Fm(wait)i Fq(statements.)25
1112	b(Then)14 b(it)g(is)-31 1695 y(necessary)e(to)f(declare)h(an)g(e)o
1113	(xplicit)e(clocking)h(signal:)-31 1775 y Fd(module)20
1114	b(env;)-31 1815 y(reg)g(clk;)-31 1894 y(initial)g(clk=0;)-31
1115	1973 y(always)g(#1)f(clk)h(=)g(!clk;)-31 2051 y(endmodule)40
1116	2149 y Fq(This)15 b(code)h(generates)h(a)f(clocking)f(signal)g
1117	Fm(clk)j Fq(with)d(a)h(c)o(ycle)h(of)f(two)f(time)g(units)g(used)h(to)g
1118	(dri)o(v)o(e)g(the)g(whole)-31 2205 y(system)e(and)i(make)e(it)h
1119	(simulatable.)27 b(In)16 b(this)e(case)i Fo(VL)p Fq(2)p
1120	Fo(MV)h Fq(must)d(be)h(in)n(v)o(oked)g(with)f(the)h(options)f
1121	Fi(-c)i(-F)p Fq(,)g(meaning)-31 2261 y(e)o(xplicit)11
1122	b(clocking)g($)p Fi(-c)p Fq($,)h(and)g(ignore)f(all)g(timing)e(\()p
1123	Fi(-F)p Fq(\).)-31 2407 y Fl(2.5)58 b(V)-6 b(erilog)15
1124	b(f)o(or)f Fh(VL)p Fu(2)p Fh(MV)p Fl(:)21 b(Hints)15
1125	b(and)h(T)l(raps)-31 2511 y Fq(In)c(this)e(section)h(a)g(list)g(of)g
1126	(hints)f(to)h(follo)o(w)m(,)g(and)h(traps)f(to)g(a)o(v)o(oid,)g(is)g
1127	(pro)o(vided)g(for)h(writing)e(V)-5 b(erilog)11 b(for)h(VIS.)26
1128	2598 y(1.)23 b(Inside)13 b(an)h Fm(always)j Fq(block,)d(only)f
1129	(blocking)g(assignments)f(to)i Fm(reg)h Fq(v)o(ariables)f(are)h(allo)o
1130	(wed.)24 b(Therefore)14 b(do)83 2654 y(not)c(write)i(to)e(an)i
1131	(intermediate)e(v)o(ariable)h(\(that)g(is)g(a)h Fm(wire)h
1132	Fq(by)e(de\256nition\))f(inside)g(an)i Fm(always)i Fq(block)c(and)h(do)
1133	83 2711 y(not)g(use)g(non-blocking)f(assignments)f(\()p
1134	Fm(<=)p Fq(\))k(e)o(v)o(er)m(.)918 2835 y(9)p eop
1135	%%Page: 10 11
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1138	(separate)i Fm(always)h Fq(blocks,)83 68 y(otherwise)11
1139	b(the)g(beha)o(vior)g(may)g(depend)h(on)f(the)g(order)h(of)f(e)o(x)o
1140	(ecution.)26 162 y(3.)23 b(Inside)11 b(an)g Fm(always)i
1141	Fq(block,)f(blocking)e(assignments)f Fm(=)j Fq(are)g(sensiti)o(v)o(e)e
1142	(to)g(the)h(order)h(of)f(the)g(statements.)16 b(Thus)83
1143	218 y(the)11 b(follo)o(wing)f(two)g(fragments)h(e)o(v)o(aluate)h(dif)o
1144	(ferently:)83 326 y Fd(state)19 b(=)h(1;)83 365 y(out)f(=)h(state;)83
1145	473 y(out)f(=)h(state;)83 513 y(state)f(=)h(1;)83 638
1146	y Fq(Since)11 b(we)f(do)g(not)g(allo)o(w)g(non-blocking)f(assignments)f
1147	($<=$)j(inside)e(an)i Fm(always)i Fq(block,)d(we)h(ha)o(v)o(e)g(to)f
1148	(analyze)83 694 y(the)h(order)h(of)f(e)o(v)o(aluation)g(to)g(be)g
1149	(certain)h(that)f(we)g(ha)o(v)o(e)h(the)g(desired)f(beha)o(vior)m(.)26
1150	788 y(4.)23 b(It)11 b(is)g(not)g(le)o(gal)g(to)g(ha)o(v)o(e)h(a)g
1151	(block)f(of)g(assignments,)f(as)i(in:)83 896 y Fd(assign)19
1152	b(begin)182 935 y(x)h(=)g(1;)182 975 y(y)g(=)g(2;)83
1153	1014 y(end)83 1139 y Fq(Ho)o(we)o(v)o(er)n(,)12 b(it)f(is)g(le)o(gal)g
1154	(to)g(ha)o(v)o(e)h(a)g(block)f(of)g(assignments)f(for)h(an)h
1155	Fm(initial)i Fq(statement:)83 1247 y Fd(initial)19 b(begin)182
1156	1287 y(x)h(=)g(1;)182 1326 y(y)g(=)g(2;)83 1365 y(end)26
1157	1490 y Fq(5.)j(In)18 b Fm(always)i Fq(blocks,)f(at)f(the)g(ne)o(xt)f
1158	(clock,)j Fm(reg)f Fq(v)o(ariables)f(keep)g(their)f(pre)o(vious)g(v)o
1159	(alues)h(if)f(the)o(y)h(are)h(not)83 1547 y(e)o(xplicitly)10
1160	b(assigned)h(to.)26 1641 y(6.)23 b(Introduce)12 b(nondeterminism)e
1161	(using)h(only)g Fm($ND)i Fq(assignments)e(to)g(wires.)19
1162	b(Unlike)11 b(in)h(HSIS,)h(multiple)e(assign-)83 1697
1163	y(ments)f(such)h(as:)83 1805 y Fd(always@\(posedge)19
1164	b(clk\))g(begin)83 1844 y(state)g(<=)h(GO;)83 1884 y(state)f(<=)h(NOGO)
1165	g(;)83 1923 y(end)83 2048 y Fq(are)12 b(not)f(considered)g(le)o(gal)g
1166	(nondeterminism)e(in)i(VIS.)26 2142 y(7.)23 b Fo(VL)p
1167	Fq(2)p Fo(MV)15 b Fq(will)d(reject)i(a)g(V)-5 b(erilog)13
1168	b(description)f(containing)h(an)g(unspeci\256ed)h(initial)e(state.)23
1169	b(If)13 b(the)h(user)f(wants)g(a)83 2199 y(nondeterministic)e(initial)h
1170	(state,)i(it)e(should)g(be)i(speci\256ed)f(e)o(xplicitly)f(using)g(a)i
1171	Fm($ND)g Fq(construct,)g(for)f(e)o(xample:)83 2255 y
1172	Fd(initial)19 b(x)h(=)g($ND$a,b,c$)p Fq(;)c(in)f(this)f(case,)j(a)e
1173	(nondeterministic)e(constant)i(will)f(be)h(created)h(with)f(a)g(name)g
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1909	% Arc
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1914	% Polyline
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1918	% Polyline
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1920	% Polyline
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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
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1932
1933	n 8203.17 2693.23 m 8100.00 2625.00 l 8223.14 2636.65 l gs col-1 s gr
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1935	n 2400.00 7125.00 m 3187.50 7012.50 l
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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
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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
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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
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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
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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
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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
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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
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2028	4425 1800 m
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2031	2925 1125 m
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2034	8775 1275 m
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2037	2700 7350 m
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2040	3300 7650 m
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2043	4425 8325 m
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2052	4875 6450 m
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2055	900 6525 m
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2058	2400 5850 m
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2061	8400 7500 m
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2100	1200 3825 m
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2150	%%Page: 16 17
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2216	%%Page: 18 19
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2439	n 4353 1443 m 4408 1583 l gs col13 0.25 tnt ef gr gs col-1 s gr
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2450	% Polyline
2451	n 3488 1453 m 3543 1593 l gs col13 0.25 tnt ef gr gs col-1 s gr
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2455	gs 1 -1 sc (Y) col-1 show gr
2456	% Polyline
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2458	n 4183.67 1132.57 m 4185.00 1218.00 l 4127.83 1154.51 l gs col-1 s gr
2459	% Polyline
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2461	n 3995.92 1153.40 m 3940.00 1218.00 l 3939.65 1132.56 l gs col-1 s gr
2462	% Polyline
2463	n 3143 1833 m 3093 1968 l gs col13 0.25 tnt ef gr gs col-1 s gr
2464	n 3148.92 1903.40 m 3093.00 1968.00 l 3092.65 1882.56 l gs col-1 s gr
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2467	gs 1 -1 sc (R) col-1 show gr
2468	% Polyline
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2470	n 3336.67 1882.57 m 3338.00 1968.00 l 3280.83 1904.51 l gs col-1 s gr
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2479	n 3458.92 1905.40 m 3403.00 1970.00 l 3402.65 1884.56 l gs col-1 s gr
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2500	n 2098.82 1014.72 m 2141.00 1131.00 l 2049.06 1048.25 l gs col-1 s gr
2501	% Polyline
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2503	n 1881.00 1281.00 m 1761.00 1251.00 l 1881.00 1221.00 l gs col-1 s gr
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2507	% Polyline
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2513	% Interp Spline
2514	n 1821 726 m
2515	1748.37 745.35 1715.87 742.85 1691 716 curveto
2516	1669.38 692.66 1685.38 651.30 1691 631 curveto
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2518	1772.00 516.70 1818.31 513.18 1841 516 curveto
2519	1862.71 518.70 1906.19 526.34 1921 551 curveto
2520	1932.06 569.41 1917.31 601.20 1916 616 curveto
2521	1915.24 624.55 1913.99 637.05 1911 666 curveto
2522	gs col-1 s gr
2523
2524	n 1949.06 589.51 m 1911.00 666.00 l 1889.38 583.34 l gs col-1 s gr
2525	% Interp Spline
2526	n 2281 1151 m
2527	2261.65 1078.00 2264.15 1045.00 2291 1021 curveto
2528	2314.34 1000.00 2355.70 1016.00 2376 1021 curveto
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2530	2490.30 1102.00 2493.82 1148.00 2491 1171 curveto
2531	2488.30 1192.00 2480.66 1236.00 2456 1251 curveto
2532	2437.59 1262.00 2405.80 1247.00 2391 1246 curveto
2533	2382.45 1245.00 2369.95 1243.00 2341 1241 curveto
2534	gs col-1 s gr
2535
2536	n 2418.74 1276.44 m 2341.00 1241.00 l 2422.88 1216.58 l gs col-1 s gr
2537	% Interp Spline
2538	n 1561 1351 m
2539	1580.00 1424.00 1577.00 1457.00 1551 1481 curveto
2540	1527.00 1502.00 1486.00 1486.00 1466 1481 curveto
2541	1438.00 1474.00 1385.00 1448.00 1366 1421 curveto
2542	1352.00 1400.00 1349.00 1354.00 1351 1331 curveto
2543	1354.00 1310.00 1362.00 1266.00 1386 1251 curveto
2544	1405.00 1240.00 1436.00 1255.00 1451 1256 curveto
2545	1459.00 1257.00 1472.00 1259.00 1501 1261 curveto
2546	gs col-1 s gr
2547
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2575	b(operators.)17 b(Each)10 b(temporal)f(operator)h(consists)f(of)h(two)f
2576	(parts)1153 1218 y Ft(1)1172 1234 y Fq(:)15 b(a)c(path)e(quanti\256er)h
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2578	1291 y(a)k(temporal)e(modality)f(\()p Fp(F)c Fq(,)14
2579	b Fp(G)p Fq(,)e Fp(X)t Fq(,)g Fp(U)5 b Fq(\).)20 b(All)11
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2581	(implicit)f(\252current)-31 1347 y(state\272.)17 b(There)11
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2593	(wing)d(intuiti)o(v)o(e)h(meaning:)26 1663 y(1.)23 b
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2595	(in)g(the)h(future\272\))h(is)f(true)g(of)h(a)f(path)g(if)g(there)h(e)o
2596	(xists)e(a)i(state)f(in)g(the)g(path)g(where)83 1719
2597	y(formula)h Fp(\036)g Fq(is)g(true.)26 1811 y(2.)23 b
2598	Fp(G)11 b(\036)g Fq(\(reads)h(\252)p Fp(\036)g Fq(holds)f
2599	(globally\272\))f(is)h(true)g(of)h(a)g(path)f(if)g Fp(\036)g
2600	Fq(is)g(true)h(at)f(e)o(v)o(ery)h(state)f(in)g(the)g(path.)26
2601	1903 y(3.)23 b Fp(X)14 b(\036)e Fq(\(reads)g(\252)p Fp(\036)g
2602	Fq(holds)e(in)h(the)g(ne)o(xt)h(state\272\))f(is)g(true)h(of)f(a)h
2603	(path)f(if)g Fp(\036)h Fq(is)f(true)g(in)g(the)g(state)g(reached)i
2604	(immediately)83 1960 y(after)f(the)f(current)h(state)f(in)g(the)g
2605	(path.)26 2052 y(4.)23 b Fp(\036)12 b(U)18 b( )13 b Fq(\(reads)g(\252)p
2606	Fp(\036)g Fq(holds)e(until)g Fp( )j Fq(holds\272,)e(called)g
2607	(\252strong)g(until\272)1189 2035 y Ft(2)1207 2052 y
2608	Fq(\))h(is)f(true)g(of)g(a)h(path)f(if)g Fp( )i Fq(is)e(true)g(in)g
2609	(some)83 2108 y(state)f(in)g(the)g(path,)h(and)f Fp(\036)g
2610	Fq(holds)g(in)g(all)g(preceding)g(states.)-31 2198 y(In)17
2611	b(the)f(VIS)i(documentation)d(there)i(is)f(a)h(description)f(of)g(the)h
2612	(syntax)f(of)g(CTL)h(in)g(the)f(document)g(entitled)g(\252CTL)-31
2613	2254 y(Syntax\272.)h(In)12 b(this)e(chapter)i(CTL)f(formulas)g(will)g
2614	(be)g(written)g(in)g(a)h(simpli\256ed)e(syntax.)40 2311
2615	y(The)j(state)h(of)f(a)h(system)f(consists)f(of)i(the)f(v)o(alues)h
2616	(stored)f(in)g(all)g(latches.)24 b(Each)14 b(formula)f(of)h(the)f
2617	(logic)g(is)g(either)-31 2367 y(true)f(or)g(false)f(in)h(a)g(gi)o(v)o
2618	(en)f(state;)h(its)f(truth)g(is)g(e)o(v)o(aluated)g(from)h(the)g(truth)
2619	f(of)h(its)e(subformulas)h(in)g(a)h(recursi)o(v)o(e)h(fashion,)-31
2620	2423 y(until)c(one)i(reaches)g(atomic)f(propositions)f(that)h(are)h
2621	(either)g(true)f(or)h(false)f(in)g(a)h(gi)o(v)o(en)f(state.)17
2622	b(A)10 b(formula)g(is)g(satis\256ed)g(by)-31 2480 y(a)h(system)e(if)i
2623	(it)e(is)h(true)h(for)g(all)f(the)g(initial)f(states)h(of)g(the)h
2624	(system.)k(If)c(the)f(property)g(does)h(not)e(hold,)i(the)f(model)g
2625	(checker)-31 2536 y(will)g(produce)h(a)h(countere)o(xample,)f(that)g
2626	(is)f(an)h(e)o(x)o(ecution)h(path)e(that)h(witnesses)f(the)h(failure.)
2627	16 b(An)11 b(ef)o(\256cient)h(algorithm)p -31 2575 768
2628	2 v 22 2603 a Fg(1)36 2619 y Ff(A)d(formula)g(that)g(contains)f(an)o(y)
2629	g(temporal)g(modality)h(\()p Fc(F)c Ff(,)10 b Fc(G)p
2630	Ff(,)f Fc(X)s Ff(,)g Fc(U)t Ff(\))g(without)g(an)f(associated)f(path)h
2631	(quanti\256er)g($)p Fc(A)p Ff(,)h Fc(E)r Ff($)h(is)f(not)p
2632	1656 2626 48 2 v 8 w(a)g(le)o(gal)g(CTL)-31 2664 y(formula.)22
2633	2695 y Fg(2)36 2711 y Ff(\252W)m(eak)f(until\272)i(is)f(when)f
2634	Fc(\036)i Ff(holds)e(fore)o(v)o(er)o(,)h(i.e.,)i Fc( )g
2635	Ff(is)e(not)g(required)g(to)g(hold)g(at)g(some)f(state)h(in)h(the)f
2636	(future.)906 2835 y Fq(19)p eop
2637	%%Page: 20 21
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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
2641	(xamples)g(of)g(e)o(v)o(aluations)g(of)g(formulas)g(on)g(the)g
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
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2901	(the)f(property)h(and)g(check)g(it)g(for)g(language)f(emptiness.)16
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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
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2915	(nondeterministic)d(property)i(may)g(be)h(hard,)g(is)f(a)h(ke)o(y)f
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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
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2928	b(to)f(use)i(language)f(containment,)f(the)h(user)h(must)e(insert)h(in)
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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)
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2934	(terms)g(of)g(fair)g(paths.)40 1423 y(As)d(a)g(\256nal)h(note,)g
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2937	(formula)f Fp(E)j(G)d(tr)q(ue)h Fq(on)f(the)h(system)e(\(system)h
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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
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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
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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
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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
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3013	(ycles.)-31 350 y(On)h(the)h(T)n(raf)o(\256c)h(Light)d(Controller)h(e)o
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3015	430 y Fd(UC)20 b(Berkeley,)f(VIS)h(Release)f(1.0)h(\(compiled)f
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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
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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
3030	1061 y(Model)h(name)f(=)h(timer)-31 1101 y(inputs)g(=)f(1,)h(outputs)g
3031	(=)g(2,)f(variables)h(=)f(40,)h(tables)g(=)f(38,)h(latches)g(=)f(1)-31
3032	1140 y(subckts)h(=)f(0)-31 1179 y(Model)h(name)f(=)h(farm_control)-31
3033	1219 y(inputs)g(=)f(4,)h(outputs)g(=)g(3,)f(variables)h(=)f(49,)h
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3035	1298 y(vis>)h(flatten_hierarchy)-31 1337 y(vis>)g(print_network_stats)
3036	-31 1377 y(main)40 b(combinational=142)e(pi=0)i(po=0)f(latches=4)h
3037	(pseudo=2)f(const=40)g(edges=206)-31 1416 y(vis>)20 b
3038	(test_network_acyclic)-31 1455 y(Network)g(has)f(no)h(combinational)f
3039	(cycles)-31 1495 y(vis>)h(ls)-31 1534 y(farm_control)-31
3040	1574 y(hwy_control)-31 1613 y(sensor)-31 1653 y(timer)-31
3041	1692 y(vis>)g(cd)g(hwy_control)-31 1731 y(vis>)g(print_io)-31
3042	1771 y(inputs:)g(car_present)f(enable_hwy)g(long_timer)g(short_timer)
3043	-31 1810 y(outputs:)g(enable_farm)h(hwy_light)f(hwy_start_timer)-31
3044	1850 y(vis>)h(print_latches)-31 1889 y(hwy_light)-31
3045	1929 y(vis>)g(flatten_hierarchy)-31 1968 y(vis>)g(print_network_stats)
3046	-31 2008 y(hwy_control)39 b(combinational=45)g(pi=4)g(po=3)h(latches=1)
3047	f(pseudo=0)g(const=12)h(edges=68)40 2105 y Fq(Note)16
3048	b(that)g(when)h(a)g(node)g(is)f(arri)o(v)o(ed)h(at)g(for)g(the)f
3049	(\256rst)h(time,)h(there)f(is)f(no)g(network)g(for)h(that)g(node)f
3050	(until)g Fi(\257at-)-31 2161 y(ten)p 28 2161 V 16 w(hier)o(ar)n(c)o(hy)
3051	c Fq(is)f(called)h(for)f(that)g(node.)40 2218 y(Also)g
3052	Fi(\257atten)p 256 2218 V 16 w(hier)o(ar)n(c)o(hy)h Fq(automatically)f
3053	(checks)h(each)h(table)f(in)g(the)g(network)f(for)h(being)g
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3055	h(completely)f(speci\256ed.)27 b(Since)16 b(this)e(checking)h(takes)f
3056	(some)g(time,)i(it)e(can)h(be)g(turned)g(of)o(f)-31 2330
3057	y(safely)d(using)e(the)h(option)f Fi(\257atten)p 513
3058	2330 V 16 w(hier)o(ar)n(c)o(hy)i(-b)p Fq(,)g(after)p
3059	773 2337 84 2 v 12 w(a)f(BLIF-MV)i(\256le)e(has)h(been)f(checked)h
3060	(once.)-31 2454 y Fk(4.1.2)51 b(Ordering)-31 2541 y Fq(The)17
3061	b(ne)o(xt)g(step)g(to)o(wards)f(v)o(eri\256cation)h(consists)f(of)h
3062	(con)n(v)o(erting)g(this)f(network)g(representation)h(into)f(a)h
3063	(functional)-31 2598 y(description)11 b(that)h(represents)g(the)g
3064	(output)e(and)i(ne)o(xt)g(state)g(v)o(ariables)g(as)g(a)g(function)g
3065	(of)g(the)f(inputs)g(and)h(current)g(state)-31 2654 y(v)o(ariables.)22
3066	b(W)l(e)14 b(use)f(the)g(BDD)h($binary)f(decision)g(diagram$)g(and)g
3067	(its)f(e)o(xtension)h(the)g(MDD)g(\(multi)o(v)o(alued)e(decision)-31
3068	2711 y(diagram\))h(to)g(represent)h(boolean)e(and)i(discrete)f
3069	(functions.)18 b(Before)c(creating)e(the)g(MDDs,)g(it)g(is)f(necessary)
3070	i(to)f(order)906 2835 y(25)p eop
3071	%%Page: 26 27
3072	26 26 bop -31 11 a Fq(the)18 b(v)o(ariables)g(in)g(the)h(support)e(of)h
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3074	1435 11 14 2 v 16 w(or)n(der)g Fq(command,)i(which)-31
3075	68 y(gi)o(v)o(es)13 b(an)h(initial)d(ordering.)23 b(Networks)12
3076	b(with)h(combinational)e(c)o(ycles)j(cannot)f(be)h(ordered.)23
3077	b(If)13 b(the)h(MDD)e(v)o(ariables)-31 124 y(ha)o(v)o(e)k(already)g
3078	(been)g(ordered,)i(then)d Fi(static)p 686 124 V 15 w(or)n(der)g
3079	Fq(does)h(nothing.)28 b(T)l(o)15 b(undo)g(the)h(current)f(ordering,)i
3080	(rein)n(v)o(oke)e(the)-31 181 y(command)e Fi(\257atten)p
3081	281 181 V 15 w(hier)o(ar)n(c)o(hy)p Fq(.)24 b(At)13 b(an)o(y)h(stage)f
3082	(the)h(current)g(v)o(ariable)f(ordering)g(can)h(be)g(written)f(out)f
3083	(to)i(a)f(\256le)h(using)-31 237 y(the)d Fi(write)p 133
3084	237 V 17 w(or)n(der)g Fq(command.)-31 362 y Fk(4.1.3)51
3085	b(Computing)11 b(FSM)h(Inf)o(ormation)-31 449 y Fq(The)17
3086	b Fi(b)o(uild)p 154 449 V 15 w(partition)p 331 449 V
3087	14 w(mdds)f Fq(command)f(computes)h(the)g(transition)f(function)g
3088	(MDDs.)31 b(Depending)16 b(on)g(the)g(parti-)-31 506
3089	y(tioning)d(method)g(selected,)i(the)f(MDDs)f(for)h(the)g
3090	(combinational)e(outputs)h($COs$)i(are)f(b)o(uilt)f(in)h(terms)f(of)h
3091	(either)g(the)-31 562 y(combinational)g(inputs)g($CIs$)i(or)f(some)g
3092	(subset)g(of)g(intermediate)g(nodes)g(of)g(the)g(network.)28
3093	b(The)16 b(MDDs)e(b)o(uilt)g(are)-31 619 y(stored)i(in)f(a)h(D)n(A)n(G)
3094	h(called)e(a)i(\252partition\272.)29 b(The)16 b(v)o(ertices)h(of)f(a)g
3095	(partition)e(correspond)i(to)g(the)f(CIs,)j(COs,)g(and)e(an)o(y)-31
3096	675 y(intermediate)9 b(nodes)f(used.)16 b(Each)9 b(v)o(erte)o(x)h(has)f
3097	(a)g(multi-v)o(alued)f(function)g($represented)i(by)f(an)g(MDD$)g(e)o
3098	(xpressing)f(the)-31 732 y(function)h(of)i(the)f(corresponding)f
3099	(network)g(node)h(in)g(terms)g(of)g(the)g(partition)f(v)o(ertices)h(in)
3100	g(its)f(transiti)o(v)o(e)g(fanin.)16 b(Hence,)-31 788
3101	y(the)c(MDDs)f(of)g(the)h(partition)e(represent)i(a)g(partial)f
3102	(collapsing)g(of)g(the)h(network.)17 b(The)11 b Fi(inout)g
3103	Fq(method)f(represents)i(one)-31 845 y(e)o(xtreme)i(where)g(no)f
3104	(intermediate)f(nodes)h(are)h(used,)g(and)f Fi(total)f
3105	Fq(represents)i(the)f(other)g(e)o(xtreme)h(where)f(e)o(v)o(ery)h(node)
3106	-31 901 y(in)h(the)h(network)f(has)h(a)g(corresponding)f(v)o(erte)o(x)h
3107	(in)g(the)f(partition.)29 b(If)16 b(no)f Fi(method)h
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3109	(v)o(alue)f(of)g(the)g(\257ag)h Fi(partition)p 717 957
3110	V 15 w(method)e Fq(is)h(used)g(as)h(default)e(\(this)h(\257ag)h(is)f
3111	(set)g(by)g(the)g(command)f Fi(set)-31 1014 y(partition)p
3112	134 1014 V 14 w(method)p Fq(\),)j(unless)e(it)g(does)g(not)g(ha)o(v)o
3113	(e)h(a)g(v)o(alue,)g(in)f(which)h(case)g(the)f Fi(inout)f
3114	Fq(method)h(is)g(used.)29 b(The)15 b(parti-)-31 1070
3115	y(tion)g(graph)g(can)h(be)g(printed)e(to)i(a)f(\256le)h(with)f(the)g
3116	Fi(print)p 879 1070 V 15 w(partition)f Fq(command.)28
3117	b(Another)15 b(related)h(command)e(is)h(the)-31 1127
3118	y Fi(print)p 62 1127 V 15 w(partition)p 239 1127 V 15
3119	w(stats)10 b Fq(command)g(that)h(prints)g(statistics)e(on)j(the)f
3120	(partition)f(graph.)40 1183 y(The)h(complete)g(set)g(of)h(commands)e
3121	(included)h(by)g Fi(init)p 913 1183 V 15 w(verify)g Fq(are:)26
3122	1277 y(1.)23 b Fi(\257atten)p 201 1277 V 15 w(hier)o(ar)n(c)o(hy)p
3123	Fq(,)26 1371 y(2.)g Fi(static)p 186 1371 V 15 w(or)n(der)p
3124	Fq(,)12 b(and)26 1465 y(3.)23 b Fi(b)o(uild)p 180 1465
3125	V 15 w(partition)p 357 1465 V 15 w(mdds)p Fq(.)-31 1554
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3130	1751 y(vis>)g(build_partition_mdds)-31 1791 y(vis>)g
3131	(print_partition_stats)-31 1830 y(Method)g(Inputs-Outputs,)e(8)i
3132	(sinks,)g(10)g(sources,)f(14)h(total)f(vertices,)g(78)h(mdd)g(nodes)-31
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3134	y Fq(Dynamic)i(ordering)g(of)h(v)o(ariables)f(may)g(be)g(enabled)h(and)
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3136	w(var)p 1513 2042 V 16 w(or)n(dering)f Fq(command.)-31
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3140	299 2155 V 15 w(hier)o(ar)n(c)o(hy)h Fq(and)g Fi(static)p
3141	682 2155 V 15 w(or)n(der)f Fq(must)g(be)g(in)n(v)o(oked)g(before)h
3142	(this)e(command.)23 b(A)m(v)o(ailable)12 b(methods)-31
3143	2212 y(for)j(dynamic)g(reordering)g(are)g Fi(window)g
3144	Fq(and)g Fi(sift)p Fq(.)26 b(Dynamic)15 b(ordering)f(may)h(be)g(time)f
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3150	y(after)e(the)f Fi(b)o(uild)p 230 2381 V 15 w(partition)p
3151	407 2381 V 15 w(mdds)f Fq(and)h Fi(print)p 698 2381 V
3152	16 w(img)p 783 2381 V 16 w(info)f Fq(commands.)18 b(If)13
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3154	2437 y(then)16 b(you)g(may)h(wish)f(to)g(sa)o(v)o(e)h(this)e(ordering)i
3155	(\(using)e Fi(write)p 977 2437 V 17 w(or)n(der)h(<\256le>)p
3156	Fq(\))g(and)h(reuse)g(it)f(\(using)f Fi(static)p 1727
3157	2437 V 16 w(or)n(der)h(-s)-31 2494 y(<method>)d(<\256le>)p
3158	Fq(\).)23 b(W)n(ith)13 b(option)f Fi(dynamic)p 737 2494
3159	V 16 w(var)p 814 2494 V 16 w(or)n(dering)h(-e)h(<method>)f
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3166	2835 y(26)p eop
3167	%%Page: 27 28
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3172	169 y(vis>)g(print_partition_stats)-31 209 y(Method)g(Inputs-Outputs,)e
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3207	b(shadow)298 b(9)80 b(3)20 b($14,)f(15$)-31 1668 y(vis>)h
3208	(write_order)f(tlc.sift)-31 1707 y(vis>)h(quit)-31 1825
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3214	(input_and_latch)e(tlc.sift)-31 2062 y(vis>)i(write_order)-31
3215	2101 y(#)g(UC)g(Berkeley,)f(VIS)h(Release)f(1.0)h(\(compiled)f
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3217	2180 y(#)g(generated:)f(Wed)h(Dec)g(13)f(14:34:08)h(1995)-31
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3224	b(shadow)298 b(4)80 b(2)20 b($7$)-31 2496 y(car_present)179
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3230	Fq(27)p eop
3231	%%Page: 28 29
3232	28 28 bop 40 11 a Fq(Dynamic)16 b(ordering)g(mo)o(v)o(es)h(around)f
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3236	(that)e(the)h(resolution)e(of)h(reading)h(and)f(writing)-31
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3243	g(in)f(the)g(\256le)h Fi(tlc.sift)p Fq(.)22 b(See)15
3244	b(for)f(e)o(xample)f(v)o(ariable)h Fm(hwy)p 1738 237
3245	14 2 v 17 w(light)-31 294 y Fq(in)h(the)g(e)o(xample)h(abo)o(v)o(e.)29
3246	b(The)16 b(only)e(information)h(that)f(is)h(used)g(from)h(the)f(\256le)
3247	h Fi(tlc.sift)e Fq(is)h(the)g(order)h(of)f(the)h(MDD)-31
3248	350 y(v)o(ariables)d(in)g(the)g(\256rst)h(column.)21
3249	b(By)14 b(editing)e(the)h(\256le)h Fi(tlc.sift)e Fq(an)o(y)i(order)g
3250	(can)f(be)h(imposed.)21 b(Gi)o(v)o(en)14 b(an)f(ordering)g(of)-31
3251	407 y(MDD)e(v)o(ariables,)h(BDD)f(v)o(ariables)h(which)f(encode)g(them)
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3254	j(Image)e(Computation)-31 657 y Fq(FSM)j(tra)o(v)o(ersal)g(is)f(the)g
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3256	b(Ef)o(\256cient)17 b(tra)o(v)o(ersal)g(requires)f(grouping)f(the)-31
3257	713 y(MDDs,)h(in)e(a)h(manner)g(optimal)e(for)j(tra)o(v)o(ersal.)27
3258	b(T)l(o)15 b(tra)o(v)o(erse)h(the)f(FSM,)h(the)e(present)h(state,)h
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3260	(ganized)g(for)g(easy)g(manipulation.)20 b(All)12 b(this)g(information)
3261	f(is)i(included)f(in)g(an)h(FSM)g(data)g(structure)-31
3262	826 y(created)j(in)f(the)f Fi(compute)p 395 826 V 17
3263	w(r)n(eac)o(h)h Fq(command.)27 b(This)14 b(also)h(in)n(v)o(okes)f(tra)o
3264	(v)o(ersal)i(of)f(the)g(entire)g(reachable)h(state)e(set)h(of)-31
3265	883 y(the)i(FSM)h(representing)e(the)h(design,)i(and)e(may)f(be)i(in)n
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3268	18 b(On)12 b(subsequent)f(calls)g(to)h Fi(compute)p 1184
3269	939 V 16 w(r)n(eac)o(h)p Fq(,)i(the)e(reachability)f(computation)g(is)
3270	-31 996 y(not)g(reperformed,)h(b)o(ut)f(statistics)f(can)i(be)f
3271	(printed)g(using)f Fi(-v)p Fq(.)40 1052 y(The)17 b(reachability)f
3272	(computation)f(makes)h(e)o(xtensi)o(v)o(e)h(use)g(of)g(image)f
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3274	1109 y(settable)7 b(options)g(that)g(af)o(fect)i(the)e(performance)i
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3276	Fi(set)f Fq(command)-31 1165 y(lists)g(these)h(options.)15
3277	b(Use)8 b(the)g(command)g Fi(set)g(image)p 821 1165 V
3278	15 w(method)g Fq(to)g(change)h(the)f(image)g(computation)f(method,)h
3279	(and)h(then)-31 1221 y(re-initialize)14 b(v)o(eri\256cation)g
3280	(\(starting)f(at)h(the)g Fi(\257atten)p 816 1221 V 16
3281	w(hier)o(ar)n(c)o(hy)g Fq(command)1212 1205 y Ft(1)1230
3282	1221 y Fq(\).)25 b(The)14 b Fi(print)p 1459 1221 V 16
3283	w(img)p 1544 1221 V 16 w(info)f Fq(prints)g(current)-31
3284	1278 y(image)f(information.)17 b(Notice)12 b(that)f(while)h
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3286	w(stats)f Fq(prints)g(information)g(on)g(the)h(ne)o(xt)g(state)g
3287	Fr(functions)p Fq(,)-31 1334 y Fi(print)p 62 1334 V 15
3288	w(img)p 146 1334 V 16 w(info)17 b Fq(prints)g(information)f(on)h(the)g
3289	(ne)o(xt)h(state)f(transition)f Fr(r)o(elations)p Fq(.)36
3290	b(The)17 b(command)g Fi(print)p 1721 1334 V 15 w(img)p
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3292	(relations)i(from)f(transition)g(functions)g(by)g(clustering)g(se)o(v)o
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3297	127 1504 V 16 w(var)p 204 1504 V 17 w(or)n(dering)f(-f)i(sift)p
3298	Fq(\))e(at)i(this)e(point)h(to)g(reorder)h(these)g(relation)f(MDDs.)19
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3304	Fi(compute)p 916 1673 V 16 w(r)n(eac)o(h)h Fq(on)f(the)g(T)n(raf)o
3305	(\256c)i(Light)d(Controller:)-31 1762 y Fd(UC)20 b(Berkeley,)f(VIS)h
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3313	(Size)f(For)h(Creating)f(Clusters)h(=)g(1000)288 2078
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3442	%%Page: 31 32
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3489	%%Page: 32 33
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3517	%%Page: 33 34
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3552	Fm(!$timer.s)q(ta)q(te=)q(ST)q(ART)q($)k Fq(disallo)o(ws)12
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3554	(er)h(in)f(the)g(state:)-31 1532 y Fd(car_present:YES)-31
3555	1572 y(farm_light:RED)-31 1611 y(hwy_light:YELLOW)-31
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3573	%%Page: 34 35
3574	34 34 bop -31 11 a Fk(4.5.3)51 b(Checking)11 b(In)n(variants)-31
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3577	(form)h Fp(AG)g(f)5 b Fq(,)16 b(where)e Fp(f)19 b Fq(is)14
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3579	b(semantics)g(of)h Fp(AG)f(f)20 b Fq(is)14 b(that)g Fp(f)19
3580	b Fq(is)14 b(true)h(in)f(all)g(reachable)i(states.)26
3581	b(The)14 b(command)-31 212 y Fi(c)o(hec)o(k)p 73 212
3582	14 2 v 18 w(in)n(variant)9 b Fq(implements)g(an)i(algorithm)e(that)h
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3585	b Fq(is)11 b(the)g(formula)-31 361 y Fm(!\(\(farm_l)q(ig)q(ht)31
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3592	(tlc.invar)-31 780 y(INV:)h(formula)f(passed)h(---)f
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3594	905 y Fk(4.5.4)51 b(Advanced)11 b(Model)h(Checking:)k(Abstraction)c
3595	(and)f(Reduction)-31 992 y Fq(When)h(performing)f(model)g(checking)h
3596	(and)g(checking)g(in)n(v)o(ariant)f(properties,)h(one)g(can)g(use)g
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3598	(checking)h(on)h(a)f(\252pruned\272)h(FSM,)g(i.e.,)h(one)e(where)h
3599	(parts)f(that)g(do)g(not)g(af)o(fect)h(the)f(formula)g(\(directly)-31
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3602	(abstraction)f(mechanism)g(a)o(v)o(ailable)g(through)g(the)g(command)
3603	-31 1218 y Fi(\257atten)p 87 1218 V 16 w(hier)o(ar)n(c)o(hy)10
3604	b(<\256le>)p Fq(.)16 b Fi(<\256le>)10 b Fq(contains)f(the)h(names)g(of)
3605	g(v)o(ariables)g(to)f(abstract.)17 b(F)o(or)11 b(each)g(v)o(ariable)f
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3607	(primary)f(input)f(node)i(named)f Fm(x$ABS)j Fq(is)d(created)h(to)f
3608	(dri)o(v)o(e)h(all)f(the)h(nodes)f(that)g(were)i(pre)o(viously)-31
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3618	Fm(tlc.abstr)q(ac)q(t)j Fq(contains)d(the)g(v)o(ariable)g
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3620	b Fm(timer.star)q(t)p Fq(,)k(the)c(timer)f(module)g(is)h(disconnected)f
3621	(from)h(the)g(rest)g(of)g(the)g(T)n(raf)o(\256c)i(Light)d(Controller)m
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3623	(property)g(read)h(from)g(the)f(\256le)h Fm(tlc.reduce)q(.ct)q(l)p
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3626	Fq(This)16 b(property)g(refers)h(only)f(to)g(the)g(timer)g(module.)31
3627	b(Since)17 b(the)g(timer)f(has)g(been)h(disconnected,)g(the)f(rest)h
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3631	g(been)h(read)g(in.)-31 2001 y Fd(UC)20 b(Berkeley,)f(VIS)h(Release)f
3632	(1.0)h($compiled)f(15-Dec-95)g(at)h(2:18)g(PM$)-31
3633	2040 y(Sourcing)f(.visrc)h(of)g(Tiziano)-31 2080 y(vis>)g(read_blif_mv)
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3635	(model)h(main.)-31 2159 y(vis>)g(flatten_hierarchy)e(tlc.abstract)-31
3636	2198 y(vis>)i(static_order)-31 2237 y(vis>)g(build_partition_mdds)-31
3637	2277 y(vis>)g(model_check)f(-i)h(-r)f(tlc.reduce.ctl)-31
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3641	2632 y(hwy_light:GREEN)-31 2671 y(timer.state:START)906
3642	2835 y Fq(34)p eop
3643	%%Page: 35 36
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3648	248 y(hwy_light:GREEN)-31 287 y(timer.state:START)-31
3649	366 y(fails)h($timer.state=START)e(->)i(AF\(timer.state=LONG$\))-31
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3652	721 y(passes)g(timer.state=START)-31 800 y(--State)-31
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3673	2292 y(in)f(the)g(CTL)h(property)f(in)g(the)g(\256le)h
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3684	%%Page: 36 37
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3687	(AG$\(state=START)g(->)h(AF\(state=LONG$\)\))40 229
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3715	986 y(The)17 b(command)e Fi(seq)p 388 986 V 17 w(verify)h
3716	Fq(tests)g(the)h(sequential)f(equi)o(v)o(alence)h(of)f(two)g(networks.)
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3725	1212 y(b)o(uilding)g(the)i(product)f(\256nite)h(state)f(machine.)24
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3730	1325 y(happens,)h(a)f(deb)o(ug)g(trace)i(is)d(pro)o(vided.)-31
3731	1471 y Fl(4.7)58 b(Simulation)-31 1574 y Fq(Simulation,)14
3732	b(although)f(not)h(\252formal)g(v)o(eri\256cation\272,)i(is)e(an)g
3733	(alternate)h(method)e(for)h(design)g(v)o(eri\256cation.)26
3734	b(After)14 b(the)-31 1631 y(command)c Fi(b)o(uild)p 257
3735	1631 V 15 w(partition)p 434 1631 V 15 w(mdds)g Fq(is)g(in)n(v)o(oked,)g
3736	(the)g(network)g(can)h(also)f(be)h(simulated.)k(In)c(VIS)g(we)g(pro)o
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3738	(description)g(generated)g(by)g Fo(VL)p Fq(2)p Fo(MV)p
3739	Fq(,)k(via)c(the)g Fi(simulate)f Fq(command.)33 b(Thus,)19
3740	b(VIS)-31 1744 y(encompasses)c(both)g(formal)h(v)o(eri\256cation)g(and)
3741	f(simulation)f(capabilities.)29 b Fi(simulate)14 b Fq(can)j(generate)f
3742	(random)f(input)-31 1800 y(patterns)c(or)h(accept)g(user)o
3743	(-speci\256ed)g(input)e(patterns.)-31 1883 y Fd(UC)20
3744	b(Berkeley,)f(VIS)h(Release)f(1.0)h(\(compiled)f(15-Dec-95)g(at)h
3745	(10:24)g(PM\))-31 1922 y(vis>)g(read_blif_mv)f(tlc.mv)-31
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5252	(deterministic)3 574 y(40.)23 b(test)p 150 574 V 16 w(network)p
5253	316 574 V 15 w(ac)o(yclic:)17 b(determine)11 b(whether)h(the)f(network)
5254	f(is)h(ac)o(yclic)3 668 y(41.)23 b(time:)15 b(pro)o(vide)c(a)h(simple)e
5255	(elapsed)i(time)e(v)o(alue)3 762 y(42.)23 b(unalias:)15
5256	b(remo)o(v)o(es)d(the)f(de\256nition)g(of)g(an)h(alias)3
5257	856 y(43.)23 b(unset:)15 b(unset)c(an)h(en)n(vironment)e(v)o(ariable)3
5258	949 y(44.)23 b(usage:)16 b(pro)o(vide)11 b(a)h(dump)e(of)i(process)f
5259	(statistics)3 1043 y(45.)23 b(which:)16 b(look)10 b(for)i(a)g(\256le)f
5260	(called)h(name)3 1137 y(46.)23 b(write)p 180 1137 V 16
5261	w(blif:)16 b(determinize,)11 b(encode)h(and)f(write)g(an)h(hnode)f(to)g
5262	(a)h(blif)e(\256le)3 1231 y(47.)23 b(write)p 180 1231
5263	V 16 w(blif)p 260 1231 V 16 w(mv:)15 b(write)d(a)f(blif-mv)g(\256le)3
5264	1325 y(48.)23 b(write)p 180 1325 V 16 w(order:)17 b(write)11
5265	b(the)g(current)h(order)g(of)f(the)g(MDD)g(v)o(ariables)g(of)h(the)f
5266	(\257attened)h(network)906 2835 y(43)p eop
5267	%%Page: 44 45
5268	44 44 bop -31 343 a Fs(Bibliograph)n(y)15 566 y Fq([1])23
5269	b(D.E.)c(Thomas,)g(P)-5 b(.R.)20 b(Moorby)m(.)34 b(The)18
5270	b(V)-5 b(erilog)17 b(Hardware)i(Description)e(Language.)35
5271	b(Kluwer)18 b(Academic)91 622 y(Publishers,)11 b(No)o(well,)g
5272	(Massachusetts,)g(1991.)15 716 y([2])23 b(S.-T)m(.)12
5273	b(Cheng.)17 b(Compiling)10 b(V)-5 b(erilog)11 b(into)f(automata.)17
5274	b(T)m(ech.)12 b(Rep.)g(UCB/ERL)g(M94/37,)f(May)g(1994.)15
5275	810 y([3])23 b(F)l(.)15 b(Balarin,)g(and)f(R.)h(Brayton,)g(and)f(S-T)m
5276	(.)h(Cheng,)g(and)f(D.)g(Kirkpatrick,)h(and)f(A.)g(Sangio)o(v)o(anni-V)
5277	m(incentelli.)91 866 y(A)i(Methodology)f(for)h(F)o(ormal)h(V)-5
5278	b(eri\256cation)16 b(of)h(Real-T)n(ime)g(Systems.)29
5279	b(T)m(ech.)17 b(Rep.)g(UCB/ERL)g(M95/11,)91 923 y(February)12
5280	b(1995.)15 1017 y([4])23 b(E.M.)10 b(Sento)o(vich)g(et)h(al.)j(SIS:)d
5281	(a)g(system)e(for)h(sequential)f(circuit)h(synthesis.)j(T)m(ech.)e
5282	(Rep.)g(M92/41,)f(May)f(1992.)15 1111 y([5])23 b(C.)12
5283	b(Mead,)g(L.)g(Conway)m(.)k(Introduction)10 b(to)h(VLSI)h(systems.)k
5284	(Addison-W)l(esle)o(y)m(,)11 b(1980.)15 1204 y([6])23
5285	b(R.)9 b(K.)g(Brayton)g(et)f(al.)k(HSIS:)d(A)f(BDD)h(based)g(system)e
5286	(for)i(formal)f(v)o(eri\256cation.)k(Proc.)e(of)e(Design)g(Automation)
5287	91 1261 y(Conference,)13 b(1994.)15 1355 y([7])23 b(E.)7
5288	b(Clarke,)i(and)e(O.)g(Grumber)o(g,)h(and)f(K.)g(McMillan,)g(and)g(X.)g
5289	(Zhao.)j(Ef)o(\256cient)d(generation)g(of)g(countere)o(xamples)91
5290	1411 y(and)k(witnesses)g(in)g(symbolic)e(model)i(checking.)17
5291	b(Proc.)12 b(of)g(Design)e(Automation)g(Conference,)j(1995.)906
5292	2835 y(44)p eop
5293	%%Trailer
5294	end
5295	userdict /end-hook known{end-hook}if
5296	%%EOF

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