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 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);
}
Automaton<T> CreateAutomaton3<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 MSOTrue<T>();
// x1<x2<x3<x4...
for (int index = 1; index < bitWidth; index++)
{
MSOFormula<T> phi1 = new MSOLt<T>(V1("x" + (index - 1)), V1("x" + index));
phi = new MSOAnd<T>(phi, phi1);
}
// bi(xi)
for (int index = 0; index < bitWidth; index++)
{
MSOFormula<T> phi1 = pred(index, V1("x" + index));
phi = new MSOAnd<T>(phi, phi1);
}
// exists forall...
for (int index = 0; index < bitWidth; index++)
{
if (index % 2 == 0)
phi = new MSOExists<T>(V1("x" + index), phi);
else
phi = new MSOForall<T>(V1("x" + index), phi);
}
var aut = phi.GetAutomaton(Z);
return aut;
}
public void TestWS1S_Forall_x_Exists_y_x_lt_y()
{
var triv = new TrivialBooleanAlgebra();
var ca = new BDDAlgebra<bool>(triv);
var x = new Variable("x", true);
var y = new Variable("y", true);
var x_lt_y = new MSOLt<bool>(x, y);
var aut_x_lt_y = x_lt_y.GetAutomaton(ca);
//aut_x_lt_y.ShowGraph("aut_x_lt_y");
var psi4 = new MSOForall<bool>(x, new MSOExists<bool>(y, (x_lt_y)));
var aut = psi4.GetAutomaton(ca);
//accepts only the empty word
Assert.IsTrue(aut.StateCount == 1 && aut.IsFinalState(aut.InitialState) && aut.MoveCount == 0);
}
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);
}
Automaton <T> CreateAutomaton3 <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 MSOTrue <T>();
// x1<x2<x3<x4...
for (int index = 1; index < bitWidth; index++)
{
MSOFormula <T> phi1 = new MSOLt <T>("x" + (index - 1), "x" + index);
phi = new MSOAnd <T>(phi, phi1);
}
// bi(xi)
for (int index = 0; index < bitWidth; index++)
{
MSOFormula <T> phi1 = pred(index, "x" + index);
phi = new MSOAnd <T>(phi, phi1);
}
// exists forall...
for (int index = 0; index < bitWidth; index++)
{
if (index % 2 == 0)
{
phi = new MSOExistsFo <T>("x" + index, phi);
}
else
{
phi = new MSOForallFo <T>("x" + index, phi);
}
}
Assert.IsTrue(phi.IsWellFormedFormula());
var aut = phi.GetAutomaton(Z);
return(aut);
}
static Automaton <T> CreateAutomaton3 <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 MSOTrue <T>();
// x1<x2<x3<x4...
for (int index = 1; index < bitWidth; index++)
{
MSOFormula <T> phi1 = new MSOLt <T>(new Variable("x" + (index - 1), true), new Variable("x" + index, true));
phi = new MSOAnd <T>(phi, phi1);
}
// bi(xi)
for (int index = 0; index < bitWidth; index++)
{
MSOFormula <T> phi1 = pred(index, "x" + index);
phi = new MSOAnd <T>(phi, phi1);
}
// exists forall...
for (int index = 0; index < bitWidth; index++)
{
if (index % 2 == 0)
{
phi = new MSOExists <T>(new Variable("x" + index, true), phi);
}
else
{
phi = new MSOForall <T>(new Variable("x" + index, true), phi);
}
}
var aut = phi.GetAutomaton(Z);
return(aut);
}
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);
}
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);
}