public void TestIntZ3()
{
var solver = new Z3Provider();
var isNeg = solver.MkLt(solver.MkVar(0, solver.IntSort), solver.MkInt(0));
var isPos = solver.MkLt(solver.MkInt(0), solver.MkVar(0, solver.IntSort));
var sort = solver.CharacterSort;
//if x has a negative label then x has successor y with a nonnegative label
var x = new Variable("x", true);
var y = new Variable("y", true);
var psi = new MSOImplies <Expr>(
new MSOPredicate <Expr>(isNeg, x),
new MSOExists <Expr>(y,
new MSOAnd <Expr>(
new MSOSuccN <Expr>(x, y, 1),
new MSOPredicate <Expr>(isPos, y)
)
)
);
//all negative labels are immediately followed by a positive label
MSOFormula <Expr> phi = new MSOForall <Expr>(x, psi);
var ca = new CartesianAlgebraBDD <Expr>(solver);
var aut_psi = psi.GetAutomaton(ca).Determinize().Minimize();
var aut_phi = phi.GetAutomaton(solver).Determinize().Minimize();
Assert.IsFalse(aut_phi.IsEmpty);
//aut_phi.ShowGraph("aut_phi");
//aut_psi.ShowGraph("aut_psi");
}
public void TestMSO_Succ()
{
var solver = new CharSetSolver(BitWidth.BV32);
var x = new Variable("x", true);
var y = new Variable("y", true);
MSOFormula <BDD> phi = new MSOForall <BDD>(x,
new MSOImplies <BDD>(
new MSOPredicate <BDD>(solver.MkCharConstraint('c'), x),
new MSOExists <BDD>(y,
new MSOAnd <BDD>(
new MSOSuccN <BDD>(x, y, 1),
new MSOPredicate <BDD>(solver.MkCharConstraint('a'), y)
)
)
)
);
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, "^(ca|[^c])*$"));
}
var aut2 = solver.RegexConverter.Convert("^(ca|[^c])*$");
Assert.IsTrue(aut2.IsEquivalentWith(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_Forall()
{
var solver = new CharSetSolver(BitWidth.BV16);
var x = new Variable("x", true);
MSOFormula<BDD> phi = new MSOForall<BDD>(x, new MSOPredicate<BDD>(solver.MkCharConstraint('c',true), x));
var aut = phi.GetAutomaton(solver);
//aut.ShowGraph("aut");
for (int i = 0; i < 10; i++)
{
TestContext.WriteLine(solver.GenerateMember(aut));
}
var aut2 = solver.RegexConverter.Convert("^(c|C)*$");
//aut2.ShowGraph("aut2");
Assert.IsTrue(aut2.IsEquivalentWith(aut));
}
public void TestMSO_Or()
{
var solver = new CharSetSolver(BitWidth.BV32);
MSOFormula<BDD> phi = new MSOForall<BDD>(V1("x"),
new MSOOr<BDD>(
new MSOPredicate<BDD>(solver.MkCharConstraint( 'c'), V1("x")),
new MSOPredicate<BDD>(solver.MkCharConstraint( 'a'), V1("x"))
)
);
var aut = phi.GetAutomaton(solver);
for (int i = 0; i < 10; i++)
{
var s = solver.GenerateMember(aut);
Assert.IsTrue(System.Text.RegularExpressions.Regex.IsMatch(s, "^[ac]*$"));
}
var aut2 = solver.RegexConverter.Convert("^[ac]*$");
Assert.IsTrue(aut2.IsEquivalentWith(aut));
}