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source: vis_dev/vis-2.1/doc/vis_user.ps @ 12

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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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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
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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
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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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1914	% Polyline
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1926
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1932
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1938
1939	n 5069.41 7210.57 m 5175.00 7275.00 l 5051.51 7267.84 l gs col-1 s gr
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1944
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1951
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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
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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
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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
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2034	8775 1275 m
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2043	4425 8325 m
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2061	8400 7500 m
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2100	1200 3825 m
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2436	n 4213 1448 m 4163 1583 l gs col13 0.25 tnt ef gr gs col-1 s gr
2437	n 4218.92 1518.40 m 4163.00 1583.00 l 4162.65 1497.56 l gs col-1 s gr
2438	% Polyline
2439	n 4353 1443 m 4408 1583 l gs col13 0.25 tnt ef gr gs col-1 s gr
2440	n 4406.67 1497.57 m 4408.00 1583.00 l 4350.83 1519.51 l gs col-1 s gr
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2442	4230 1389 m
2443	gs 1 -1 sc (R) col-1 show gr
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2445	4007 1024 m
2446	gs 1 -1 sc (R) col-1 show gr
2447	% Polyline
2448	n 3348 1458 m 3298 1593 l gs col13 0.25 tnt ef gr gs col-1 s gr
2449	n 3353.92 1528.40 m 3298.00 1593.00 l 3297.65 1507.56 l gs col-1 s gr
2450	% Polyline
2451	n 3488 1453 m 3543 1593 l gs col13 0.25 tnt ef gr gs col-1 s gr
2452	n 3541.67 1507.57 m 3543.00 1593.00 l 3485.83 1529.51 l gs col-1 s gr
2453	/Times-Roman findfont 180.00 scalefont setfont
2454	3369 1404 m
2455	gs 1 -1 sc (Y) col-1 show gr
2456	% Polyline
2457	n 4130 1078 m 4185 1218 l gs col13 0.25 tnt ef gr gs col-1 s gr
2458	n 4183.67 1132.57 m 4185.00 1218.00 l 4127.83 1154.51 l gs col-1 s gr
2459	% Polyline
2460	n 3990 1083 m 3940 1218 l gs col13 0.25 tnt ef gr gs col-1 s gr
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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2466	3790 649 m
2467	gs 1 -1 sc (R) col-1 show gr
2468	% Polyline
2469	n 3283 1828 m 3338 1968 l gs col13 0.25 tnt ef gr gs col-1 s gr
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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2476	gs 1 -1 sc (G) col-1 show gr
2477	% Polyline
2478	n 3453 1835 m 3403 1970 l gs col13 0.25 tnt ef gr gs col-1 s gr
2479	n 3458.92 1905.40 m 3403.00 1970.00 l 3402.65 1884.56 l gs col-1 s gr
2480	% Polyline
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2482	n 3646.67 1884.57 m 3648.00 1970.00 l 3590.83 1906.51 l gs col-1 s gr
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2485	gs 1 -1 sc (Y) col-1 show gr
2486	% Polyline
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2488	n 3651.92 1523.40 m 3596.00 1588.00 l 3595.65 1502.56 l gs col-1 s gr
2489	% Polyline
2490	n 3786 1448 m 3841 1588 l gs col13 0.25 tnt ef gr gs col-1 s gr
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2492	/Times-Roman findfont 180.00 scalefont setfont
2493	3667 1399 m
2494	gs 1 -1 sc (G) col-1 show gr
2495	% Polyline
2496	n 3693 1078 m 3748 1218 l gs col13 0.25 tnt ef gr gs col-1 s gr
2497	n 3746.67 1132.57 m 3748.00 1218.00 l 3690.83 1154.51 l gs col-1 s gr
2498	% Polyline
2499	n 1986 901 m 2141 1131 l gs col-1 s gr
2500	n 2098.82 1014.72 m 2141.00 1131.00 l 2049.06 1048.25 l gs col-1 s gr
2501	% Polyline
2502	n 2086 1251 m 1761 1251 l gs col-1 s gr
2503	n 1881.00 1281.00 m 1761.00 1251.00 l 1881.00 1221.00 l gs col-1 s gr
2504	% Polyline
2505	n 1651 1121 m 1831 901 l gs col-1 s gr
2506	n 1731.79 974.88 m 1831.00 901.00 l 1778.23 1012.87 l gs col-1 s gr
2507	% Polyline
2508	n 3773 708 m 3723 843 l gs col13 0.25 tnt ef gr gs col-1 s gr
2509	n 3778.92 778.40 m 3723.00 843.00 l 3722.65 757.56 l gs col-1 s gr
2510	% Polyline
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2512	n 3966.67 757.57 m 3968.00 843.00 l 3910.83 779.51 l gs col-1 s gr
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
2517	1698.71 603.15 1724.16 549.28 1751 531 curveto
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
2529	2403.85 1028.00 2457.72 1054.00 2476 1081 curveto
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
2548	n 1423.25 1225.57 m 1501.00 1261.00 l 1419.13 1285.42 l gs col-1 s gr
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2550	2520 875 m
2551	gs 1 -1 sc (unwind) col-1 show gr
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2553	2605 1035 m
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2559	2151 1281 m
2560	gs 1 -1 sc (G) col-1 show gr
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2563	gs 1 -1 sc (Y) col-1 show gr
2564	$F2psEnd
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2570	(graph.)40 1122 y(F)o(ormulae)g(in)f(CTL)h(are)g(b)o(uilt)f(from)g
2571	(atomic)g(propositions)e(\(where)k(each)f(proposition)e(corresponds)h
2572	(to)g(a)h(v)o(ariable)-31 1178 y(in)16 b(the)h(model\),)g(standard)f
2573	(boolean)h(connecti)o(v)o(es)f(of)h(propositional)d(logic)i(\(e.g.,)j
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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
2577	(\()p Fp(A)g Fq(or)g Fp(E)s Fq(\))f(follo)o(wed)g(by)-31
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
2580	b(temporal)g(operators)h(are)h(interpreted)f(relati)o(v)o(e)g(to)g(an)g
2581	(implicit)f(\252current)-31 1347 y(state\272.)17 b(There)11
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2585	(indicates)f(whether)h(the)f(modality)f(de\256nes)j(a)f(property)f
2586	(that)h(should)e(be)i(true)-31 1460 y(of)e(all)g(those)g(possible)f
2587	(paths)h(\(denoted)g(by)g(uni)o(v)o(ersal)g(path)g(quanti\256er)g
2588	Fp(A)p Fq(\))g(or)h(whether)f(the)g(property)g(needs)g(only)g(hold)-31
2589	1517 y(on)i(some)f(path)g(\(denoted)g(by)h(e)o(xistential)f(path)g
2590	(quanti\256er)h Fp(E)s Fq(\).)16 b(The)10 b(temporal)g(modalities)f
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2593	(wing)d(intuiti)o(v)o(e)h(meaning:)26 1663 y(1.)23 b
2594	Fp(F)17 b(\036)10 b Fq(\(reads)h(\252)p Fp(\036)f Fq(holds)g(sometime)f
2595	(in)g(the)h(future\272\))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
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2894	Fp(L)p Fb(\()p Fp(S)s Fb(\))i Fj(\022)h Fp(L)p Fb(\()p
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2896	Fb(\()p Fp(S)s Fb(\))d Fj(\\)p 1461 424 100 2 v 11 w
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2913	b(The)8 b(fact)g(that)f(complementation)f(of)i(a)g(deterministic)e
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2919	(and)-31 1028 y(dif)o(\256culty)j(of)h(complementation.)31
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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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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
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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
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2967	(consists)f(of)i(modules)e(\(also)h(called)h Fi(hnodes)p
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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
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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
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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
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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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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
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3025	824 y(Model)h(name)f(=)h(sensor)-31 864 y(inputs)g(=)f(0,)h(outputs)g
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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
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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)
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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
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3052	Fi(\257atten)p 256 2218 V 16 w(hier)o(ar)n(c)o(hy)h Fq(automatically)f
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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
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3061	b(ne)o(xt)g(step)g(to)o(wards)f(v)o(eri\256cation)h(consists)f(of)h
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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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3076	b(with)h(combinational)e(c)o(ycles)j(cannot)f(be)h(ordered.)23
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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
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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
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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
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3101	y(the)c(MDDs)f(of)g(the)h(partition)e(represent)i(a)g(partial)f
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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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3684	%%Page: 36 37
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3732	b(although)f(not)h(\252formal)g(v)o(eri\256cation\272,)i(is)e(an)g
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3735	1631 V 15 w(partition)p 434 1631 V 15 w(mdds)g Fq(is)g(in)n(v)o(oked,)g
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3740	b(VIS)-31 1744 y(encompasses)c(both)g(formal)h(v)o(eri\256cation)g(and)
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5248	(v)o(ariables)g(of)h(the)f(\257attened)h(network)3 480
5249	y(39.)23 b(test)p 150 480 V 16 w(det)p 222 480 V 16 w(and)p
5250	304 480 V 16 w(comp)p 422 480 V 16 w(spec:)16 b(test)11
5251	b(if)h(the)f(outputs)f(are)i(completely)e(speci\256ed)i(and)f
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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