public void WS1SNot()
{
var solver = new CharSetSolver(BitWidth.BV64); //new solver using ASCII encoding
List <char> alph = new List <char> {
'a', 'b'
};
HashSet <char> al = new HashSet <char>(alph);
WS1SFormula f1 = new WS1SUnaryPred("X", solver.MkCharConstraint(false, 'a'));
WS1SFormula f2 = new WS1SSingleton("X");
WS1SFormula f = new WS1SAnd(f1, f2);
WS1SFormula phi = new WS1SNot(new WS1SExists("X", f));
var dfa = phi.getDFA(al, solver);
var test = solver.Convert(@"^b*$");
Assert.IsTrue(dfa.IsEquivalentWith(test, solver));
string file = "../../../MSOZ3Test/DotFiles/nota";
solver.SaveAsDot(dfa, "aut", file); //extension .dot is added automatically when missing
}
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 WS1SLt <BDD>(x, y);
var xLTzLTy = (new WS1SLt <BDD>(x, z)) & (new WS1SLt <BDD>(z, y));
var Ez = new WS1SExists <BDD>(z, xLTzLTy);
var notEz = new WS1SNot <BDD>(Ez);
var xSyDef = new WS1SAnd <BDD>(xLTy, notEz);
var aut_xSyDef = xSyDef.GetAutomatonBDD(solver, nrOfLabelBits, x, y);
var aut_xLTzLTy = xLTzLTy.GetAutomatonBDD(solver, nrOfLabelBits, x, y, z);
var aut_Ez = Ez.GetAutomatonBDD(solver, nrOfLabelBits, x, y).Determinize(solver).Minimize(solver);
var aut_notEz = notEz.GetAutomatonBDD(solver, nrOfLabelBits, x, y);
var aut_xLTy = xLTy.GetAutomatonBDD(solver, nrOfLabelBits, x, y);
//aut_xSyDef.ShowGraph("aut_xSyDEf");
//aut_xLTzLTy.ShowGraph("aut_xLTzLTy");
//aut_Ez.ShowGraph("aut_Ez");
//aut_notEz.ShowGraph("aut_notEz");
var xSyPrim = new WS1SSuccN <BDD>(x, y, 1);
var aut_xSyPrim = xSyPrim.GetAutomatonBDD(solver, nrOfLabelBits, x, y);
var equiv = aut_xSyPrim.IsEquivalentWith(aut_xSyDef, solver);
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 WS1SLt <BDD>(x, y);
var xLTzLTy = (new WS1SLt <BDD>(x, z)) & (new WS1SLt <BDD>(z, y));
var Ez = new WS1SExists <BDD>(z, xLTzLTy);
var notEz = new WS1SNot <BDD>(Ez);
var xSyDef = new WS1SAnd <BDD>(xLTy, notEz);
var ca = new CartesianAlgebraBDD <BDD>(solver);
var aut_xSyDef = xSyDef.GetAutomaton(ca, x, y);
var aut_xLTzLTy = xLTzLTy.GetAutomaton(ca, x, y, z);
var aut_Ez = Ez.GetAutomaton(ca, x, y);
var aut_notEz = notEz.GetAutomaton(ca, x, y);
var aut_xLTy = xLTy.GetAutomaton(ca, x, y);
//aut_xSyDef.ShowGraph("aut_xSyDEf");
//aut_xLTzLTy.ShowGraph("aut_xLTzLTy");
//aut_Ez.ShowGraph("aut_Ez");
//aut_notEz.ShowGraph("aut_notEz");
var xSyPrim = new WS1SSuccN <BDD>(x, y, 1);
var aut_xSyPrim = xSyPrim.GetAutomaton(ca, x, y);
var equiv = aut_xSyPrim.IsEquivalentWith(aut_xSyDef, ca);
Assert.IsTrue(equiv);
}
public void TestWS1S_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);
var fo = new WS1SSingleton <BDD>(x) & new WS1SSingleton <BDD>(y);
var aut_fo = fo.GetAutomaton(ca, x, y);
WS1SFormula <BDD> not_xLTy = new WS1SNot <BDD>(new WS1SLt <BDD>(x, y));
not_xLTy = new WS1SAnd <BDD>(not_xLTy, fo); //*
WS1SFormula <BDD> xEQy = new WS1SEq <BDD>(x, y);
xEQy = new WS1SAnd <BDD>(xEQy, fo); //*
var yGTx = new WS1SLt <BDD>(y, x);
var xEQy_or_yGTx = new WS1SAnd <BDD>(new WS1SOr <BDD>(xEQy, yGTx), fo);
var aut_not_xLTy = not_xLTy.GetAutomaton(ca, x, y);
var B = xEQy_or_yGTx.GetAutomaton(ca, x, y);
var c_aut_xLTy = (new WS1SLt <BDD>(x, y)).GetAutomaton(ca, x, y).Complement(ca).Determinize(ca).Minimize(ca);
//c_aut_xLTy = c_aut_xLTy.Intersect(aut_fo, ca).Determinize(ca).Minimize(ca); //*
//aut_not_xLTy.ShowGraph("aut_not_xLTy");
//B.ShowGraph("x_geq_y");
//c_aut_xLTy.ShowGraph("c_aut_xLTy");
var equiv1 = aut_not_xLTy.IsEquivalentWith(B, ca);
//var equiv2 = aut_not_xLTy.IsEquivalentWith(c_aut_xLTy, ca);
Assert.IsTrue(equiv1);
//Assert.IsTrue(equiv2);
}
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 WS1SLt <BoolExpr>(x, y);
var xLTzLTy = (new WS1SLt <BoolExpr>(x, z)) & (new WS1SLt <BoolExpr>(z, y));
var Ez = new WS1SExists <BoolExpr>(z, xLTzLTy);
var notEz = new WS1SNot <BoolExpr>(Ez);
var xSyDef = new WS1SAnd <BoolExpr>(xLTy, notEz);
var aut_xSyDef = xSyDef.GetAutomaton(alg, x, y);
var aut_xLTzLTy = xLTzLTy.GetAutomaton(alg, x, y, z);
var aut_Ez = Ez.GetAutomaton(alg, x, y);
var aut_notEz = notEz.GetAutomaton(alg, x, y);
var aut_xLTy = xLTy.GetAutomaton(alg, x, y);
//aut_xSyDef.ShowGraph("aut_xSyDEf");
//aut_xLTzLTy.ShowGraph("aut_xLTzLTy");
//aut_Ez.ShowGraph("aut_Ez");
//aut_notEz.ShowGraph("aut_notEz");
var xSyPrim = new WS1SSuccN <BoolExpr>(x, y, 1);
var aut_xSyPrim = xSyPrim.GetAutomaton(alg, x, y);
var equiv = aut_xSyPrim.IsEquivalentWith(aut_xSyDef, alg);
Assert.IsTrue(equiv);
}
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 WS1SPred <BDD>(solver.MkCharConstraint('c'), x);
var fo_x = new WS1SSingleton <BDD>(x);
var ca = new CartesianAlgebraBDD <BDD>(solver);
var lab = new WS1SAnd <BDD>(pred, fo_x);
WS1SFormula <BDD> not_lab = new WS1SNot <BDD>(lab);
var not_lab_actual = new WS1SAnd <BDD>(not_lab, fo_x);
var aut_not_lab = not_lab_actual.GetAutomaton(ca, x);
var aut_not_lab_prelim = not_lab.GetAutomaton(ca, x);
var c_aut_lab = lab.GetAutomaton(ca, x).Complement(ca).Minimize(ca);
//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
}
