public void TestMSO_Succ()
{
var solver = new CharSetSolver(BitWidth.BV32);
MSOFormula <BDD> phi = new MSOForallFo <BDD>("x",
new MSOIf <BDD>(
new MSOPredicate <BDD>(solver.MkCharConstraint('c'), "x"),
new MSOExistsFo <BDD>("y",
new MSOAnd <BDD>(
new MSOSucc <BDD>("x", "y"),
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, solver));
}
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 psi = new MSOIf <Expr>(
new MSOPredicate <Expr>(isNeg, "x"),
new MSOExistsFo <Expr>("y",
new MSOAnd <Expr>(
new MSOSucc <Expr>("x", "y"),
new MSOPredicate <Expr>(isPos, "y")
)
)
);
//all negative labels are immediately followed by a positive label
MSOFormula <Expr> phi = new MSOForallFo <Expr>("x", psi);
var ca = new CartesianAlgebraBDD <Expr>(solver);
var aut_psi = psi.GetAutomaton(ca, "x").Determinize(ca).Minimize(ca);
var aut_phi = phi.GetAutomaton(solver).Determinize(solver).Minimize(solver);
Assert.IsFalse(aut_phi.IsEmpty);
//aut_phi.ShowGraph("aut_phi");
//aut_psi.ShowGraph("aut_psi");
}
public void TestMSO_Forall()
{
var solver = new CharSetSolver(BitWidth.BV16);
MSOFormula <BDD> phi = new MSOForallFo <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, solver));
}
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);
}