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 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 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);
}
/// <summary>
/// If t is a variable name then returns t as a f-o variable and sets psi=null.
/// Else returns a fresh f-o variable x and outputs psi(x) s.t. psi(x) iff x=t.
/// </summary>
Variable ConvertTerm1(MonaExpr t, MapStack <string, MonaParam> locals, out MSOFormula <BDD> psi)
{
switch (t.symbol.Kind)
{
case Tokens.NAME:
{
MonaParam p;
if (locals.TryGetValue(t.symbol.text, out p))
{
if (p.kind == MonaParamKind.var1)
{
psi = null;
return(new Variable(t.symbol.text, true));
}
else
{
throw new NotImplementedException(t.ToString());
}
}
else
{
MonaDecl d;
if (globals.TryGetValue(t.symbol.text, out d))
{
if (d.kind == MonaDeclKind.constant)
{
int n = ((MonaConstDecl)d).def.ToInt(globals);
Variable x = MkNewVar1();
var pred = new MSOeqN <BDD>(x, n);
psi = pred;
return(x);
}
else
{
throw new NotImplementedException(t.ToString());
}
}
else
{
throw new NotImplementedException(t.ToString());
}
}
}
case Tokens.PLUS:
{
Variable y = MkNewVar1();
if (t[0].symbol.Kind == Tokens.NAME)
{
int n = t[1].ToInt(globals);
Variable x = new Variable(t[0].symbol.text, true);
psi = new MSOSuccN <BDD>(x, y, n); // y = x + n
}
else
{
int n = t.ToInt(globals);
psi = new MSOeqN <BDD>(y, n); // y = n
}
return(y);
}
case Tokens.MIN:
{
MSOFormula <BDD> X_psi;
Variable X = ConvertTerm2(t[0], locals, out X_psi);
Variable x = MkNewVar1();
MSOFormula <BDD> min = new MSOMin <BDD>(x, X);
if (X_psi != null)
{
min = new MSOExists <BDD>(X, new MSOAnd <BDD>(X_psi, min));
}
psi = min;
return(x);
}
case Tokens.MAX:
{
MSOFormula <BDD> X_psi;
Variable X = ConvertTerm2(t[0], locals, out X_psi);
Variable x = MkNewVar1();
MSOFormula <BDD> max = new MSOMax <BDD>(x, X);
if (X_psi != null)
{
max = new MSOExists <BDD>(X, new MSOAnd <BDD>(X_psi, max));
}
psi = max;
return(x);
}
default:
throw new NotImplementedException(t.ToString());
}
}
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;
}
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);
}
/// <summary>
/// If t is a variable name then returns t as a f-o variable and sets psi=null.
/// Else returns a fresh f-o variable x and outputs psi(x) s.t. psi(x) iff x=t.
/// </summary>
Variable ConvertTerm1(MonaExpr t, MapStack<string, MonaParam> locals, out MSOFormula<BDD> psi)
{
switch (t.symbol.Kind)
{
case Tokens.NAME:
{
MonaParam p;
if (locals.TryGetValue(t.symbol.text, out p))
{
if (p.kind == MonaParamKind.var1)
{
psi = null;
return new Variable(t.symbol.text, true);
}
else
throw new NotImplementedException(t.ToString());
}
else
{
MonaDecl d;
if (globals.TryGetValue(t.symbol.text, out d))
{
if (d.kind == MonaDeclKind.constant)
{
int n = ((MonaConstDecl)d).def.ToInt(globals);
Variable x = MkNewVar1();
var pred = new MSOeqN<BDD>(x, n);
psi = pred;
return x;
}
else if (d.kind == MonaDeclKind.var1)
{
psi = null;
return new Variable(t.symbol.text, true);
}
else
throw new NotImplementedException(t.ToString());
}
else
throw new NotImplementedException(t.ToString());
}
}
case Tokens.PLUS:
{
Variable y = MkNewVar1();
if (t[0].symbol.Kind == Tokens.NAME)
{
int n = t[1].ToInt(globals);
Variable x = new Variable(t[0].symbol.text, true);
psi = new MSOSuccN<BDD>(x, y, n); // y = x + n
}
else
{
int n = t.ToInt(globals);
psi = new MSOeqN<BDD>(y, n); // y = n
}
return y;
}
case Tokens.MIN:
{
MSOFormula<BDD> X_psi;
Variable X = ConvertTerm2(t[0], locals, out X_psi);
Variable x = MkNewVar1();
MSOFormula<BDD> min = new MSOMin<BDD>(x, X);
if (X_psi != null)
min = new MSOExists<BDD>(X, new MSOAnd<BDD>(X_psi, min));
psi = min;
return x;
}
case Tokens.MAX:
{
MSOFormula<BDD> X_psi;
Variable X = ConvertTerm2(t[0], locals, out X_psi);
Variable x = MkNewVar1();
MSOFormula<BDD> max = new MSOMax<BDD>(x, X);
if (X_psi != null)
max = new MSOExists<BDD>(X, new MSOAnd<BDD>(X_psi, max));
psi = max;
return x;
}
case Tokens.NUMBER:
{
Variable x = MkNewVar1();
int num = t.symbol.ToInt();
psi = new MSOeqN<BDD>(x,num);
return x;
}
default:
throw new NotImplementedException(t.ToString());
}
}