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_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 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 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 TestMSO_Eq()
{
var solver = new CharSetSolver(BitWidth.BV16);
//var phi = new MSOTrue();
MSOFormula<BDD> phi = new MSOExists<BDD>(V1("x"), new MSOExists<BDD>(V1("y"), new MSONot<BDD>(new MSOEq<BDD>(V1("x"), V1("y")))));
var aut = phi.GetAutomaton(solver);
var aut2 = solver.RegexConverter.Convert(".{2,}", System.Text.RegularExpressions.RegexOptions.Singleline);
Assert.IsTrue(aut.IsEquivalentWith(aut2));
}
public void TestIntExZ3()
{
var solver = new Z3Provider();
var sort = solver.CharacterSort;
//var phi = new MSOTrue();
MSOFormula <Expr> phi = new MSOExists <Expr>(V1("x"),
new MSOPredicate <Expr>(solver.MkLe(solver.MkVar(0, solver.IntSort), solver.MkInt(0)), V1("x"))
);
var aut = phi.GetAutomaton(solver);
}
public void TestMSO_FirstC()
{
var solver = new CharSetSolver(BitWidth.BV16);
//var phi = new MSOTrue();
var x = new Variable("x", true);
MSOFormula<BDD> phi = new MSOExists<BDD>(x,
new MSOAnd<BDD>(new MSOPredicate<BDD>(solver.MkCharConstraint('C'), x), new MSOeqN<BDD>(x,0)));
var aut = phi.GetAutomaton(solver);
var aut2 = solver.RegexConverter.Convert("^C");
Assert.IsTrue(aut2.IsEquivalentWith(aut));
}
public void TestMSO_FirstLastZ3()
{
var solver = new CharSetSolver(BitWidth.BV16);
var x = new Variable("x", true);
MSOFormula<BDD> phi = new MSOExists<BDD>(x, new MSOAnd<BDD>(new MSOeqN<BDD>(x,0), new MSOLast<BDD>(x)));
var aut = phi.GetAutomaton(solver);
var res = solver.Convert("^[\0-\uFFFF]$");
//solver.ShowGraph(res,"res");
//solver.SaveAsDgml(res, "res");
var eq = aut.IsEquivalentWith(res);
Assert.IsTrue(eq);
}
static Automaton <T> CreateAutomaton1 <T>(Func <int, T> f, int bitWidth, IBooleanAlgebra <T> Z)
{
Func <int, string, MSOPredicate <T> > pred = (i, s) => new MSOPredicate <T>(f(i), new Variable(s, true));
MSOFormula <T> phi = new MSOFalse <T>();
for (int index = 0; index < bitWidth; index++)
{
var phi1 = pred(index, "var");
phi = new MSOOr <T>(phi, phi1);
}
phi = new MSOExists <T>(new Variable("var", true), phi);
var aut = phi.GetAutomaton(Z);
return(aut);
}
public void TestCountNoProduct2()
{
int maxvars = 13;
var solver = new CharSetSolver(BitWidth.BV7);
Stopwatch sw = new Stopwatch();
var tries = 1;
var times = new long[maxvars - 1];
var x = new Variable("x", true);
var y = new Variable("y", true);
for (int k = 0; k < tries; k++)
{
for (int vars = 8; vars <= maxvars; vars++)
{
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int i = 1; i < vars; i++)
{
phi = new MSOAnd <BDD>(phi, new MSOLt <BDD>(new Variable("x" + i, true), new Variable("x" + (i + 1), true)));
phi = new MSOAnd <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('a'), new Variable("x" + i, true)));
phi = new MSOOr <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('k'), new Variable("x" + i, true)));
}
phi = new MSOAnd <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('a'), new Variable("x" + vars, true)));
phi = new MSOOr <BDD>(phi,
new MSOExists <BDD>(y,
new MSOPredicate <BDD>(solver.MkCharConstraint('c'), y)));
for (int i = vars; i >= 1; i--)
{
phi = new MSOExists <BDD>(new Variable("x" + i, true), phi);
}
sw.Restart();
//var aut1 = phi.GetAutomaton(new CartesianAlgebraBDD<BDD>(solver));
var aut1 = phi.GetAutomaton(solver);
sw.Stop();
times[vars - 2] += sw.ElapsedMilliseconds;
//Console.WriteLine("States {0} Trans {1}",aut1.StateCount,aut1.MoveCount);
if (k == tries - 1)
{
TestContext.WriteLine(string.Format("{0} variables; {1} ms", vars, times[vars - 2] / tries));
}
//solver.ShowGraph(aut1, "a"+vars);
}
}
}
Automaton <T> CreateAutomaton2 <T>(Func <int, T> f, int bitWidth, IBooleanAlgebra <T> Z)
{
Func <int, Variable, MSOPredicate <T> > pred = (i, s) => new MSOPredicate <T>(f(i), s);
MSOFormula <T> phi = new MSOFalse <T>();
for (int index = 0; index < bitWidth; index++)
{
MSOFormula <T> phi1 = pred(index, V1("var"));
phi1 = new MSOExists <T>(V1("var"), phi1);
phi = new MSOOr <T>(phi, phi1);
}
phi = new MSOExists <T>(V1("var"), phi);
var aut = phi.GetAutomaton(Z);
return(aut);
}
public void TestCount()
{
int maxvars = 10;
var solver = new CharSetSolver(BitWidth.BV16);
Stopwatch sw = new Stopwatch();
var tries = 1;
var times = new long[maxvars - 1];
for (int k = 0; k < tries; k++)
{
for (int vars = 8; vars <= maxvars; vars++)
{
MSOFormula <BDD> phi = new MSOTrue <BDD>();
for (int i = 1; i < vars; i++)
{
phi = new MSOAnd <BDD>(phi, new MSOLt <BDD>(V1("x" + i), V1("x" + (i + 1))));
phi = new MSOAnd <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('a'), V1("x" + i)));
}
phi = new MSOAnd <BDD>(phi, new MSOPredicate <BDD>(solver.MkCharConstraint('a'), V1("x" + vars)));
phi = new MSOOr <BDD>(phi,
new MSOExists <BDD>(V1("y"),
new MSOPredicate <BDD>(solver.MkCharConstraint('c'), V1("y"))));
for (int i = vars; i >= 1; i--)
{
phi = new MSOExists <BDD>(V1("x" + i), phi);
}
sw.Restart();
//var aut1 = phi.GetAutomaton(new CartesianAlgebraBDD<BDD>(solver));
var aut1 = phi.GetAutomaton(solver);
//aut1.ShowGraph();
sw.Stop();
times[vars - 2] += sw.ElapsedMilliseconds;
if (k == tries - 1)
{
TestContext.WriteLine(string.Format("{0} variables; {1} ms", vars, times[vars - 2] / tries));
}
}
}
}
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 TestMSO_Le()
{
var solver = new CharSetSolver(BitWidth.BV16);
//var phi = new MSOTrue();
var x = new Variable("x", true);
var y = new Variable("y", true);
var z = new Variable("z", true);
MSOFormula<BDD> phi = new MSOExists<BDD>(z, new MSOExists<BDD>(x, new MSOExists<BDD>(y,
new MSOAnd<BDD>(
new MSOLt<BDD>(x, y),
new MSOLt<BDD>(y, z)
)
)));
var aut = phi.GetAutomaton(solver);
var aut2 = solver.RegexConverter.Convert(".{3,}", System.Text.RegularExpressions.RegexOptions.Singleline);
Assert.IsTrue(aut.IsEquivalentWith(aut2));
//solver.ShowGraph(aut, "SFA");
}
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);
}
}
}
