private Variable ConvertSet(MonaExpr set, MapStack <string, MonaParam> locals, out MSOFormula <BDD> psi)
{
if (set.NrOfSubexprs == 0)
{
return(ConvertEmptyset(out psi));
}
MSOFormula <BDD> disj = null;
Variable x = MkNewVar1();
Variable X = MkNewVar2();
for (int i = 0; i < set.NrOfSubexprs; i++)
{
MonaExpr t = set[i];
if (t.symbol.Kind == Tokens.RANGE)
{
MSOFormula <BDD> from_psi;
Variable from = ConvertTerm1(t[0], locals, out from_psi);
MSOFormula <BDD> to_psi;
Variable to = ConvertTerm1(t[1], locals, out to_psi);
MSOFormula <BDD> range = AddConstraints(from_psi, from, to_psi, to,
new MSOAnd <BDD>(new MSOLe <BDD>(from, x), new MSOLe <BDD>(x, to)));
if (disj == null)
{
disj = range;
}
else
{
disj = new MSOOr <BDD>(disj, range);
}
}
else
{
MSOFormula <BDD> y_psi;
Variable y = ConvertTerm1(t, locals, out y_psi);
MSOFormula <BDD> elem = new MSOEq <BDD>(x, y);
if (y_psi != null)
{
elem = new MSOExists <BDD>(y, new MSOAnd <BDD>(y_psi, elem));
}
if (disj == null)
{
disj = elem;
}
else
{
disj = new MSOOr <BDD>(disj, elem);
}
}
}
var pred = new MSOForall <BDD>(x, new MSOEquiv <BDD>(new MSOIn <BDD>(x, X), disj));
psi = pred;
return(X);
}
public void TestMSO_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);
MSOFormula<BDD> not_xLTy = new MSONot<BDD>(new MSOLt<BDD>(x,y));
MSOFormula<BDD> xEQy = new MSOEq<BDD>(x, y);
var xGTy = new MSOLt<BDD>(y, x);
var xGEy = new MSOOr<BDD>(xEQy, xGTy);
var aut_not_xLTy = not_xLTy.GetAutomaton(ca);
var aut_xGEy = xGEy.GetAutomaton(ca);
var c_aut_xLTy = (new MSOLt<BDD>(x,y)).GetAutomaton(ca).Complement().Determinize().Minimize();
//c_aut_xLTy = c_aut_xLTy.Intersect(aut_fo, ca).Determinize(ca).Minimize(ca); //*
//aut_not_xLTy.ShowGraph("aut_not_xLTy");
//aut_xGEy.ShowGraph("aut_xGEy");
//c_aut_xLTy.ShowGraph("c_aut_xLTy");
var equiv1 = aut_not_xLTy.IsEquivalentWith(aut_xGEy);
//var equiv2 = aut_not_xLTy.IsEquivalentWith(c_aut_xLTy, ca);
Assert.IsTrue(equiv1);
//Assert.IsTrue(equiv2);
}
private Variable ConvertSet(MonaExpr set, MapStack<string, MonaParam> locals, out MSOFormula<BDD> psi)
{
if (set.NrOfSubexprs == 0)
return ConvertEmptyset(out psi);
MSOFormula<BDD> disj = null;
Variable x = MkNewVar1();
Variable X = MkNewVar2();
for (int i=0; i < set.NrOfSubexprs; i++)
{
MonaExpr t = set[i];
if (t.symbol.Kind == Tokens.RANGE)
{
MSOFormula<BDD> from_psi;
Variable from = ConvertTerm1(t[0], locals, out from_psi);
MSOFormula<BDD> to_psi;
Variable to = ConvertTerm1(t[1], locals, out to_psi);
MSOFormula<BDD> range = AddConstraints(from_psi, from, to_psi, to,
new MSOAnd<BDD>(new MSOLe<BDD>(from, x), new MSOLe<BDD>(x, to)));
if (disj == null)
disj = range;
else
disj = new MSOOr<BDD>(disj, range);
}
else
{
MSOFormula<BDD> y_psi;
Variable y = ConvertTerm1(t, locals, out y_psi);
MSOFormula<BDD> elem = new MSOEq<BDD>(x, y);
if (y_psi != null)
elem = new MSOExists<BDD>(y, new MSOAnd<BDD>(y_psi, elem));
if (disj == null)
disj = elem;
else
disj = new MSOOr<BDD>(disj, elem);
}
}
var pred = new MSOForall<BDD>(x, new MSOEquiv<BDD>(new MSOIn<BDD>(x, X), disj));
psi = pred;
return X;
}
private MSOFormula<BDD> ConvertPredApp(MonaPredApp predApp, MapStack<string, MonaParam> locals)
{
var predDef = predMap[predApp.symbol.text];
var predDecl = (MonaPredDecl)globals[predApp.symbol.text];
int k = predDecl.parameters.Count;
if (k != predApp.NrOfSubexprs)
throw new ArgumentException("invalid call of " + predDecl.name);
if (k == 0)
return predDef;
var newVars = new Variable[k];
Dictionary<string, Variable> substitution = new Dictionary<string, Variable>();
var argPreds = new MSOFormula<BDD>[k];
var argVars = new Variable[k];
for (int i = 0; i < k; i++)
{
if (predDecl.parameters[i].kind != MonaParamKind.var1 && predDecl.parameters[i].kind != MonaParamKind.var2)
throw new NotImplementedException("parameter kind " + predDecl.parameters[i].kind.ToString());
MSOFormula<BDD> argPreds_i;
Variable argVars_i;
if (predDecl.parameters[i].kind == MonaParamKind.var1)
{
argVars_i = ConvertTerm1(predApp[i], locals, out argPreds_i);
if (argPreds_i == null)
{
var tmp1 = MkNewVar1();
argPreds_i = new MSOEq<BDD>(tmp1, argVars_i);
argVars_i = tmp1;
}
}
else
{
argVars_i = ConvertTerm2(predApp[i], locals, out argPreds_i);
if (argPreds_i == null)
{
var tmp2 = MkNewVar2();
argPreds_i = new MSOEq<BDD>(tmp2, argVars_i);
argVars_i = tmp2;
}
}
argPreds[i] = argPreds_i;
argVars[i] = argVars_i;
substitution[predDecl.parameters[i].Token.text] = argVars_i;
}
MSOFormula<BDD> psi = predDef.SubstituteVariables(substitution);
for (int i = k - 1; i >= 0; i--)
psi = new MSOExists<BDD>(argVars[i], argPreds[i] & psi);
return psi;
}
private MSOFormula <BDD> ConvertPredApp(MonaPredApp predApp, MapStack <string, MonaParam> locals)
{
var predDef = predMap[predApp.symbol.text];
var predDecl = (MonaPredDecl)globals[predApp.symbol.text];
int k = predDecl.parameters.Count;
if (k != predApp.NrOfSubexprs)
{
throw new ArgumentException("invalid call of " + predDecl.name);
}
if (k == 0)
{
return(predDef);
}
var newVars = new Variable[k];
Dictionary <string, Variable> substitution = new Dictionary <string, Variable>();
var argPreds = new MSOFormula <BDD> [k];
var argVars = new Variable[k];
for (int i = 0; i < k; i++)
{
if (predDecl.parameters[i].kind != MonaParamKind.var1 && predDecl.parameters[i].kind != MonaParamKind.var2)
{
throw new NotImplementedException("parameter kind " + predDecl.parameters[i].kind.ToString());
}
MSOFormula <BDD> argPreds_i;
Variable argVars_i;
if (predDecl.parameters[i].kind == MonaParamKind.var1)
{
argVars_i = ConvertTerm1(predApp[i], locals, out argPreds_i);
if (argPreds_i == null)
{
var tmp1 = MkNewVar1();
argPreds_i = new MSOEq <BDD>(tmp1, argVars_i);
argVars_i = tmp1;
}
}
else
{
argVars_i = ConvertTerm2(predApp[i], locals, out argPreds_i);
if (argPreds_i == null)
{
var tmp2 = MkNewVar2();
argPreds_i = new MSOEq <BDD>(tmp2, argVars_i);
argVars_i = tmp2;
}
}
argPreds[i] = argPreds_i;
argVars[i] = argVars_i;
substitution[predDecl.parameters[i].Token.text] = argVars_i;
}
MSOFormula <BDD> psi = predDef.SubstituteVariables(substitution);
for (int i = k - 1; i >= 0; i--)
{
psi = new MSOExists <BDD>(argVars[i], argPreds[i] & psi);
}
return(psi);
}