private FormulaNode GenLC1(FormulaNode stateSet, SymbolicState state)
{
List <FormulaNode> terms = new List <FormulaNode>();
foreach (var e in elementary)
{
if (e.GetLogicOperator() != LogicOperator.EX)
{
continue;
}
string nextName = "succ" + uniqueId.GetTicket().ToString();
SymbolicState next = new SymbolicState(elementary, nextName);
FormulaNode existsInState = state.ValueOf(e);
FormulaNode notExistsInState = new FormulaNode(LogicOperator.NOT, existsInState, null);
FormulaNode nextValid = SymbolicState.Substitute(stateSet, state, next);
FormulaNode transition = GenTransition(state, next);
FormulaNode body = e[0];
FormulaNode occursNext = next.ValueOf(body);
FormulaNode hasSucc = new FormulaNode(LogicOperator.AND, nextValid, transition);
hasSucc = new FormulaNode(LogicOperator.AND, hasSucc, occursNext);
hasSucc = next.Quantify(LogicOperator.EXISTS, hasSucc);
terms.Add(new FormulaNode(LogicOperator.OR, notExistsInState, hasSucc));
}
return(JoinTerms(LogicOperator.AND, terms));
}
/*
* <au> is an elementary formula of the form EX(ER(p,q))
*/
private FormulaNode ComputeAUFragment(FormulaNode au, FormulaNode stateSet, SymbolicState state)
{
#if DEBUG
Console.WriteLine("Computing fragment for " + au);
#endif
FormulaNode frag = FormulaParser.Parse("~TRUE");
FormulaNode notLeft = new FormulaNode(LogicOperator.NOT, au[0][0], null);
FormulaNode notRight = new FormulaNode(LogicOperator.NOT, au[0][1], null);
while (true)
{
string nextName = "succ" + uniqueId.GetTicket().ToString();
SymbolicState next = new SymbolicState(elementary, nextName);
FormulaNode transition = GenTransition(state, next);
FormulaNode memberOf = SymbolicState.Substitute(stateSet, state, next);
FormulaNode nextFrag = SymbolicState.Substitute(frag, state, next);
FormulaNode newFrag = new FormulaNode(LogicOperator.AND, transition, memberOf);
newFrag = new FormulaNode(LogicOperator.AND, newFrag, nextFrag);
newFrag = next.Quantify(LogicOperator.EXISTS, newFrag);
newFrag = new FormulaNode(LogicOperator.AND, state.ValueOf(notLeft.NNF()), newFrag);
// Add the big conjunction needed for fragAU
List <FormulaNode> fragTerms = new List <FormulaNode>();
foreach (FormulaNode el in elementary)
{
if (el.GetLogicOperator() != LogicOperator.EX)
{
continue;
}
nextName = "succ" + uniqueId.GetTicket().ToString();
next = new SymbolicState(elementary, nextName);
transition = GenTransition(state, next);
memberOf = SymbolicState.Substitute(stateSet, state, next);
nextFrag = SymbolicState.Substitute(frag, state, next);
FormulaNode lhs = state.ValueOf(el);
FormulaNode rhs = new FormulaNode(LogicOperator.AND, transition, memberOf);
rhs = new FormulaNode(LogicOperator.AND, rhs, nextFrag);
rhs = new FormulaNode(LogicOperator.AND, rhs, next.ValueOf(SymbolicState.Substitute(el[0], state, next)));
rhs = next.Quantify(LogicOperator.EXISTS, rhs);
fragTerms.Add(new FormulaNode(LogicOperator.IMP, lhs, rhs));
}
newFrag = new FormulaNode(LogicOperator.AND, newFrag, JoinTerms(LogicOperator.AND, fragTerms));
newFrag = new FormulaNode(LogicOperator.OR, state.ValueOf(notRight.NNF()), newFrag);
if (IsFixpoint(newFrag, frag, state))
{
return(frag);
}
frag = newFrag;
}
}
/* Generates a formula representing the fact that <state> has a
* successor in <stateSet>. Does not guarantee that <state> itself
* belongs to the set.
*/
private FormulaNode GenSucc(FormulaNode stateSet, SymbolicState state)
{
string nextName = "succ" + uniqueId.GetTicket().ToString();
SymbolicState next = new SymbolicState(elementary, nextName);
FormulaNode transition = GenTransition(state, next);
FormulaNode memberOf = SymbolicState.Substitute(stateSet, state, next);
FormulaNode result = new FormulaNode(LogicOperator.AND, transition, memberOf);
result = next.Quantify(LogicOperator.EXISTS, result);
return(result);
}
private void ComputeEUFragments(FormulaNode stateSet, SymbolicState state)
{
#if DEBUG
Console.WriteLine("Compute fragments");
#endif
foreach (var e in elementary)
{
if (e.GetLogicOperator() != LogicOperator.EX)
{
continue;
}
if (e[0].GetLogicOperator() != LogicOperator.EU)
{
continue;
}
#if DEBUG
Console.WriteLine("Computing fragment for " + e);
#endif
FormulaNode frag = FormulaParser.Parse("~TRUE");
while (true)
{
string nextName = "succ" + uniqueId.GetTicket().ToString();
SymbolicState next = new SymbolicState(elementary, nextName);
FormulaNode transition = GenTransition(state, next);
FormulaNode memberOf = SymbolicState.Substitute(stateSet, state, next);
FormulaNode nextFrag = SymbolicState.Substitute(frag, state, next);
FormulaNode newFrag = new FormulaNode(LogicOperator.AND, transition, memberOf);
newFrag = new FormulaNode(LogicOperator.AND, newFrag, nextFrag);
newFrag = next.Quantify(LogicOperator.EXISTS, newFrag);
newFrag = new FormulaNode(LogicOperator.AND, state.ValueOf(e[0][0]), newFrag);
newFrag = new FormulaNode(LogicOperator.OR, state.ValueOf(e[0][1]), newFrag);
if (IsFixpoint(newFrag, frag, state))
{
break;
}
frag = newFrag;
}
fragEU[e[0]] = frag;
}
}
