private Variable ConvertSet(MonaExpr set, MapStack <string, MonaParam> locals, out MSOFormula <BDD> psi)
{
if (set.NrOfSubexprs == 0)
{
return(ConvertEmptyset(out psi));
}
MSOFormula <BDD> disj = null;
Variable x = MkNewVar1();
Variable X = MkNewVar2();
for (int i = 0; i < set.NrOfSubexprs; i++)
{
MonaExpr t = set[i];
if (t.symbol.Kind == Tokens.RANGE)
{
MSOFormula <BDD> from_psi;
Variable from = ConvertTerm1(t[0], locals, out from_psi);
MSOFormula <BDD> to_psi;
Variable to = ConvertTerm1(t[1], locals, out to_psi);
MSOFormula <BDD> range = AddConstraints(from_psi, from, to_psi, to,
new MSOAnd <BDD>(new MSOLe <BDD>(from, x), new MSOLe <BDD>(x, to)));
if (disj == null)
{
disj = range;
}
else
{
disj = new MSOOr <BDD>(disj, range);
}
}
else
{
MSOFormula <BDD> y_psi;
Variable y = ConvertTerm1(t, locals, out y_psi);
MSOFormula <BDD> elem = new MSOEq <BDD>(x, y);
if (y_psi != null)
{
elem = new MSOExists <BDD>(y, new MSOAnd <BDD>(y_psi, elem));
}
if (disj == null)
{
disj = elem;
}
else
{
disj = new MSOOr <BDD>(disj, elem);
}
}
}
var pred = new MSOForall <BDD>(x, new MSOEquiv <BDD>(new MSOIn <BDD>(x, X), disj));
psi = pred;
return(X);
}
static Automaton <T> CreateAutomaton1 <T>(Func <int, T> f, int bitWidth, IBooleanAlgebra <T> Z)
{
Func <int, string, MSOPredicate <T> > pred = (i, s) => new MSOPredicate <T>(f(i), new Variable(s, true));
MSOFormula <T> phi = new MSOFalse <T>();
for (int index = 0; index < bitWidth; index++)
{
var phi1 = pred(index, "var");
phi = new MSOOr <T>(phi, phi1);
}
phi = new MSOExists <T>(new Variable("var", true), phi);
var aut = phi.GetAutomaton(Z);
return(aut);
}
public void TestCountNoProduct2()
{
int maxvars = 13;
var solver = new CharSetSolver(BitWidth.BV7);
Stopwatch sw = new Stopwatch();
var tries = 1;
var times = new long[maxvars - 1];
var x = new Variable("x", true);
var y = new Variable("y", true);
for (int k = 0; k < tries; k++)
{
for (int vars = 8; vars <= maxvars; vars++)
{
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int i = 1; i < vars; i++)
{
phi = new MSOAnd <BDD>(phi, new MSOLt <BDD>(new Variable("x" + i, true), new Variable("x" + (i + 1), true)));
phi = new MSOAnd <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('a'), new Variable("x" + i, true)));
phi = new MSOOr <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('k'), new Variable("x" + i, true)));
}
phi = new MSOAnd <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('a'), new Variable("x" + vars, true)));
phi = new MSOOr <BDD>(phi,
new MSOExists <BDD>(y,
new MSOPredicate <BDD>(solver.MkCharConstraint('c'), y)));
for (int i = vars; i >= 1; i--)
{
phi = new MSOExists <BDD>(new Variable("x" + i, true), phi);
}
sw.Restart();
//var aut1 = phi.GetAutomaton(new CartesianAlgebraBDD<BDD>(solver));
var aut1 = phi.GetAutomaton(solver);
sw.Stop();
times[vars - 2] += sw.ElapsedMilliseconds;
//Console.WriteLine("States {0} Trans {1}",aut1.StateCount,aut1.MoveCount);
if (k == tries - 1)
{
TestContext.WriteLine(string.Format("{0} variables; {1} ms", vars, times[vars - 2] / tries));
}
//solver.ShowGraph(aut1, "a"+vars);
}
}
}
Automaton <T> CreateAutomaton2 <T>(Func <int, T> f, int bitWidth, IBooleanAlgebra <T> Z)
{
Func <int, Variable, MSOPredicate <T> > pred = (i, s) => new MSOPredicate <T>(f(i), s);
MSOFormula <T> phi = new MSOFalse <T>();
for (int index = 0; index < bitWidth; index++)
{
MSOFormula <T> phi1 = pred(index, V1("var"));
phi1 = new MSOExists <T>(V1("var"), phi1);
phi = new MSOOr <T>(phi, phi1);
}
phi = new MSOExists <T>(V1("var"), phi);
var aut = phi.GetAutomaton(Z);
return(aut);
}
Automaton <T> CreateAutomaton1 <T>(Func <int, T> f, int bitWidth, IBooleanAlgebra <T> Z)
{
Func <int, string, MSOPredicate <T> > pred = (i, s) => new MSOPredicate <T>(f(i), s);
MSOFormula <T> phi = new MSOFalse <T>();
for (int index = 0; index < bitWidth; index++)
{
var phi1 = pred(index, "var");
phi = new MSOOr <T>(phi, phi1);
}
phi = new MSOExistsFo <T>("var", phi);
var aut = phi.GetAutomaton(Z);
//aut.ShowGraph("aut");
return(aut);
}
public void TestCount()
{
int maxvars = 10;
var solver = new CharSetSolver(BitWidth.BV16);
Stopwatch sw = new Stopwatch();
var tries = 1;
var times = new long[maxvars - 1];
for (int k = 0; k < tries; k++)
{
for (int vars = 8; vars <= maxvars; vars++)
{
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int i = 1; i < vars; i++)
{
phi = new MSOAnd <BDD>(phi, new MSOLt <BDD>(V1("x" + i), V1("x" + (i + 1))));
phi = new MSOAnd <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('a'), V1("x" + i)));
}
phi = new MSOAnd <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('a'), V1("x" + vars)));
phi = new MSOOr <BDD>(phi,
new MSOExists <BDD>(V1("y"),
new MSOPredicate <BDD>(solver.MkCharConstraint('c'), V1("y"))));
for (int i = vars; i >= 1; i--)
{
phi = new MSOExists <BDD>(V1("x" + i), phi);
}
sw.Restart();
//var aut1 = phi.GetAutomaton(new CartesianAlgebraBDD<BDD>(solver));
var aut1 = phi.GetAutomaton(solver);
//aut1.ShowGraph();
sw.Stop();
times[vars - 2] += sw.ElapsedMilliseconds;
if (k == tries - 1)
{
TestContext.WriteLine(string.Format("{0} variables; {1} ms", vars, times[vars - 2] / tries));
}
}
}
}
public void TestMSO_NotLt()
{
var solver = new CharSetSolver(BitWidth.BV7);
var ca = new CartesianAlgebraBDD<BDD>(solver);
var x = new Variable("x", true);
var y = new Variable("y", true);
MSOFormula<BDD> not_xLTy = new MSONot<BDD>(new MSOLt<BDD>(x,y));
MSOFormula<BDD> xEQy = new MSOEq<BDD>(x, y);
var xGTy = new MSOLt<BDD>(y, x);
var xGEy = new MSOOr<BDD>(xEQy, xGTy);
var aut_not_xLTy = not_xLTy.GetAutomaton(ca);
var aut_xGEy = xGEy.GetAutomaton(ca);
var c_aut_xLTy = (new MSOLt<BDD>(x,y)).GetAutomaton(ca).Complement().Determinize().Minimize();
//c_aut_xLTy = c_aut_xLTy.Intersect(aut_fo, ca).Determinize(ca).Minimize(ca); //*
//aut_not_xLTy.ShowGraph("aut_not_xLTy");
//aut_xGEy.ShowGraph("aut_xGEy");
//c_aut_xLTy.ShowGraph("c_aut_xLTy");
var equiv1 = aut_not_xLTy.IsEquivalentWith(aut_xGEy);
//var equiv2 = aut_not_xLTy.IsEquivalentWith(c_aut_xLTy, ca);
Assert.IsTrue(equiv1);
//Assert.IsTrue(equiv2);
}
private static Pair<MSOFormula<BoolExpr>, List<BoolExpr>> GenerateMSOFormula(int maxVarIndex)
{
int randomNumber = random.Next(0, 8);
size--;
if (size <= 0)
{
int variable = random.Next(0, maxVarIndex-1);
BoolExpr b = GeneratePredicateOut(200);
List<BoolExpr> l = new List<BoolExpr>();
l.Add(b);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(new MSOPredicate<BoolExpr>(b, new Variable("x"+variable, true)), l);
}
switch (randomNumber)
{
case 0:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex + 1);
MSOFormula<BoolExpr> phi = new MSOExists<BoolExpr>(new Variable("x"+maxVarIndex, true), phi1.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, phi1.Second);
}
case 1:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex + 1);
MSOFormula<BoolExpr> phi = new MSOForall<BoolExpr>(new Variable("x" + maxVarIndex, true), phi1.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, phi1.Second);
}
case 2:
case 3:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex);
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi2 = GenerateMSOFormula(maxVarIndex);
MSOFormula<BoolExpr> phi = new MSOAnd<BoolExpr>(phi1.First, phi2.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, new List<BoolExpr>(phi1.Second.Union(phi2.Second)));
}
case 4:
case 5:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex);
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi2 = GenerateMSOFormula(maxVarIndex);
MSOFormula<BoolExpr> phi = new MSOOr<BoolExpr>(phi1.First, phi2.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, new List<BoolExpr>(phi1.Second.Union(phi2.Second)));
}
case 6:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex);
MSOFormula<BoolExpr> phi = new MSONot<BoolExpr>(phi1.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, phi1.Second);
}
case 7:
{
if (maxVarIndex > 1)
{
int variable1 = random.Next(0, maxVarIndex - 1);
int variable2 = random.Next(0, maxVarIndex - 1);
if (variable1 == variable2)
{
if (variable1 == maxVarIndex - 1)
variable1 = variable1 - 1;
else
variable2 = variable2 + 1;
}
//Successor
MSOFormula<BoolExpr> phi = new MSOSuccN<BoolExpr>(varOf(variable1),varOf(variable2),random.Next(1,4));
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, new List<BoolExpr>());
}
else
{
int variable = random.Next(0, maxVarIndex - 1);
BoolExpr b = GeneratePredicate();
List<BoolExpr> l = new List<BoolExpr>();
l.Add(b);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(new MSOPredicate<BoolExpr>(b, new Variable("x" + variable, true)), l);
}
}
case 8:
{
int variable1 = random.Next(0, maxVarIndex - 1);
int variable2 = random.Next(0, maxVarIndex - 1);
//less than
MSOFormula<BoolExpr> phi = new MSOLe<BoolExpr>(varOf(variable1), varOf(variable2));
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, new List<BoolExpr>());
}
}
return null;
}
public static void RunPOPLTests()
{
//// all x1...xn. xi<xi+1
List <Pair <MSOFormula <BDD>, CharSetSolver> > phis = new List <Pair <MSOFormula <BDD>, CharSetSolver> >();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver();
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, leq);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
phis.Add(new Pair <MSOFormula <BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"..\popl14-1.csv"), phis);
// all x1...xn. xi<xi+1 and a(xi)
phis = new List <Pair <MSOFormula <BDD>, CharSetSolver> >();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new MSOPredicate <BDD>(
solver.MkCharConstraint('a', false), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
phis.Add(new Pair <MSOFormula <BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"..\popl14-2.csv"), phis);
// all x1...xn. (xi<xi+1 and a(xi)) and ex y. c(y)
phis = new List <Pair <MSOFormula <BDD>, CharSetSolver> >();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new MSOPredicate <BDD>(solver.MkCharConstraint('a', false), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
var exycy = new MSOExists <BDD>(new Variable("y", true), new MSOPredicate <BDD>(solver.MkCharConstraint('c', false), new Variable("y", true)));
phi = new MSOAnd <BDD>(phi, exycy);
phis.Add(new Pair <MSOFormula <BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"..\popl14-3.csv"), phis);
// all x1...xn. (xi<xi+1 and a(xi) \/ c(xi))
phis = new List <Pair <MSOFormula <BDD>, CharSetSolver> >();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
var axk = new MSOPredicate <BDD>(solver.MkCharConstraint('a', false), new Variable("x" + (k - 1), true));
var cxk = new MSOPredicate <BDD>(solver.MkCharConstraint('c', false), new Variable("x" + (k - 1), true));
var inter = new MSOOr <BDD>(new MSOAnd <BDD>(leq, axk), cxk);
phi = new MSOAnd <BDD>(phi, inter);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
MSOFormula <BDD> exycy = new MSOExists <BDD>(new Variable("y", true), new MSOPredicate <BDD>(solver.MkCharConstraint('c', false), new Variable("y", true)));
phi = new MSOAnd <BDD>(phi, exycy);
phis.Add(new Pair <MSOFormula <BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"..\popl14-4.csv"), phis, 10, 10, 11);
}
private static Pair <MSOFormula <BoolExpr>, List <BoolExpr> > GenerateMSOFormula(int maxVarIndex)
{
int randomNumber = random.Next(0, 8);
size--;
if (size <= 0)
{
int variable = random.Next(0, maxVarIndex - 1);
BoolExpr b = GeneratePredicateOut(200);
List <BoolExpr> l = new List <BoolExpr>();
l.Add(b);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(new MSOPredicate <BoolExpr>(b, new Variable("x" + variable, true)), l));
}
switch (randomNumber)
{
case 0:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex + 1);
MSOFormula <BoolExpr> phi = new MSOExists <BoolExpr>(new Variable("x" + maxVarIndex, true), phi1.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, phi1.Second));
}
case 1:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex + 1);
MSOFormula <BoolExpr> phi = new MSOForall <BoolExpr>(new Variable("x" + maxVarIndex, true), phi1.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, phi1.Second));
}
case 2:
case 3:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex);
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi2 = GenerateMSOFormula(maxVarIndex);
MSOFormula <BoolExpr> phi = new MSOAnd <BoolExpr>(phi1.First, phi2.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, new List <BoolExpr>(phi1.Second.Union(phi2.Second))));
}
case 4:
case 5:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex);
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi2 = GenerateMSOFormula(maxVarIndex);
MSOFormula <BoolExpr> phi = new MSOOr <BoolExpr>(phi1.First, phi2.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, new List <BoolExpr>(phi1.Second.Union(phi2.Second))));
}
case 6:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex);
MSOFormula <BoolExpr> phi = new MSONot <BoolExpr>(phi1.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, phi1.Second));
}
case 7:
{
if (maxVarIndex > 1)
{
int variable1 = random.Next(0, maxVarIndex - 1);
int variable2 = random.Next(0, maxVarIndex - 1);
if (variable1 == variable2)
{
if (variable1 == maxVarIndex - 1)
{
variable1 = variable1 - 1;
}
else
{
variable2 = variable2 + 1;
}
}
//Successor
MSOFormula <BoolExpr> phi = new MSOSuccN <BoolExpr>(varOf(variable1), varOf(variable2), random.Next(1, 4));
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, new List <BoolExpr>()));
}
else
{
int variable = random.Next(0, maxVarIndex - 1);
BoolExpr b = GeneratePredicate();
List <BoolExpr> l = new List <BoolExpr>();
l.Add(b);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(new MSOPredicate <BoolExpr>(b, new Variable("x" + variable, true)), l));
}
}
case 8:
{
int variable1 = random.Next(0, maxVarIndex - 1);
int variable2 = random.Next(0, maxVarIndex - 1);
//less than
MSOFormula <BoolExpr> phi = new MSOLe <BoolExpr>(varOf(variable1), varOf(variable2));
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, new List <BoolExpr>()));
}
}
return(null);
}
private Variable ConvertSet(MonaExpr set, MapStack<string, MonaParam> locals, out MSOFormula<BDD> psi)
{
if (set.NrOfSubexprs == 0)
return ConvertEmptyset(out psi);
MSOFormula<BDD> disj = null;
Variable x = MkNewVar1();
Variable X = MkNewVar2();
for (int i=0; i < set.NrOfSubexprs; i++)
{
MonaExpr t = set[i];
if (t.symbol.Kind == Tokens.RANGE)
{
MSOFormula<BDD> from_psi;
Variable from = ConvertTerm1(t[0], locals, out from_psi);
MSOFormula<BDD> to_psi;
Variable to = ConvertTerm1(t[1], locals, out to_psi);
MSOFormula<BDD> range = AddConstraints(from_psi, from, to_psi, to,
new MSOAnd<BDD>(new MSOLe<BDD>(from, x), new MSOLe<BDD>(x, to)));
if (disj == null)
disj = range;
else
disj = new MSOOr<BDD>(disj, range);
}
else
{
MSOFormula<BDD> y_psi;
Variable y = ConvertTerm1(t, locals, out y_psi);
MSOFormula<BDD> elem = new MSOEq<BDD>(x, y);
if (y_psi != null)
elem = new MSOExists<BDD>(y, new MSOAnd<BDD>(y_psi, elem));
if (disj == null)
disj = elem;
else
disj = new MSOOr<BDD>(disj, elem);
}
}
var pred = new MSOForall<BDD>(x, new MSOEquiv<BDD>(new MSOIn<BDD>(x, X), disj));
psi = pred;
return X;
}
public static void RunPOPLTests()
{
//// all x1...xn. xi<xi+1
List<Pair<MSOFormula<BDD>, CharSetSolver>> phis = new List<Pair<MSOFormula<BDD>, CharSetSolver>>();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver();
MSOFormula<BDD> phi = new MSOTrue<BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt<BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, leq);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists<BDD>(new Variable("x" + k, true), phi);
}
phis.Add(new Pair<MSOFormula<BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"popl14-1.csv"), phis);
// all x1...xn. xi<xi+1 and a(xi)
phis = new List<Pair<MSOFormula<BDD>, CharSetSolver>>();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula<BDD> phi = new MSOTrue<BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt<BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new MSOPredicate<BDD>(
solver.MkCharConstraint('a', false), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists<BDD>(new Variable("x" + k, true), phi);
}
phis.Add(new Pair<MSOFormula<BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"popl14-2.csv"), phis);
// all x1...xn. (xi<xi+1 and a(xi)) and ex y. c(y)
phis = new List<Pair<MSOFormula<BDD>, CharSetSolver>>();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula<BDD> phi = new MSOTrue<BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt<BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new MSOPredicate<BDD>(solver.MkCharConstraint('a', false), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists<BDD>(new Variable("x" + k, true), phi);
}
var exycy = new MSOExists<BDD>(new Variable("y", true), new MSOPredicate<BDD>(solver.MkCharConstraint('c', false), new Variable("y", true)));
phi = new MSOAnd<BDD>(phi, exycy);
phis.Add(new Pair<MSOFormula<BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"popl14-3.csv"), phis);
// all x1...xn. (xi<xi+1 and a(xi) \/ c(xi))
phis = new List<Pair<MSOFormula<BDD>, CharSetSolver>>();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula<BDD> phi = new MSOTrue<BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt<BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
var axk = new MSOPredicate<BDD>(solver.MkCharConstraint('a', false), new Variable("x" + (k - 1), true));
var cxk = new MSOPredicate<BDD>(solver.MkCharConstraint('c', false), new Variable("x" + (k - 1), true));
var inter = new MSOOr<BDD>(new MSOAnd<BDD>(leq, axk), cxk);
phi = new MSOAnd<BDD>(phi, inter);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists<BDD>(new Variable("x" + k, true), phi);
}
MSOFormula<BDD> exycy = new MSOExists<BDD>(new Variable("y", true), new MSOPredicate<BDD>(solver.MkCharConstraint('c', false), new Variable("y", true)));
phi = new MSOAnd<BDD>(phi, exycy);
phis.Add(new Pair<MSOFormula<BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"popl14-4.csv"), phis, 11, 11, 11);
}
