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);
}
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);
}
