public void TestWS1S_SuccDef_GetAutomaton()
{
var solver = new CharSetSolver(BitWidth.BV7);
var x = new Variable("x", true);
var y = new Variable("y", true);
var z = new Variable("z", true);
var xLTy = new MSOLt <BDD>(x, y);
var xLTzLTy = new MSOAnd <BDD>(new MSOLt <BDD>(x, z), new MSOLt <BDD>(z, y));
var Ez = new MSOExists <BDD>(z, xLTzLTy);
var notEz = new MSONot <BDD>(Ez);
var xSyDef = new MSOAnd <BDD>(xLTy, notEz);
var ca = new CartesianAlgebraBDD <BDD>(solver);
var aut_xSyDef = xSyDef.GetAutomaton(ca);
var aut_xLTzLTy = xLTzLTy.GetAutomaton(ca);
var aut_Ez = Ez.GetAutomaton(ca);
var aut_notEz = notEz.GetAutomaton(ca);
var aut_xLTy = xLTy.GetAutomaton(ca);
//aut_xSyDef.ShowGraph("aut_xSyDEf");
//aut_xLTzLTy.ShowGraph("aut_xLTzLTy");
//aut_Ez.ShowGraph("aut_Ez");
//aut_notEz.ShowGraph("aut_notEz");
var xSyPrim = new MSOSuccN <BDD>(x, y, 1);
var aut_xSyPrim = xSyPrim.GetAutomaton(ca);
var equiv = aut_xSyPrim.IsEquivalentWith(aut_xSyDef);
Assert.IsTrue(equiv);
}
public void TestWS1S_SuccDef_GetAutomatonBDD()
{
var solver = new CharSetSolver(BitWidth.BV7);
var nrOfLabelBits = (int)BitWidth.BV7;
var x = new Variable("x", true);
var y = new Variable("y", true);
var z = new Variable("z", true);
var xLTy = new MSOLt <BDD>(x, y);
var xLTzLTy = new MSOAnd <BDD>(new MSOLt <BDD>(x, z), new MSOLt <BDD>(z, y));
var Ez = new MSOExists <BDD>(z, xLTzLTy);
var notEz = new MSONot <BDD>(Ez);
var xSyDef = new MSOAnd <BDD>(xLTy, notEz);
var aut_xSyDef = xSyDef.GetAutomaton(solver);
var aut_xLTzLTy = xLTzLTy.GetAutomaton(solver);
var aut_Ez = Ez.GetAutomaton(solver).Determinize().Minimize();
var aut_notEz = notEz.GetAutomaton(solver);
var aut_xLTy = xLTy.GetAutomaton(solver);
//aut_xSyDef.ShowGraph("aut_xSyDEf");
//aut_xLTzLTy.ShowGraph("aut_xLTzLTy");
//aut_Ez.ShowGraph("aut_Ez");
//aut_notEz.ShowGraph("aut_notEz");
var xSyPrim = new MSOSuccN <BDD>(x, y, 1);
var aut_xSyPrim = xSyPrim.GetAutomaton(solver);
var equiv = aut_xSyPrim.IsEquivalentWith(aut_xSyDef);
Assert.IsTrue(equiv);
}
public void BooleanAlgebraZ3_test2()
{
var ctx = new Context();
var sort = ctx.IntSort;
var solver = new Z3BoolAlg(ctx, sort);
var alg = new BDDAlgebra <BoolExpr>(solver);
var x = new Variable("x", true);
var y = new Variable("y", true);
var z = new Variable("z", true);
var xLTy = new MSOLt <BoolExpr>(x, y);
var xLTzLTy = new MSOAnd <BoolExpr>((new MSOLt <BoolExpr>(x, z)), (new MSOLt <BoolExpr>(z, y)));
var Ez = new MSOExists <BoolExpr>(z, xLTzLTy);
var notEz = new MSONot <BoolExpr>(Ez);
var xSyDef = new MSOAnd <BoolExpr>(xLTy, notEz);
var aut_xSyDef = xSyDef.GetAutomaton(alg);
var aut_xLTzLTy = xLTzLTy.GetAutomaton(alg);
var aut_Ez = Ez.GetAutomaton(alg);
var aut_notEz = notEz.GetAutomaton(alg);
var aut_xLTy = xLTy.GetAutomaton(alg);
//aut_xSyDef.ShowGraph("aut_xSyDEf");
//aut_xLTzLTy.ShowGraph("aut_xLTzLTy");
//aut_Ez.ShowGraph("aut_Ez");
//aut_notEz.ShowGraph("aut_notEz");
var xSyPrim = new MSOSuccN <BoolExpr>(x, y, 1);
var aut_xSyPrim = xSyPrim.GetAutomaton(alg);
var equiv = aut_xSyPrim.IsEquivalentWith(aut_xSyDef);
Assert.IsTrue(equiv);
}
public void TestMSO_Neg()
{
var solver = new CharSetSolver(BitWidth.BV7);
//var phi = new MSOTrue();
MSOFormula<BDD> phi = new MSONot<BDD>(new MSOExists<BDD>(V1("x"), new MSOPredicate<BDD>(solver.MkCharConstraint( 'c'), V1("x"))));
var aut = phi.GetAutomaton(solver);
for (int i = 0; i < 10; i++)
{
var s = solver.GenerateMember(aut);
Assert.IsTrue(System.Text.RegularExpressions.Regex.IsMatch(s, "^[^c]*$"));
}
var aut2 = solver.RegexConverter.Convert("^[^c]*$");
Assert.IsTrue(aut2.IsEquivalentWith(aut));
}
public void TestWS1S_NotLabel()
{
var solver = new CharSetSolver(BitWidth.BV7);
//var x1 = new Variable("x1", false);
var x = new Variable("x", false);
var pred = new MSOPredicate <BDD>(solver.MkCharConstraint('c'), x);
var fo_x = new MSOIsSingleton <BDD>(x);
var ca = new CartesianAlgebraBDD <BDD>(solver);
var lab = new MSOAnd <BDD>(pred, fo_x);
MSOFormula <BDD> not_lab = new MSONot <BDD>(lab);
var not_lab_actual = new MSOAnd <BDD>(not_lab, fo_x);
var aut_not_lab = not_lab_actual.GetAutomaton(ca);
var aut_not_lab_prelim = not_lab.GetAutomaton(ca);
var c_aut_lab = lab.GetAutomaton(ca).Complement().Minimize();
//c_aut_lab.ShowGraph("c_aut_lab");
//aut_not_lab.ShowGraph("aut_not_lab");
//aut_not_lab_prelim.ShowGraph("aut_not_lab_prelim");
//TBD: equivalence
}
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;
}
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);
}
