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_Forall_x_Exists_y_x_lt_y()
{
var triv = new TrivialBooleanAlgebra();
var ca = new BDDAlgebra <bool>(triv);
var x = new Variable("x", false);
var y = new Variable("y", false);
var x_lt_y = new WS1SLt <bool>(x, y);
var psi4 = ~(new WS1SExists <bool>(x, new WS1SSingleton <bool>(x) & ~(new WS1SExists <bool>(y, new WS1SSingleton <bool>(y) & (x_lt_y)))));
var aut = psi4.GetAutomaton(ca, x, y);
//aut.ShowGraph("aut");
//accepts only the empty word
Assert.IsTrue(aut.StateCount == 1 && aut.IsFinalState(aut.InitialState) && aut.MoveCount == 0);
}
public static void MintermTest()
{
var sw = new Stopwatch();
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"..\msomintermp1s1.txt"))
{
for (int size = 2; size < kminterm; size++)
{
// Tsolve no force
var s1 = new CharSetSolver(BitWidth.BV64);
var solver = new CartesianAlgebraBDD <BDD>(s1);
WS1SFormula <BDD> phi = new WS1STrue <BDD>();
for (int k = 1; k < size; k++)
{
var leq = new WS1SLt <BDD>(new Variable <BDD>("x" + (k - 1)), new Variable <BDD>("x" + k));
phi = new WS1SAnd <BDD>(phi, leq);
}
for (int k = 0; k < size; k++)
{
var axk = new WS1SPred <BDD>(s1.MkBitTrue(k), new Variable <BDD>("x" + k));
phi = new WS1SAnd <BDD>(phi, axk);
}
for (int k = size - 1; k >= 0; k--)
{
phi = new WS1SExists <BDD>(new Variable <BDD>("x" + k), phi);
}
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.GetAutomaton(solver);
}
sw.Stop();
var t1 = sw.ElapsedMilliseconds;
file.WriteLine((double)t1 / numTests);
Console.WriteLine((double)t1 / numTests);
}
}
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"..\msomintermp2s1.txt"))
{
for (int size = 2; size < kminterm; size++)
{
// Tsolve force
var s1 = new CharSetSolver(BitWidth.BV64);
var solver = new CartesianAlgebraBDD <BDD>(s1);
WS1SFormula <BDD> phi = new WS1STrue <BDD>();
for (int k = 0; k < size; k++)
{
var axk = new WS1SPred <BDD>(s1.MkBitTrue(k), new Variable <BDD>("x" + k));
phi = new WS1SAnd <BDD>(phi, axk);
}
for (int k = size - 1; k >= 0; k--)
{
phi = new WS1SExists <BDD>(new Variable <BDD>("x" + k), phi);
}
var t1 = 60000L;
if (size <= maxmint)
{
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.GetAutomaton(solver);
}
sw.Stop();
t1 = sw.ElapsedMilliseconds;
}
file.WriteLine((double)t1 / numTests);
Console.WriteLine((double)t1 / numTests);
}
}
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"..\msomintermp1s2.txt"))
{
for (int size = 2; size < kminterm; size++)
{
// Tsolve solver 2
var solver = new CharSetSolver(BitWidth.BV64);
var alg = new BDDAlgebra <BDD>(solver);
WS1SFormula <BDD> phi = new WS1STrue <BDD>();
for (int k = 1; k < size; k++)
{
var leq = new WS1SLt <BDD>(new Variable <BDD>("x" + (k - 1)), new Variable <BDD>("x" + k));
phi = new WS1SAnd <BDD>(phi, leq);
}
for (int k = 0; k < size; k++)
{
var axk = new WS1SPred <BDD>(solver.MkBitTrue(k), new Variable <BDD>("x" + k));
phi = new WS1SAnd <BDD>(phi, axk);
}
for (int k = size - 1; k >= 0; k--)
{
phi = new WS1SExists <BDD>(new Variable <BDD>("x" + k), phi);
}
var t1 = 60000L;
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.GetAutomaton(alg);
}
sw.Stop();
t1 = sw.ElapsedMilliseconds;
file.WriteLine((double)t1 / numTests);
Console.WriteLine((double)t1 / numTests);
}
}
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"..\msomintermp2s2.txt"))
{
for (int size = 2; size < kminterm; size++)
{
var solver = new CharSetSolver(BitWidth.BV64);
var alg = new BDDAlgebra <BDD>(solver);
//Tforce sol 2
WS1SFormula <BDD> phi = new WS1STrue <BDD>();
for (int k = 0; k < size; k++)
{
var axk = new WS1SPred <BDD>(solver.MkBitTrue(k), new Variable <BDD>("x" + k));
phi = new WS1SAnd <BDD>(phi, axk);
}
for (int k = size - 1; k >= 0; k--)
{
phi = new WS1SExists <BDD>(new Variable <BDD>("x" + k), phi);
}
var t1 = 60000L;
if (size <= maxmint)
{
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.GetAutomaton(alg);
}
sw.Stop();
t1 = sw.ElapsedMilliseconds;
}
file.WriteLine((double)t1 / numTests);
Console.WriteLine((double)t1 / numTests);
}
}
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"..\msominterm.txt"))
{
for (int size = 2; size < kminterm; size++)
{
//Tminterm
var 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 t1 = 60000L * numTests;
if (size <= maxmint)
{
sw.Restart();
for (int t = 0; t < numTests; t++)
{
var mint = solver.GenerateMinterms(predicates).ToList();
}
sw.Stop();
t1 = sw.ElapsedMilliseconds;
}
file.WriteLine((double)t1 / numTests);
Console.WriteLine((double)t1 / numTests);
}
}
}
//public static void POPLTestsInt()
//{
// var sw = new Stopwatch();
// using (System.IO.StreamWriter file =
// new System.IO.StreamWriter(@"..\mso-int.txt"))
// {
// for (int to = 2; to < kpopl; to++)
// {
// // T1
// var ctx = new Context();
// var sort = ctx.IntSort;
// var solver = new BooleanAlgebraZ3(ctx, sort);
// var alg = new BDDAlgebra<BoolExpr>(solver);
// var pred = new MSOPredicate<BoolExpr>(ctx.MkEq(solver.x, ctx.MkNumeral(42, sort)), "x");
// WS1SFormula<BoolExpr> phi = new WS1STrue<BoolExpr>();
// for (int k = 1; k < to; k++)
// {
// var leq = new WS1SLt<BoolExpr>(new Variable<BDD>("x" + (k - 1)), new Variable<BDD>("x" + k));
// phi = new WS1SAnd<BoolExpr>(phi, leq);
// }
// for (int k = to - 1; k >= 0; k--)
// {
// phi = new WS1SExists<BoolExpr>(new Variable<BDD>("x" + k), phi);
// }
// sw.Restart();
// for (int t = 0; t < numTests; t++)
// {
// phi.GetAutomaton(solver);
// }
// sw.Stop();
// var t1 = sw.ElapsedMilliseconds;
// //T2
// ctx = new Context();
// sort = ctx.IntSort;
// solver = new BooleanAlgebraZ3(ctx, sort);
// alg = new BDDAlgebra<BoolExpr>(solver);
// pred = new MSOPredicate<BoolExpr>(ctx.MkEq(solver.x, ctx.MkNumeral(42, sort)), "x");
// phi = new WS1STrue<BoolExpr>();
// for (int k = 1; k < to; k++)
// {
// var leq = new WS1SLt<BoolExpr>(new Variable<BDD>("x" + (k - 1)), new Variable<BDD>("x" + k));
// phi = new WS1SAnd<BoolExpr>(phi, leq);
// }
// for (int k = 0; k < to; k++)
// {
// var axk = new WS1SPred<BoolExpr>(
// ctx.MkLe((IntExpr)solver.x, (IntExpr)ctx.MkNumeral(42+k, sort)),
// "x" + k);
// phi = new WS1SAnd<BoolExpr>(phi, axk);
// }
// for (int k = to - 1; k >= 0; k--)
// {
// phi = new WS1SExists<BoolExpr>(new Variable<BDD>("x" + k), phi);
// }
// sw.Restart();
// for (int t = 0; t < numTests; t++)
// {
// phi.GetAutomaton(solver);
// }
// sw.Stop();
// var t2 = sw.ElapsedMilliseconds;
// // T3
// ctx = new Context();
// sort = ctx.IntSort;
// solver = new BooleanAlgebraZ3(ctx, sort);
// alg = new BDDAlgebra<BoolExpr>(solver);
// pred = new MSOPredicate<BoolExpr>(ctx.MkEq(solver.x, ctx.MkNumeral(42, sort)), "x");
// phi = new WS1STrue<BoolExpr>();
// for (int k = 1; k < to; k++)
// {
// var leq = new WS1SLt<BoolExpr>(new Variable<BDD>("x" + (k - 1)), new Variable<BDD>("x" + k));
// phi = new WS1SAnd<BoolExpr>(phi, leq);
// }
// for (int k = 0; k < to; k++)
// {
// var axk = new WS1SPred<BoolExpr>(ctx.MkLe((IntExpr)solver.x, (IntExpr)ctx.MkNumeral(42+k, sort)), new Variable<BDD>("x" + k));
// phi = new WS1SAnd<BoolExpr>(phi, axk);
// }
// for (int k = to - 1; k >= 0; k--)
// {
// phi = new WS1SExists<BoolExpr>(new Variable<BDD>("x" + k), phi);
// }
// var exycy = new WS1SExists<BoolExpr>(new Variable<BDD>("y"), new WS1SPred<BoolExpr>(
// ctx.MkLe((IntExpr)solver.x, (IntExpr)ctx.MkNumeral(1000, sort)), new Variable<BDD>("y")));
// phi = new WS1SAnd<BoolExpr>(phi, exycy);
// sw.Restart();
// for (int t = 0; t < numTests; t++)
// {
// phi.GetAutomaton(solver);
// }
// sw.Stop();
// var t3 = sw.ElapsedMilliseconds;
// //T4
// ctx = new Context();
// sort = ctx.IntSort;
// solver = new BooleanAlgebraZ3(ctx, sort);
// alg = new BDDAlgebra<BoolExpr>(solver);
// pred = new MSOPredicate<BoolExpr>(ctx.MkEq(solver.x, ctx.MkNumeral(42, sort)), "x");
// phi = new WS1STrue<BoolExpr>();
// for (int k = 1; k < to; k++)
// {
// var leq = new WS1SLt<BoolExpr>(new Variable<BDD>("x" + (k - 1)), new Variable<BDD>("x" + k));
// var axk = new WS1SPred<BoolExpr>(ctx.MkLe((IntExpr)solver.x, (IntExpr)ctx.MkNumeral(42+k, sort)), new Variable<BDD>("x" + (k - 1)));
// var cxk = new WS1SPred<BoolExpr>(ctx.MkLe((IntExpr)solver.x, (IntExpr)ctx.MkNumeral(1000, sort)), new Variable<BDD>("x" + (k - 1)));
// var inter = new WS1SOr<BoolExpr>(new WS1SAnd<BoolExpr>(leq, axk), cxk);
// phi = new WS1SAnd<BoolExpr>(phi, inter);
// }
// for (int k = to - 1; k >= 0; k--)
// {
// phi = new WS1SExists<BoolExpr>(new Variable<BDD>("x" + k), phi);
// }
// exycy = new WS1SExists<BoolExpr>(new Variable<BDD>("y"), new WS1SPred<BoolExpr>(
// ctx.MkLe((IntExpr)solver.x, (IntExpr)ctx.MkNumeral(1000, sort)),
// "y"));
// phi = new WS1SAnd<BoolExpr>(phi, exycy);
// var t4 = 60000L * numTests;
// if (to <= maxmphipop)
// {
// sw.Restart();
// for (int t = 0; t < numTests; t++)
// {
// phi.GetAutomaton(solver);
// }
// sw.Stop();
// t4 = sw.ElapsedMilliseconds;
// }
// file.WriteLine(to + "," + (double)t1 / numTests + "," + (double)t2 / numTests + "," + (double)t3 / numTests + "," + (double)t4 / numTests);
// Console.WriteLine(to + "," + (double)t1 / numTests + "," + (double)t2 / numTests + "," + (double)t3 / numTests + "," + (double)t4 / numTests);
// }
// }
//}
public static void POPLTestsOld()
{
var sw = new Stopwatch();
using (System.IO.StreamWriter file =
new System.IO.StreamWriter(@"..\msobddold.txt"))
{
for (int to = 2; to < kpopl; to++)
{
// T1
var s1 = new CharSetSolver(BitWidth.BV64);
WS1SFormula phi = new WS1STrue();
for (int k = 1; k < to; k++)
{
var leq = new WS1SLt("x" + (k - 1), "x" + k);
phi = new WS1SAnd(phi, leq);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new WS1SExists("x" + k, phi);
}
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.getAutomaton(s1);
}
sw.Stop();
var t1 = sw.ElapsedMilliseconds;
//T2
s1 = new CharSetSolver(BitWidth.BV64);
phi = new WS1STrue();
for (int k = 1; k < to; k++)
{
var leq = new WS1SLt("x" + (k - 1), ("x" + k));
phi = new WS1SAnd(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new WS1SPred(s1.MkCharConstraint('a', false), "x" + k);
phi = new WS1SAnd(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new WS1SExists("x" + k, phi);
}
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.getAutomaton(s1);
}
sw.Stop();
var t2 = sw.ElapsedMilliseconds;
// T3
s1 = new CharSetSolver(BitWidth.BV64);
phi = new WS1STrue();
for (int k = 1; k < to; k++)
{
var leq = new WS1SLt("x" + (k - 1), ("x" + k));
phi = new WS1SAnd(phi, leq);
}
for (int k = 0; k < to; k++)
{
var axk = new WS1SPred(s1.MkCharConstraint('a', false), ("x" + k));
phi = new WS1SAnd(phi, axk);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new WS1SExists(("x" + k), phi);
}
var exycy = new WS1SExists(("y"), new WS1SPred(s1.MkCharConstraint('c', false), ("y")));
phi = new WS1SAnd(phi, exycy);
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.getAutomaton(s1);
}
sw.Stop();
var t3 = sw.ElapsedMilliseconds;
//T4
s1 = new CharSetSolver(BitWidth.BV64);
phi = new WS1STrue();
for (int k = 1; k < to; k++)
{
var leq = new WS1SLt(("x" + (k - 1)), ("x" + k));
var axk = new WS1SPred(s1.MkCharConstraint('a', false), ("x" + (k - 1)));
var cxk = new WS1SPred(s1.MkCharConstraint('c', false), ("x" + (k - 1)));
var inter = new WS1SOr(new WS1SAnd(leq, axk), cxk);
phi = new WS1SAnd(phi, inter);
}
for (int k = to - 1; k >= 0; k--)
{
phi = new WS1SExists(("x" + k), phi);
}
exycy = new WS1SExists(("y"), new WS1SPred(s1.MkCharConstraint('c', false), ("y")));
phi = new WS1SAnd(phi, exycy);
var t4 = 60000L * numTests;
if (to <= maxmphipopold)
{
sw.Restart();
for (int t = 0; t < numTests; t++)
{
phi.getAutomaton(s1);
}
sw.Stop();
t4 = sw.ElapsedMilliseconds;
}
file.WriteLine(to + "," + (double)t1 / numTests + "," + (double)t2 / numTests + "," + (double)t3 / numTests + "," + (double)t4 / numTests);
Console.WriteLine(to + "," + (double)t1 / numTests + "," + (double)t2 / numTests + "," + (double)t3 / numTests + "," + (double)t4 / numTests);
}
}
}
