/// <summary>
/// Create a new variable which know whether event is tick or not
/// Later all event information is removed from the transition
/// Return the justice based on that new varaible
/// justice: event = tick, event != tick
/// </summary>
/// <param name="modelBDD"></param>
/// <param name="model"></param>
/// <returns></returns>
public List <CUDDNode> GetJustices(AutomataBDD modelBDD, Model model)
{
model.AddLocalVar(EVENT_DUMMY, 0, 1);
//Because later event variables are removed, add new variable to check whether it is tick or not
Expression guard = Expression.OR(
Expression.AND(
TimeBehaviors.GetTickTransExpression(),
new Assignment(EVENT_DUMMY,
new IntConstant(1))),
Expression.AND(
TimeBehaviors.GetNotTickTransExpression(),
new Assignment(EVENT_DUMMY,
new IntConstant(0))));
modelBDD.transitionBDD = CUDD.Function.And(modelBDD.transitionBDD, guard.TranslateBoolExpToBDD(model).GuardDDs);
//the cycle must contain tick transition (zeno) and other transitions (progress)
List <CUDDNode> justices = new List <CUDDNode>();
guard = Expression.EQ(new Variable(EVENT_DUMMY),
new IntConstant(0));
justices.Add(CUDD.Function.Or(guard.TranslateBoolExpToBDD(model).GuardDDs));
guard = Expression.EQ(new Variable(EVENT_DUMMY),
new IntConstant(1));
justices.Add(CUDD.Function.Or(guard.TranslateBoolExpToBDD(model).GuardDDs));
return(justices);
}
/// <summary>
/// Find the deadlock state. This state can be reached by a terminate event.
/// Later termination transition is removed from the transition to finding path
/// [ REFS: , DEREFS: ]
/// </summary>
/// <param name="transitions"></param>
/// <param name="model"></param>
/// <returns></returns>
public static CUDDNode GetDeadlockDD(List <CUDDNode> transitions, Model model)
{
CUDDNode result = CUDD.Constant(1);
//result contains state not having not tick outgoing transition
foreach (CUDDNode transition in transitions)
{
CUDD.Ref(transition);
CUDDNode notTickTrans = CUDD.Function.And(transition, CUDD.Function.Not(TimeBehaviors.GetTickTransEncoding(model)));
//having not tick outgoing transition
CUDDNode notDeadlockState = CUDD.Abstract.ThereExists(notTickTrans, model.AllColVars);
CUDDNode deadlockState = CUDD.Function.Not(notDeadlockState);
result = CUDD.Function.And(result, deadlockState);
}
CUDD.Ref(transitions);
List <CUDDNode> tickTrans = CUDD.Function.And(transitions, TimeBehaviors.GetTickTransEncoding(model));
CUDD.Ref(tickTrans);
CUDDNode stateHasTickTrans = CUDD.Function.Or(CUDD.Abstract.ThereExists(tickTrans, model.AllColVars));
List <int> eventIndex = model.GetEventIndex();
for (int i = 0; i < model.GetNumberOfVars(); i++)
{
if (!eventIndex.Contains(i))
{
CUDD.Ref(model.varIdentities[i]);
tickTrans = CUDD.Function.And(tickTrans, model.varIdentities[i]);
}
}
CUDDNode stateHasLoopTick = CUDD.Function.Or(CUDD.Abstract.ThereExists(tickTrans, model.AllColVars));
//Deadlock state: not having not tick transition and if has tick, then it must loop tick
CUDD.Ref(result);
result = CUDD.Function.Or(CUDD.Function.And(result, CUDD.Function.Not(stateHasTickTrans)), CUDD.Function.And(result, stateHasLoopTick));
return(result);
}
