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 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 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 TestMSO_Member()
{
var solver = new CharSetSolver(BitWidth.BV7);
var ca = new CartesianAlgebraBDD <BDD>(solver);
var x = new Variable("x", false);
var y = new Variable("y", false);
var fo_x = new MSOIsSingleton <BDD>(x);
MSOFormula <BDD> xSy = new MSOSubset <BDD>(x, y);
var mem = new MSOAnd <BDD>(xSy, fo_x);
var aut_mem = mem.GetAutomaton(ca);
//aut_mem.ShowGraph("aut_mem");
}
public void TestMSO_Equal()
{
var solver = new CharSetSolver(BitWidth.BV7);
var ca = new CartesianAlgebraBDD<BDD>(solver);
var x = new Variable("x", false);
var y = new Variable("y", false);
var fo_x = new MSOIsSingleton<BDD>(x) ;
var fo_y = new MSOIsSingleton<BDD>(y);
MSOFormula<BDD> fo = new MSOAnd<BDD>(fo_x, fo_y);
MSOFormula<BDD> xSy = new MSOSubset<BDD>(x, y);
MSOFormula<BDD> ySx = new MSOSubset<BDD>(y, x);
MSOFormula<BDD> yEQx = new MSOAnd<BDD>(xSy, ySx);
yEQx = new MSOAnd<BDD>(yEQx, fo);
var aut_yEQx = yEQx.GetAutomaton(ca);
//aut_yEQx.ShowGraph("aut_yEQx");
}
//Automaton<T> Restrict<T>(Automaton<IMonadicPredicate<BDD, T>> autom)
//{
// List<Move<T>> moves = new List<Move<T>>();
// foreach (var move in autom.GetMoves())
// moves.Add(new Move<T>(move.SourceState, move.TargetState, move.Label.ProjectSecond()));
// var res = Automaton<T>.Create(autom.InitialState, autom.GetFinalStates(), moves);
// return res;
//}
public void TestWS1S_UseOfCharRangePreds <T>(IBooleanAlgebra <T> solver, T isDigit, T isWordLetter, IRegexConverter <T> regexConverter)
{
var ca = new CartesianAlgebraBDD <T>(solver);
var x = new Variable("x", false);
var y = new Variable("y", false);
var z = new Variable("z", false);
var X = new Variable("X", false);
//there are at least two distinct positions x and y
var xy = new MSOAnd <T>(new MSOAnd <T>(new MSONot <T>(new MSOEq <T>(x, y)), new MSOIsSingleton <T>(x)), new MSOIsSingleton <T>(y));
//there is a set X containing x and y and all positions z in X have characters that satisfy isWordLetter
var phi = new MSOExists <T>(X, new MSOAnd <T>(
new MSOAnd <T>(new MSOSubset <T>(x, X), new MSOSubset <T>(y, X)),
new MSONot <T>(new MSOExists <T>(z, new MSONot <T>(
new MSOOr <T>(new MSONot <T>(new MSOAnd <T>(new MSOIsSingleton <T>(z), new MSOSubset <T>(z, X))),
new MSOPredicate <T>(isWordLetter, z)))))));
var psi2 = new MSOAnd <T>(xy, phi);
var atLeast2wEE = new MSOExists <T>(x, new MSOExists <T>(y, psi2));
var psi1 = new MSOAnd <T>(new MSOIsSingleton <T>(x), new MSOPredicate <T>(isDigit, x));
var aut_psi1 = psi1.GetAutomaton(ca);
//aut_psi1.ShowGraph("SFA(psi1)");
var atLeast1d = new MSOExists <T>(x, psi1);
var psi = new MSOAnd <T>(atLeast2wEE, atLeast1d);
var aut1 = psi.GetAutomaton(ca);
//var aut_atLeast1d = atLeast1d.GetAutomaton(solver);
var aut2 = regexConverter.Convert(@"\w.*\w", System.Text.RegularExpressions.RegexOptions.Singleline).Intersect(regexConverter.Convert(@"\d"));
//aut1.ShowGraph("aut1");
//aut2.ShowGraph("aut2");
bool equiv = aut2.IsEquivalentWith(BasicAutomata.Restrict(aut1));
Assert.IsTrue(equiv);
//solver.ShowGraph(aut_atLeast1d, "aut_atLeast1d");
var aut_psi2 = psi2.GetAutomaton(ca);
// var aut_atLeast2wEE = atLeast2wEE.GetAutomaton(ca, "x", "y");
// var aut_atLeast2wEE2 = atLeast2wEE.GetAutomaton(solver);
//aut_psi2.ShowGraph("SFA(psi2)");
//aut_atLeast2wEE.ShowGraph("aut_atLeast2wEE");
//aut_atLeast2wEE2.ShowGraph("aut_atLeast2wEE2");
//solver.ShowGraph(aut_atLeast2wEE2, "aut_atLeast2wEE2");
}
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 MSOPredicate <BDD>(solver.MkCharConstraint('c'), x);
var fo_x = new MSOIsSingleton <BDD>(x);
var ca = new CartesianAlgebraBDD <BDD>(solver);
var lab = new MSOAnd <BDD>(pred, fo_x);
MSOFormula <BDD> not_lab = new MSONot <BDD>(lab);
var not_lab_actual = new MSOAnd <BDD>(not_lab, fo_x);
var aut_not_lab = not_lab_actual.GetAutomaton(ca);
var aut_not_lab_prelim = not_lab.GetAutomaton(ca);
var c_aut_lab = lab.GetAutomaton(ca).Complement().Minimize();
//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
}