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 MSOFirstLastSucc()
{
var solver = new CharSetSolver(BitWidth.BV64); //new solver using ASCII encoding
List <char> alph = new List <char> {
'a', 'b'
};
HashSet <char> al = new HashSet <char>(alph);
//ex x. first(x)
MSOFormula first = new MSOFirst("x");
MSOFormula last = new MSOLast("y");
MSOFormula succ = new MSOSucc("x", "y");
MSOFormula and = new MSOAnd(new MSOAnd(first, last), succ);
MSOFormula formula = new MSOExistsFO("x", new MSOExistsFO("y", and));
Assert.IsTrue(formula.CheckUseOfVars());
var dfa = formula.getDFA(al, solver);
var test = solver.Convert(@"^(a|b){2}$");
Assert.IsTrue(dfa.IsEquivalentWith(test, solver));
string file = "../../../MSOZ3Test/DotFiles/ab";
solver.SaveAsDot(dfa, "aut", file); //extension .dot is added automatically when missing
}
Automaton<T> CreateAutomaton3<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 MSOTrue<T>();
// x1<x2<x3<x4...
for (int index = 1; index < bitWidth; index++)
{
MSOFormula<T> phi1 = new MSOLt<T>(V1("x" + (index - 1)), V1("x" + index));
phi = new MSOAnd<T>(phi, phi1);
}
// bi(xi)
for (int index = 0; index < bitWidth; index++)
{
MSOFormula<T> phi1 = pred(index, V1("x" + index));
phi = new MSOAnd<T>(phi, phi1);
}
// exists forall...
for (int index = 0; index < bitWidth; index++)
{
if (index % 2 == 0)
phi = new MSOExists<T>(V1("x" + index), phi);
else
phi = new MSOForall<T>(V1("x" + index), phi);
}
var aut = phi.GetAutomaton(Z);
return aut;
}
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_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 MSO2a2b()
{
var solver = new CharSetSolver(BitWidth.BV64); //new solver using ASCII encoding
List <char> alph = new List <char> {
'a', 'b'
};
HashSet <char> al = new HashSet <char>(alph);
MSOFormula formula1 = new MSOExistsFO("x1",
new MSOExistsFO("x2",
new MSOAnd(
new MSOAnd(
new MSOLabel("x1", 'a'),
new MSOLabel("x2", 'a')),
new MSONot(
new MSOEqual("x1", "x2")))));
MSOFormula formula2 = new MSOExistsFO("x1",
new MSOExistsFO("x2",
new MSOAnd(
new MSOAnd(
new MSOLabel("x1", 'b'),
new MSOLabel("x2", 'b')),
new MSONot(
new MSOEqual("x1", "x2")))));
MSOFormula formula = new MSOAnd(formula1, formula2);
Assert.IsTrue(formula.CheckUseOfVars());
var WS1S = formula.ToWS1S(solver);
var dfa = WS1S.getDFA(al, solver);
var timer = new Stopwatch();
var tt = 100;
var acc = 0L;
for (int k = 0; k < tt; k++)
{
timer.Reset();
timer.Start();
dfa = WS1S.getDFA(al, solver);
timer.Stop();
acc += timer.ElapsedMilliseconds;
}
Console.WriteLine("time: " + acc / tt + " ms");
//var test = solver.Convert(@"^(a|b)$");
//Assert.IsTrue(dfa.IsEquivalentWith(test, solver));
string file = "../../../MSOZ3Test/DotFiles/a2b2";
solver.SaveAsDot(dfa, "aut", file); //extension .dot is added automatically when missing
}
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 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);
}
}
}
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 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));
}
}
}
}
Automaton <T> CreateAutomaton3 <T>(Func <int, T> f, int bitWidth, IBooleanAlgebra <T> Z)
{
Func <int, string, MSOPredicate <T> > pred = (i, s) => new MSOPredicate <T>(f(i), s);
MSOFormula <T> phi = new MSOTrue <T>();
// x1<x2<x3<x4...
for (int index = 1; index < bitWidth; index++)
{
MSOFormula <T> phi1 = new MSOLt <T>("x" + (index - 1), "x" + index);
phi = new MSOAnd <T>(phi, phi1);
}
// bi(xi)
for (int index = 0; index < bitWidth; index++)
{
MSOFormula <T> phi1 = pred(index, "x" + index);
phi = new MSOAnd <T>(phi, phi1);
}
// exists forall...
for (int index = 0; index < bitWidth; index++)
{
if (index % 2 == 0)
{
phi = new MSOExistsFo <T>("x" + index, phi);
}
else
{
phi = new MSOForallFo <T>("x" + index, phi);
}
}
Assert.IsTrue(phi.IsWellFormedFormula());
var aut = phi.GetAutomaton(Z);
return(aut);
}
static Automaton <T> CreateAutomaton3 <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 MSOTrue <T>();
// x1<x2<x3<x4...
for (int index = 1; index < bitWidth; index++)
{
MSOFormula <T> phi1 = new MSOLt <T>(new Variable("x" + (index - 1), true), new Variable("x" + index, true));
phi = new MSOAnd <T>(phi, phi1);
}
// bi(xi)
for (int index = 0; index < bitWidth; index++)
{
MSOFormula <T> phi1 = pred(index, "x" + index);
phi = new MSOAnd <T>(phi, phi1);
}
// exists forall...
for (int index = 0; index < bitWidth; index++)
{
if (index % 2 == 0)
{
phi = new MSOExists <T>(new Variable("x" + index, true), phi);
}
else
{
phi = new MSOForall <T>(new Variable("x" + index, true), phi);
}
}
var aut = phi.GetAutomaton(Z);
return(aut);
}
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);
}
}
}
private static Pair<MSOFormula<BoolExpr>, List<BoolExpr>> GenerateMSOFormula(int maxVarIndex)
{
int randomNumber = random.Next(0, 8);
size--;
if (size <= 0)
{
int variable = random.Next(0, maxVarIndex-1);
BoolExpr b = GeneratePredicateOut(200);
List<BoolExpr> l = new List<BoolExpr>();
l.Add(b);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(new MSOPredicate<BoolExpr>(b, new Variable("x"+variable, true)), l);
}
switch (randomNumber)
{
case 0:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex + 1);
MSOFormula<BoolExpr> phi = new MSOExists<BoolExpr>(new Variable("x"+maxVarIndex, true), phi1.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, phi1.Second);
}
case 1:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex + 1);
MSOFormula<BoolExpr> phi = new MSOForall<BoolExpr>(new Variable("x" + maxVarIndex, true), phi1.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, phi1.Second);
}
case 2:
case 3:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex);
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi2 = GenerateMSOFormula(maxVarIndex);
MSOFormula<BoolExpr> phi = new MSOAnd<BoolExpr>(phi1.First, phi2.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, new List<BoolExpr>(phi1.Second.Union(phi2.Second)));
}
case 4:
case 5:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex);
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi2 = GenerateMSOFormula(maxVarIndex);
MSOFormula<BoolExpr> phi = new MSOOr<BoolExpr>(phi1.First, phi2.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, new List<BoolExpr>(phi1.Second.Union(phi2.Second)));
}
case 6:
{
Pair<MSOFormula<BoolExpr>, List<BoolExpr>> phi1 = GenerateMSOFormula(maxVarIndex);
MSOFormula<BoolExpr> phi = new MSONot<BoolExpr>(phi1.First);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, phi1.Second);
}
case 7:
{
if (maxVarIndex > 1)
{
int variable1 = random.Next(0, maxVarIndex - 1);
int variable2 = random.Next(0, maxVarIndex - 1);
if (variable1 == variable2)
{
if (variable1 == maxVarIndex - 1)
variable1 = variable1 - 1;
else
variable2 = variable2 + 1;
}
//Successor
MSOFormula<BoolExpr> phi = new MSOSuccN<BoolExpr>(varOf(variable1),varOf(variable2),random.Next(1,4));
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, new List<BoolExpr>());
}
else
{
int variable = random.Next(0, maxVarIndex - 1);
BoolExpr b = GeneratePredicate();
List<BoolExpr> l = new List<BoolExpr>();
l.Add(b);
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(new MSOPredicate<BoolExpr>(b, new Variable("x" + variable, true)), l);
}
}
case 8:
{
int variable1 = random.Next(0, maxVarIndex - 1);
int variable2 = random.Next(0, maxVarIndex - 1);
//less than
MSOFormula<BoolExpr> phi = new MSOLe<BoolExpr>(varOf(variable1), varOf(variable2));
return new Pair<MSOFormula<BoolExpr>, List<BoolExpr>>(phi, new List<BoolExpr>());
}
}
return null;
}
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);
}
private static Pair <MSOFormula <BoolExpr>, List <BoolExpr> > GenerateMSOFormula(int maxVarIndex)
{
int randomNumber = random.Next(0, 8);
size--;
if (size <= 0)
{
int variable = random.Next(0, maxVarIndex - 1);
BoolExpr b = GeneratePredicateOut(200);
List <BoolExpr> l = new List <BoolExpr>();
l.Add(b);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(new MSOPredicate <BoolExpr>(b, new Variable("x" + variable, true)), l));
}
switch (randomNumber)
{
case 0:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex + 1);
MSOFormula <BoolExpr> phi = new MSOExists <BoolExpr>(new Variable("x" + maxVarIndex, true), phi1.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, phi1.Second));
}
case 1:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex + 1);
MSOFormula <BoolExpr> phi = new MSOForall <BoolExpr>(new Variable("x" + maxVarIndex, true), phi1.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, phi1.Second));
}
case 2:
case 3:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex);
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi2 = GenerateMSOFormula(maxVarIndex);
MSOFormula <BoolExpr> phi = new MSOAnd <BoolExpr>(phi1.First, phi2.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, new List <BoolExpr>(phi1.Second.Union(phi2.Second))));
}
case 4:
case 5:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex);
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi2 = GenerateMSOFormula(maxVarIndex);
MSOFormula <BoolExpr> phi = new MSOOr <BoolExpr>(phi1.First, phi2.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, new List <BoolExpr>(phi1.Second.Union(phi2.Second))));
}
case 6:
{
Pair <MSOFormula <BoolExpr>, List <BoolExpr> > phi1 = GenerateMSOFormula(maxVarIndex);
MSOFormula <BoolExpr> phi = new MSONot <BoolExpr>(phi1.First);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, phi1.Second));
}
case 7:
{
if (maxVarIndex > 1)
{
int variable1 = random.Next(0, maxVarIndex - 1);
int variable2 = random.Next(0, maxVarIndex - 1);
if (variable1 == variable2)
{
if (variable1 == maxVarIndex - 1)
{
variable1 = variable1 - 1;
}
else
{
variable2 = variable2 + 1;
}
}
//Successor
MSOFormula <BoolExpr> phi = new MSOSuccN <BoolExpr>(varOf(variable1), varOf(variable2), random.Next(1, 4));
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, new List <BoolExpr>()));
}
else
{
int variable = random.Next(0, maxVarIndex - 1);
BoolExpr b = GeneratePredicate();
List <BoolExpr> l = new List <BoolExpr>();
l.Add(b);
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(new MSOPredicate <BoolExpr>(b, new Variable("x" + variable, true)), l));
}
}
case 8:
{
int variable1 = random.Next(0, maxVarIndex - 1);
int variable2 = random.Next(0, maxVarIndex - 1);
//less than
MSOFormula <BoolExpr> phi = new MSOLe <BoolExpr>(varOf(variable1), varOf(variable2));
return(new Pair <MSOFormula <BoolExpr>, List <BoolExpr> >(phi, new List <BoolExpr>()));
}
}
return(null);
}