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 override MSOFormula Contains(FreshGen fg, string v)
{
string zi, ziPrev, z0 = "_z0";
int i = str.Length - 1;
MSOFormula phi = new MSOTrue();
while (i > 0)
{
zi = "_z" + i.ToString();
ziPrev = "_z" + (i - 1).ToString();
phi = new MSOExistsFO(zi, new MSOAnd(phi, new MSOAnd(new MSOLabel(zi, str[i]), new MSOSucc(ziPrev, zi))));
i--;
}
phi = new MSOExistsFO(z0, new MSOAnd(phi, new MSOAnd(new MSOLabel(z0, str[0]), new MSOEqual(z0, v))));
return(phi);
}
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 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);
}
}
}
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);
}