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 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 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 WS1SVariable <BoolExpr>("x");
var y = new WS1SVariable <BoolExpr>("y");
var z = new WS1SVariable <BoolExpr>("z");
var xLTy = x < y;
var xLTzLTy = (x < z) & (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 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 Minimize_NFA_Z3A()
{
var z3Context = new Context();
var S = z3Context.IntSort;
var solver = new Z3BoolAlg(z3Context, S);
var a = z3Context.MkEq(solver.x, z3Context.MkNumeral(0, S));
var b = z3Context.MkNot(a);
var sfa = Automaton <BoolExpr> .Create(solver, 0, new int[] { 3, 4, 5 },
new Move <BoolExpr>[] {
Move <BoolExpr> .Create(0, 1, a),
Move <BoolExpr> .Create(0, 2, b),
Move <BoolExpr> .Create(1, 4, a),
Move <BoolExpr> .Create(1, 5, a), //<-- nondeterminism
Move <BoolExpr> .Create(1, 3, b),
Move <BoolExpr> .Create(2, 4, b),
Move <BoolExpr> .Create(2, 5, a),
//Move<BoolExpr>.Create(3, 6, a),
Move <BoolExpr> .Create(3, 4, b),
//Move<BoolExpr>.Create(4, 6, a),
Move <BoolExpr> .Create(4, 3, b),
Move <BoolExpr> .Create(5, 5, a),
//Move<BoolExpr>.Create(5, 6, b),
//Move<BoolExpr>.Create(6, 6, solver.True)
});
var sfa_min = sfa.Minimize();
var sfa_det = sfa_min.Determinize();
var sfa_det_min = sfa_det.Minimize();
bool equiv1 = sfa.IsEquivalentWith(sfa_min);
bool equiv2 = sfa.IsEquivalentWith(sfa_det);
Assert.IsTrue(equiv1);
Assert.IsTrue(equiv2);
//pretend that sfa is deterministic
sfa.isDeterministic = true;
//only the smaller half of a split set is pushed
var sfa_min2 = sfa.Minimize();
//the result is incorrect
bool equiv3 = sfa_min.IsEquivalentWith(sfa_min2);
Assert.IsFalse(equiv3);
}
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()
{
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"randomMSOInt.csv", false))
{
Console.WriteLine("num-predicates, num-minterms, minterm-time, generic-bdd, product ");
file.WriteLine("num-predicates, num-minterms, minterm-time, generic-bdd, product ");
}
random = new Random(0);
currSeed = 0;
for (int maxConst = 3; maxConst < 4; maxConst++)
for (int phisize = 5; phisize < 8; phisize += 1)
{
//Console.WriteLine(maxConst + "," + phisize);
for (int i = 0; i < howMany; i++)
{
c = new Context();
z3 = new Z3BoolAlg(c, c.IntSort, timeout);
size = phisize;
try
{
var pair = GenerateMSOZ3Formula();
if (maxConst == 4 && phisize > 5)
break;
formula = pair.First;
predicates = pair.Second;
if (predicates.Count > 2)
{
var bddsolver = new BDDAlgebra<BoolExpr>(z3);
var sw = new Stopwatch();
sw.Restart();
long tbdd = timeout;
try
{
formula.GetAutomaton(bddsolver, false);
sw.Stop();
tbdd = sw.ElapsedMilliseconds;
if (tbdd > timeout)
tbdd = timeout;
}
catch (Z3Exception e)
{
tbdd = timeout;
}
catch (AutomataException e)
{
tbdd = timeout;
}
if (tbdd != timeout)
{
long tcart = timeout;
try
{
var bdd = new BDDAlgebra();
solver = new CartesianAlgebraBDD<BoolExpr>(bdd, z3);
sw.Restart();
formula.GetAutomaton(solver);
sw.Stop();
tcart = sw.ElapsedMilliseconds;
if (tcart > timeout)
tcart = timeout;
}
catch (Z3Exception e)
{
tcart = timeout;
}
catch (AutomataException e)
{
tcart = timeout;
}
sw.Restart();
long tminterm = timeout;
List<Pair<bool[], BoolExpr>> mint = new List<Pair<bool[], BoolExpr>>();
try
{
mint = z3.GenerateMinterms(predicates.ToArray()).ToList();
sw.Stop();
tminterm = sw.ElapsedMilliseconds;
if (tminterm > timeout)
tminterm = timeout;
}
catch (Z3Exception e)
{
tminterm = timeout;
}
using (System.IO.StreamWriter file = new System.IO.StreamWriter(@"randomMSOInt.csv", true))
{
Console.WriteLine(predicates.Count + ", " + (tminterm == timeout ? (int)Math.Pow(2, predicates.Count) : mint.Count) + ", " + (double)tminterm + ", " + (double)tbdd + ", " + (double)tcart);
file.WriteLine(predicates.Count + ", " + (tminterm == timeout ? (int)Math.Pow(2, predicates.Count) : mint.Count) + ", " + (double)tminterm + ", " + (double)tbdd + ", " + (double)tcart);
}
}
else {
//Console.WriteLine("moving to next one");
}
}
else
{
// Console.WriteLine("moving to next one");
}
}
catch (Z3Exception e)
{
Console.WriteLine("Z3 out of memory");
return;
}
catch (OutOfMemoryException e)
{
Console.WriteLine("Out of memory");
return;
}
}
}
}
public static void Run()
{
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"randomMSOInt.csv", false))
{
Console.WriteLine("num-predicates, num-minterms, minterm-time, generic-bdd, product ");
file.WriteLine("num-predicates, num-minterms, minterm-time, generic-bdd, product ");
}
random = new Random(0);
currSeed = 0;
for (int maxConst = 3; maxConst < 4; maxConst++)
{
for (int phisize = 5; phisize < 8; phisize += 1)
{
//Console.WriteLine(maxConst + "," + phisize);
for (int i = 0; i < howMany; i++)
{
c = new Context();
z3 = new Z3BoolAlg(c, c.IntSort, timeout);
size = phisize;
try
{
var pair = GenerateMSOZ3Formula();
if (maxConst == 4 && phisize > 5)
{
break;
}
formula = pair.First;
predicates = pair.Second;
if (predicates.Count > 2)
{
var bddsolver = new BDDAlgebra <BoolExpr>(z3);
var sw = new Stopwatch();
sw.Restart();
long tbdd = timeout;
try
{
formula.GetAutomaton(bddsolver, false);
sw.Stop();
tbdd = sw.ElapsedMilliseconds;
if (tbdd > timeout)
{
tbdd = timeout;
}
}
catch (Z3Exception e)
{
tbdd = timeout;
}
catch (AutomataException e)
{
tbdd = timeout;
}
if (tbdd != timeout)
{
long tcart = timeout;
try
{
var bdd = new BDDAlgebra();
solver = new CartesianAlgebraBDD <BoolExpr>(bdd, z3);
sw.Restart();
formula.GetAutomaton(solver);
sw.Stop();
tcart = sw.ElapsedMilliseconds;
if (tcart > timeout)
{
tcart = timeout;
}
}
catch (Z3Exception e)
{
tcart = timeout;
}
catch (AutomataException e)
{
tcart = timeout;
}
sw.Restart();
long tminterm = timeout;
List <Pair <bool[], BoolExpr> > mint = new List <Pair <bool[], BoolExpr> >();
try
{
mint = z3.GenerateMinterms(predicates.ToArray()).ToList();
sw.Stop();
tminterm = sw.ElapsedMilliseconds;
if (tminterm > timeout)
{
tminterm = timeout;
}
}
catch (Z3Exception e)
{
tminterm = timeout;
}
using (System.IO.StreamWriter file = new System.IO.StreamWriter(@"randomMSOInt.csv", true))
{
Console.WriteLine(predicates.Count + ", " + (tminterm == timeout ? (int)Math.Pow(2, predicates.Count) : mint.Count) + ", " + (double)tminterm + ", " + (double)tbdd + ", " + (double)tcart);
file.WriteLine(predicates.Count + ", " + (tminterm == timeout ? (int)Math.Pow(2, predicates.Count) : mint.Count) + ", " + (double)tminterm + ", " + (double)tbdd + ", " + (double)tcart);
}
}
else
{
//Console.WriteLine("moving to next one");
}
}
else
{
// Console.WriteLine("moving to next one");
}
}
catch (Z3Exception e)
{
Console.WriteLine("Z3 out of memory");
return;
}
catch (OutOfMemoryException e)
{
Console.WriteLine("Out of memory");
return;
}
}
}
}
}
