public void MSO_Succ_Z3A()
{
var z3Context = new Context();
var S = z3Context.IntSort;
var solver = new Z3BoolAlg(z3Context, S);
Func <int, BoolExpr> IsPos = (i => z3Context.MkEq(solver.x, z3Context.MkInt(i)));
var x = new Variable("x", true);
var y = new Variable("y", true);
var x_is_0 = new MSOPredicate <BoolExpr>(IsPos(0), x);
var y_is_1 = new MSOPredicate <BoolExpr>(IsPos(1), y);
//every 0 is immediately followed by a 1
MSOFormula <BoolExpr> phi = Forall(x, Implies(x_is_0, Exists(y, And(Succ(x, y), y_is_1))));
//var ca = new CartesianAlgebraBDD<BoolExpr>(solver);
var aut = phi.GetAutomaton(solver);
//aut.ShowGraph();
//Automaton<BoolExpr> aut1 = Automaton<BoolExpr>.ProjectSecond<BDD>(aut);
var expected_automaton = Automaton <BoolExpr> .Create(solver, 0, new int[] { 0 },
new Move <BoolExpr>[] {
Move <BoolExpr> .Create(0, 0, z3Context.MkNot(IsPos(0))),
Move <BoolExpr> .Create(0, 1, IsPos(0)),
Move <BoolExpr> .Create(1, 0, IsPos(1))
});
bool equiv = aut.IsEquivalentWith(expected_automaton);
//Assert.IsTrue(equiv, "the automata must be equivalent");
}
public void TestWS1S_GetAutomatonBDD_eq_GetAutomaton()
{
var solver = new CharSetSolver(BitWidth.BV7);
//var nrOfLabelBits = (int)BitWidth.BV7;
var isDigit = solver.MkCharSetFromRegexCharClass(@"\d");
var isLetter = solver.MkCharSetFromRegexCharClass(@"(c|C)");
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 <BDD>(new MSONot <BDD>(new MSOEq <BDD>(x, y)), new MSOAnd <BDD>(new MSOIsSingleton <BDD>(x), new MSOIsSingleton <BDD>(y)));
//there is a set X containing x and y and all positions z in X have characters that satisfy isWordLetter
var x_sub_X = new MSOSubset <BDD>(x, X);
var y_sub_X = new MSOSubset <BDD>(y, X);
var z_sub_X = new MSOSubset <BDD>(z, X);
var isletter_z = new MSOPredicate <BDD>(isLetter, z);
var psi = new MSOExists <BDD>(X, (x_sub_X & y_sub_X & ~(new MSOExists <BDD>(z, ~((~((new MSOIsSingleton <BDD>(z)) & z_sub_X)) | isletter_z)))));
var atLeast2w = xy & psi;
var atLeast2wEE = new MSOExists <BDD>(x, (new MSOExists <BDD>(y, atLeast2w)));
var autBDD = atLeast2w.GetAutomaton(solver);
var ca = new CartesianAlgebraBDD <BDD>(solver);
var autPROD = atLeast2w.GetAutomaton(ca);
//autBDD.ShowGraph("autBDD");
//autPROD.ShowGraph("autPROD");
var aut_atLeast2wEE1 = BasicAutomata.Restrict(atLeast2wEE.GetAutomaton(ca));
var aut_atLeast2wEE2 = atLeast2wEE.GetAutomaton(solver);
//aut_atLeast2wEE1.ShowGraph("aut_atLeast2wEE1");
//aut_atLeast2wEE2.ShowGraph("aut_atLeast2wEE2");
Assert.IsTrue(aut_atLeast2wEE1.IsEquivalentWith(aut_atLeast2wEE2));
}
public void TestWS1S_Label()
{
var solver = new CharSetSolver(BitWidth.BV7);
var x = new Variable("X", false);
var pred = new MSOPredicate <BDD>(solver.MkCharConstraint('c'), x);
var ca = new CartesianAlgebraBDD <BDD>(solver);
var lab = pred & new MSOIsSingleton <BDD>(x);
var lab_aut = lab.GetAutomaton(ca);
//lab_aut.ShowGraph("lab_aut");
}
public void BooleanAlgebraZ3_test1()
{
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 pred = new MSOPredicate <BoolExpr>(ctx.MkEq(solver.x, ctx.MkNumeral(42, sort)), x);
MSOFormula <BoolExpr> phi = new MSOExists <BoolExpr>(x, pred);
var pred_aut = pred.GetAutomaton(alg);
//pred_aut.ShowGraph("pred_aut");
}
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
}
public void TestMSO_Pred()
{
var solver = new CharSetSolver(BitWidth.BV16);
var x = new Variable("x", true);
var pred = new MSOPredicate<BDD>(solver.MkCharConstraint( 'c'), x);
MSOFormula<BDD> phi = new MSOExists<BDD>(x, pred);
var ca = new CartesianAlgebraBDD<BDD>(solver);
var pred_aut = pred.GetAutomaton(ca);
//pred_aut.ShowGraph("pred_aut");
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, "c"), "regex mismatch");
}
var aut2 = solver.RegexConverter.Convert("c", System.Text.RegularExpressions.RegexOptions.Singleline);
//aut2.ShowGraph("aut2");
//aut.ShowGraph("aut");
Assert.IsTrue(aut2.IsEquivalentWith(aut), "automata not equialent");
}
public void MSO_Succ_Z3A()
{
var z3Context = new Context();
var S = z3Context.IntSort;
var solver = new Z3BoolAlg(z3Context, S);
Func <int, BoolExpr> IsInt = (i => z3Context.MkEq(solver.x, z3Context.MkInt(i)));
var x_is_0 = new MSOPredicate <BoolExpr>(IsInt(0), "x");
var y_is_1 = new MSOPredicate <BoolExpr>(IsInt(1), "y");
//every 0 is immediately followed by a 1
MSOFormula <BoolExpr> phi = Forall("x", Implies(x_is_0, Exists("y", And(Succ("x", "y"), y_is_1))));
var aut = phi.GetAutomaton(solver);
var expected_automaton = Automaton <BoolExpr> .Create(solver, 0, new int[] { 0 },
new Move <BoolExpr>[] {
Move <BoolExpr> .Create(0, 0, z3Context.MkNot(IsInt(0))),
Move <BoolExpr> .Create(0, 1, IsInt(0)),
Move <BoolExpr> .Create(1, 0, IsInt(1))
});
bool equiv = aut.IsEquivalentWith(expected_automaton, solver);
Assert.IsTrue(equiv, "the automata must be equivalent");
}
public static void Run()
{
var sw = new Stopwatch();
//ex x1 x2... a(x1) /\ a(x2).../\ x1<x2...
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"..\mso-minterm-p1.csv"))
{
file.WriteLine("k, old, cartesian, trie, minterm");
for (int size = 2; size < kminterm; size++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula <BDD> phi = new MSOTrue <BDD>();
//x1<x2 /\...
for (int k = 1; k < size; k++)
{
var leq = new MSOSuccN <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true), 1);
phi = new MSOAnd <BDD>(phi, leq);
}
//ai(xi) /\ ...
for (int k = 0; k < size; k++)
{
var axk = new MSOPredicate <BDD>(solver.MkBitTrue(k), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, axk);
}
phi = new MSOAnd <BDD>(new MSOeqN <BDD>(new Variable("x" + 0, true), 0), phi);
for (int k = size - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
//Old
sw.Restart();
for (int t = 0; t < numTests; t++)
{
var aut = phi.GetAutomaton(solver);
}
var told = sw.ElapsedMilliseconds;
//BDD
sw.Restart();
for (int t = 0; t < numTests; t++)
{
var aut = phi.GetAutomaton(new CartesianAlgebraBDD <BDD>(solver));
}
sw.Stop();
var t1 = sw.ElapsedMilliseconds;
//Trie
sw.Restart();
for (int t = 0; t < numTests; t++)
{
var aut = phi.GetAutomaton(new BDDAlgebra <BDD>(solver), false);
}
var t2 = sw.ElapsedMilliseconds;
//Tminterm
solver = new CharSetSolver(BitWidth.BV64);
BDD[] predicates = new BDD[size];
solver.GenerateMinterms();
for (int k = 0; k < size; k++)
{
predicates[k] = solver.MkBitTrue(k);
}
var t3 = 60000L * numTests;
if (size <= maxmint)
{
sw.Restart();
for (int t = 0; t < numTests; t++)
{
var mint = solver.GenerateMinterms(predicates).ToList();
}
sw.Stop();
t3 = sw.ElapsedMilliseconds;
}
file.WriteLine(size + ", " + (double)told / numTests + ", " + (double)t1 / numTests + ", " + (double)t2 / numTests + ", " + (double)t3 / numTests);
Console.WriteLine(size + ", " + (double)told / numTests + ", " + (double)t1 / numTests + ", " + (double)t2 / numTests + ", " + (double)t3 / numTests);
}
}
//ex x1 x2... a(x1) /\ a(x2)...
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"..\mso-minterm-p2.csv"))
{
file.WriteLine("k, old, cartesian, trie, minterm");
for (int size = 2; size < 10; size++)
{
// Tsolve force
var solver = new CharSetSolver();
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 0; k < size; k++)
{
var axk = new MSOPredicate <BDD>(solver.MkBitTrue(k), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, axk);
}
for (int k = size - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
//Old
sw.Restart();
for (int t = 0; t < numTests; t++)
{
var aut = phi.GetAutomaton(solver);
}
var told = sw.ElapsedMilliseconds;
//Cartesian
var t1 = 60000L * numTests;
if (size <= 7)
{
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.GetAutomaton(new CartesianAlgebraBDD <BDD>(solver));
}
sw.Stop();
t1 = sw.ElapsedMilliseconds;
}
//Trie
var t2 = 60000L * numTests;
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.GetAutomaton(new BDDAlgebra <BDD>(solver), false);
}
sw.Stop();
t2 = sw.ElapsedMilliseconds;
//Tminterm
solver = new CharSetSolver(BitWidth.BV64);
BDD[] predicates = new BDD[size];
solver.GenerateMinterms();
for (int k = 0; k < size; k++)
{
predicates[k] = solver.MkBitTrue(k);
}
var t3 = 60000L * numTests;
if (size <= maxmint)
{
sw.Restart();
for (int t = 0; t < numTests; t++)
{
var mint = solver.GenerateMinterms(predicates).ToList();
}
sw.Stop();
t3 = sw.ElapsedMilliseconds;
}
file.WriteLine(size + ", " + (double)told / numTests + ", " + (double)t1 / numTests + ", " + (double)t2 / numTests + ", " + (double)t3 / numTests);
Console.WriteLine(size + ", " + (double)told / numTests + ", " + (double)t1 / numTests + ", " + (double)t2 / numTests + ", " + (double)t3 / numTests);
}
}
}
public static void RunPOPLTests()
{
//// all x1...xn. xi<xi+1
List <Pair <MSOFormula <BDD>, CharSetSolver> > phis = new List <Pair <MSOFormula <BDD>, CharSetSolver> >();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver();
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, leq);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
phis.Add(new Pair <MSOFormula <BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"..\popl14-1.csv"), phis);
// all x1...xn. xi<xi+1 and a(xi)
phis = new List <Pair <MSOFormula <BDD>, CharSetSolver> >();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new MSOPredicate <BDD>(
solver.MkCharConstraint('a', false), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
phis.Add(new Pair <MSOFormula <BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"..\popl14-2.csv"), phis);
// all x1...xn. (xi<xi+1 and a(xi)) and ex y. c(y)
phis = new List <Pair <MSOFormula <BDD>, CharSetSolver> >();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new MSOPredicate <BDD>(solver.MkCharConstraint('a', false), new Variable("x" + k, true));
phi = new MSOAnd <BDD>(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
var exycy = new MSOExists <BDD>(new Variable("y", true), new MSOPredicate <BDD>(solver.MkCharConstraint('c', false), new Variable("y", true)));
phi = new MSOAnd <BDD>(phi, exycy);
phis.Add(new Pair <MSOFormula <BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"..\popl14-3.csv"), phis);
// all x1...xn. (xi<xi+1 and a(xi) \/ c(xi))
phis = new List <Pair <MSOFormula <BDD>, CharSetSolver> >();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt <BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
var axk = new MSOPredicate <BDD>(solver.MkCharConstraint('a', false), new Variable("x" + (k - 1), true));
var cxk = new MSOPredicate <BDD>(solver.MkCharConstraint('c', false), new Variable("x" + (k - 1), true));
var inter = new MSOOr <BDD>(new MSOAnd <BDD>(leq, axk), cxk);
phi = new MSOAnd <BDD>(phi, inter);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists <BDD>(new Variable("x" + k, true), phi);
}
MSOFormula <BDD> exycy = new MSOExists <BDD>(new Variable("y", true), new MSOPredicate <BDD>(solver.MkCharConstraint('c', false), new Variable("y", true)));
phi = new MSOAnd <BDD>(phi, exycy);
phis.Add(new Pair <MSOFormula <BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"..\popl14-4.csv"), phis, 10, 10, 11);
}
public static void RunPOPLTests()
{
//// all x1...xn. xi<xi+1
List<Pair<MSOFormula<BDD>, CharSetSolver>> phis = new List<Pair<MSOFormula<BDD>, CharSetSolver>>();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver();
MSOFormula<BDD> phi = new MSOTrue<BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt<BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, leq);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists<BDD>(new Variable("x" + k, true), phi);
}
phis.Add(new Pair<MSOFormula<BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"popl14-1.csv"), phis);
// all x1...xn. xi<xi+1 and a(xi)
phis = new List<Pair<MSOFormula<BDD>, CharSetSolver>>();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula<BDD> phi = new MSOTrue<BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt<BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new MSOPredicate<BDD>(
solver.MkCharConstraint('a', false), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists<BDD>(new Variable("x" + k, true), phi);
}
phis.Add(new Pair<MSOFormula<BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"popl14-2.csv"), phis);
// all x1...xn. (xi<xi+1 and a(xi)) and ex y. c(y)
phis = new List<Pair<MSOFormula<BDD>, CharSetSolver>>();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula<BDD> phi = new MSOTrue<BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt<BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new MSOPredicate<BDD>(solver.MkCharConstraint('a', false), new Variable("x" + k, true));
phi = new MSOAnd<BDD>(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists<BDD>(new Variable("x" + k, true), phi);
}
var exycy = new MSOExists<BDD>(new Variable("y", true), new MSOPredicate<BDD>(solver.MkCharConstraint('c', false), new Variable("y", true)));
phi = new MSOAnd<BDD>(phi, exycy);
phis.Add(new Pair<MSOFormula<BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"popl14-3.csv"), phis);
// all x1...xn. (xi<xi+1 and a(xi) \/ c(xi))
phis = new List<Pair<MSOFormula<BDD>, CharSetSolver>>();
for (int to = 2; to < kpopl; to++)
{
var solver = new CharSetSolver(BitWidth.BV64);
MSOFormula<BDD> phi = new MSOTrue<BDD>();
for (int k = 1; k < to; k++)
{
var leq = new MSOLt<BDD>(new Variable("x" + (k - 1), true), new Variable("x" + k, true));
var axk = new MSOPredicate<BDD>(solver.MkCharConstraint('a', false), new Variable("x" + (k - 1), true));
var cxk = new MSOPredicate<BDD>(solver.MkCharConstraint('c', false), new Variable("x" + (k - 1), true));
var inter = new MSOOr<BDD>(new MSOAnd<BDD>(leq, axk), cxk);
phi = new MSOAnd<BDD>(phi, inter);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new MSOExists<BDD>(new Variable("x" + k, true), phi);
}
MSOFormula<BDD> exycy = new MSOExists<BDD>(new Variable("y", true), new MSOPredicate<BDD>(solver.MkCharConstraint('c', false), new Variable("y", true)));
phi = new MSOAnd<BDD>(phi, exycy);
phis.Add(new Pair<MSOFormula<BDD>, CharSetSolver>(phi, solver));
}
RunTest(new StreamWriter(@"popl14-4.csv"), phis, 11, 11, 11);
}
