/// <summary>
/// Return a computation of a buchi automata in form "prefix (period)*"
/// [ REFS: 'prefix, period', DEREFS:]
/// </summary>
/// <param name="automataBDD"></param>
/// <param name="model"></param>
public void MC(AutomataBDD automataBDD, Model model)
{
//Clear the old data
this.transitionsNoEvents.Clear();
this.prefix.Clear();
this.period.Clear();
ExpressionBDDEncoding initEncoding = automataBDD.initExpression.TranslateBoolExpToBDD(model);
if (initEncoding.GuardDDs.Count == 0)
{
return;
}
ExpressionBDDEncoding finalStateEncoding = automataBDD.acceptanceExpression.TranslateBoolExpToBDD(model);
if (finalStateEncoding.GuardDDs.Count == 0)
{
return;
}
CUDDNode initState = CUDD.Function.Or(initEncoding.GuardDDs);
CUDDNode finalState = CUDD.Function.Or(finalStateEncoding.GuardDDs);
CUDDNode finalStateWithNoEvent = CUDD.Abstract.ThereExists(finalState, model.GetAllEventVars());
CUDD.Ref(automataBDD.transitionBDD);
this.transitionsNoEvents = CUDD.Abstract.ThereExists(automataBDD.transitionBDD, model.GetAllEventVars());
CUDDNode allSCCs = SCCHull(model, initState, finalStateWithNoEvent);
if (!allSCCs.Equals(CUDD.ZERO) && VerificationOutput.GenerateCounterExample)
{
this.VerificationOutput.VerificationResult = VerificationResultType.INVALID;
//Transitions out from allSCCs
CUDD.Ref(transitionsNoEvents);
CUDD.Ref(allSCCs);
List<CUDDNode> R = CUDD.Function.And(transitionsNoEvents, allSCCs);
//pick one state from the set final
CUDD.Ref(allSCCs);
CUDDNode s = CUDD.RestrictToFirst(allSCCs, model.AllRowVars);
//while the states from which we can reach s are not all states that can be reached from s
CUDDNode scc;
while (true)
{
CUDD.Ref(s);
CUDDNode backwardOfS = model.PredecessorsStart(s, R);
CUDD.Ref(s);
CUDDNode forwardOfS = model.SuccessorsStart(s, R);
//
CUDD.Ref(backwardOfS, forwardOfS);
CUDDNode temp = CUDD.Function.Different(backwardOfS, forwardOfS);
if (temp.Equals(CUDD.ZERO))
{
scc = backwardOfS;
CUDD.Deref(forwardOfS, temp);
break;
}
else
{
CUDD.Deref(backwardOfS, forwardOfS, s);
s = CUDD.RestrictToFirst(temp, model.AllRowVars);
}
}
//R now contains only transitions within the SCC scc
CUDD.Ref(scc, scc, scc, scc);
R[0] = CUDD.Function.And(CUDD.Function.And(R[0], scc), model.SwapRowColVars(scc));
R[1] = CUDD.Function.And(CUDD.Function.And(R[1], scc), model.SwapRowColVars(scc));
CUDD.Ref(scc);
CUDDNode notInSCC = CUDD.Function.Not(scc);
List<CUDDNode> transitionNotInSCC = new List<CUDDNode>();
CUDD.Ref(transitionsNoEvents, transitionsNoEvents);
CUDD.Ref(notInSCC, notInSCC);
transitionNotInSCC.AddRange(CUDD.Function.And(transitionsNoEvents, notInSCC));
transitionNotInSCC.AddRange(CUDD.Function.And(transitionsNoEvents, model.SwapRowColVars(notInSCC)));
//prefix is now a shortest path from an initial state to a state in final
model.Path(initState, scc, transitionNotInSCC, prefix, true);
CUDD.Deref(transitionNotInSCC[0], transitionNotInSCC[1]);
//Dummy value
period.Add((prefix.Count == 0) ? initState : prefix[prefix.Count - 1]);
//cycle must pass final state
CUDD.Ref(period);
CUDD.Ref(finalStateWithNoEvent);
CUDDNode temp1 = CUDD.Function.And(CUDD.Function.Or(period), finalStateWithNoEvent);
if (temp1.Equals(CUDD.ZERO))
{
CUDD.Ref(scc, finalStateWithNoEvent);
CUDDNode acceptanceStateInCyle = CUDD.Function.And(scc, finalStateWithNoEvent);
model.Path(period[period.Count - 1], acceptanceStateInCyle, R, period, true);
CUDD.Deref(acceptanceStateInCyle);
}
CUDD.Deref(temp1);
//
bool isEmptyPathAllowed = period.Count != 1;
model.Path(period[period.Count - 1], period[0], R, period, isEmptyPathAllowed);
//Remove dummy
CUDD.Deref(period[0]); period.RemoveAt(0);
//
CUDD.Deref(initState, finalStateWithNoEvent, allSCCs, s, scc, notInSCC);
CUDD.Deref(transitionsNoEvents[0], transitionsNoEvents[1]);
CUDD.Deref(R[0], R[1]);
}
else
{
this.VerificationOutput.VerificationResult = VerificationResultType.VALID;
CUDD.Deref(initState, finalStateWithNoEvent, allSCCs);
CUDD.Deref(transitionsNoEvents[0], transitionsNoEvents[1]);
}
}
/// <summary>
/// Return strongly connected components
/// Does not include Event variable
/// this.transitionsNoEvents is the transtion from reachble states
/// From Feasible algorithm in the article "LTL Symbolic MC"
/// [ REFS: 'result', DEREFS:]
/// </summary>
/// <param name="model"></param>
/// <param name="initState"></param>
/// <param name="finalState"></param>
/// <returns></returns>
private CUDDNode SCCHull(Model model, CUDDNode initState, CUDDNode finalState)
{
CUDDNode old = CUDD.Constant(0);
CUDD.Ref(initState);
CUDDNode New = model.SuccessorsStart(initState, this.transitionsNoEvents);
//Limit transition to transition of reachable states
CUDD.Ref(New);
transitionsNoEvents = CUDD.Function.And(transitionsNoEvents, New);
//Pruning step: remove states whose succeessors are not belong to that set
while (!New.Equals(old))
{
CUDD.Deref(old);
CUDD.Ref(New);
old = New;
//final state as justice requirement
//new = (new and J) x R*
CUDD.Ref(finalState);
New = model.SuccessorsStart(CUDD.Function.And(New, finalState), this.transitionsNoEvents);
//while new is not comprised of the set of all successors of new states
while (true)
{
CUDD.Ref(New, New);
CUDDNode temp = CUDD.Function.And(New, model.Successors(New, this.transitionsNoEvents));
if (temp.Equals(New))
{
CUDD.Deref(temp);
break;
}
else
{
CUDD.Deref(New);
New = temp;
}
}
}
return New;
}
