/// <summary>
/// P.var : P1.var
/// </summary>
private static void GuardSetVariable(AutomataBDD P1, Model model, AutomataBDD result)
{
result.variableIndex.AddRange(P1.variableIndex);
result.newLocalVarName = Model.GetNewTempVarName();
model.AddLocalVar(result.newLocalVarName, 0, 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
}
/// <summary>
/// P.var : P1.var ∪ {temp}
/// </summary>
private static void EventPrefixSetVariable(AutomataBDD P1, Model model, AutomataBDD result)
{
result.variableIndex.AddRange(P1.variableIndex);
result.newLocalVarName = Model.GetNewTempVarName();
model.AddLocalVar(result.newLocalVarName, 0, 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
}
/// <summary>
/// P.var : [∪ {i = 1..n}Pi.var] ∪ {temp}
/// </summary>
private static void InternalChoiceSetVariable(List <AutomataBDD> choices, Model model, AutomataBDD result)
{
foreach (AutomataBDD choice in choices)
{
result.variableIndex.AddRange(choice.variableIndex);
}
result.newLocalVarName = Model.GetNewTempVarName();
model.AddLocalVar(result.newLocalVarName, -1, choices.Count - 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
}
private static void ChannelInputSetVariable(List<Expression> exps, AutomataBDD P1, Model model, AutomataBDD result)
{
//Add new variable used in channel input
foreach (var expression in exps)
{
if (!(expression is IntConstant) && !model.ContainsVar(expression.ExpressionID))
{
model.AddLocalVar(expression.ExpressionID, Model.MIN_ELEMENT_BUFFER, Model.MAX_ELEMENT_BUFFER);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
}
}
EventPrefixSetVariable(P1, model, result);
}
private static void ChannelInputSetVariable(List <Expression> exps, AutomataBDD P1, Model model, AutomataBDD result)
{
//Add new variable used in channel input
foreach (var expression in exps)
{
if (!(expression is IntConstant) && !model.ContainsVar(expression.ExpressionID))
{
model.AddLocalVar(expression.ExpressionID, Model.MIN_ELEMENT_BUFFER, Model.MAX_ELEMENT_BUFFER);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
}
}
EventPrefixSetVariable(P1, model, result);
}
/// <summary>
/// P.var : P1.var ∪ P2.var ∪{isP1Terminate}
/// </summary>
public static List <string> SequenceSetVariable(AutomataBDD P1, AutomataBDD P2, Model model, AutomataBDD result)
{
//
result.variableIndex.AddRange(P1.variableIndex);
result.variableIndex.AddRange(P2.variableIndex);
string isP1Terminate = Model.GetNewTempVarName();
model.AddLocalVar(isP1Terminate, 0, 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
return(new List <string>()
{
isP1Terminate
});
}
/// <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;
}
/// <summary>
/// General algorithm of the intersection of 2 automata
/// Follow the algorithm in Linear Temporal Logic Symbolic Model Checking at http://ti.arc.nasa.gov/m/profile/kyrozier/papers/COSREV_62.pdf page 23
/// [ REFS: 'result', DEREFS:'automata1, automata2' ]
/// </summary>
/// <param name="automata1"></param>
/// <param name="automata2"></param>
/// <param name="model"></param>
/// <returns></returns>
public static AutomataBDD IntersectionGeneralAutomata(AutomataBDD automata1, AutomataBDD automata2, Model model)
{
//AddIdleTransAtDeadlockStates(automata1, model);
AutomataBDD result = new AutomataBDD();
string newVarName = Model.GetNewTempVarName();
//Set var
result.variableIndex.AddRange(automata1.variableIndex);
result.variableIndex.AddRange(automata2.variableIndex);
model.AddLocalVar(newVarName, 0, 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
//Set Init
Expression initTemp = Expression.AND(automata1.initExpression, automata2.initExpression);
Expression initValueOfT = Expression.EQ(new Variable(newVarName), new IntConstant(0));
result.initExpression = Expression.AND(initTemp, initValueOfT);
//Set Acceptance State
result.acceptanceExpression = Expression.AND(automata1.acceptanceExpression, initValueOfT);
//Set Transition
//(temp = 0 and automata1.accept) or (temp = 1 and buchi.accept)
Expression guard = Expression.OR(
Expression.AND(
new PrimitiveApplication(
PrimitiveApplication.EQUAL,
new Variable(newVarName),
new IntConstant(0)),
automata1.acceptanceExpression),
Expression.AND(
new PrimitiveApplication(
PrimitiveApplication.EQUAL,
new Variable(newVarName),
new IntConstant(1)),
automata2.acceptanceExpression));
//guard and (temp' = 1 - temp)
Expression transition1Exp = Expression.AND(guard,
new Assignment(newVarName,
new PrimitiveApplication(
PrimitiveApplication.MINUS,
new IntConstant(1),
new Variable(newVarName))));
List <CUDDNode> transition1 = transition1Exp.TranslateBoolExpToBDD(model).GuardDDs;
//!guard and (temp' = temp)
Expression transition2Exp = Expression.AND(
Expression.NOT(guard),
new Assignment(newVarName, new Variable(newVarName)));
List <CUDDNode> transition2 = transition2Exp.TranslateBoolExpToBDD(model).GuardDDs;
//transition must happen at both automata1 + negation LTL
List <CUDDNode> bothTransition = CUDD.Function.And(automata1.transitionBDD, automata2.transitionBDD);
CUDD.Ref(bothTransition);
transition1 = CUDD.Function.And(transition1, bothTransition);
result.transitionBDD.AddRange(transition1);
transition2 = CUDD.Function.And(transition2, bothTransition);
result.transitionBDD.AddRange(transition2);
//
CUDD.Deref(automata1.channelInTransitionBDD, automata1.channelOutTransitionBDD, automata2.channelInTransitionBDD, automata2.channelOutTransitionBDD);
return(result);
}
/// <summary>
/// P.var : m0 ∪ m1 ∪ {clk}
/// </summary>
private static List<string> TimeInterruptSetVariable(AutomataBDD m0, AutomataBDD m1, int t, Model model, AutomataBDD result)
{
result.variableIndex.AddRange(m0.variableIndex);
result.variableIndex.AddRange(m1.variableIndex);
//
string clk = Model.GetNewTempVarName();
model.AddLocalVar(clk, -1, t + 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
return new List<string>() { clk };
}
/// <summary>
/// P.var = {temp}
/// </summary>
private static void SkipSetVariable(Model model, AutomataBDD result)
{
result.newLocalVarName = Model.GetNewTempVarName();
model.AddLocalVar(result.newLocalVarName, 0, 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
}
/// <summary>
/// General algorithm of the intersection of 2 automata
/// Follow the algorithm in Linear Temporal Logic Symbolic Model Checking at http://ti.arc.nasa.gov/m/profile/kyrozier/papers/COSREV_62.pdf page 23
/// [ REFS: 'result', DEREFS:'automata1, automata2' ]
/// </summary>
/// <param name="automata1"></param>
/// <param name="automata2"></param>
/// <param name="model"></param>
/// <returns></returns>
public static AutomataBDD IntersectionGeneralAutomata(AutomataBDD automata1, AutomataBDD automata2, Model model)
{
//AddIdleTransAtDeadlockStates(automata1, model);
AutomataBDD result = new AutomataBDD();
string newVarName = Model.GetNewTempVarName();
//Set var
result.variableIndex.AddRange(automata1.variableIndex);
result.variableIndex.AddRange(automata2.variableIndex);
model.AddLocalVar(newVarName, 0, 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
//Set Init
Expression initTemp = Expression.AND(automata1.initExpression, automata2.initExpression);
Expression initValueOfT = Expression.EQ(new Variable(newVarName), new IntConstant(0));
result.initExpression = Expression.AND(initTemp, initValueOfT);
//Set Acceptance State
result.acceptanceExpression = Expression.AND(automata1.acceptanceExpression, initValueOfT);
//Set Transition
//(temp = 0 and automata1.accept) or (temp = 1 and buchi.accept)
Expression guard = Expression.OR(
Expression.AND(
new PrimitiveApplication(
PrimitiveApplication.EQUAL,
new Variable(newVarName),
new IntConstant(0)),
automata1.acceptanceExpression),
Expression.AND(
new PrimitiveApplication(
PrimitiveApplication.EQUAL,
new Variable(newVarName),
new IntConstant(1)),
automata2.acceptanceExpression));
//guard and (temp' = 1 - temp)
Expression transition1Exp = Expression.AND(guard,
new Assignment(newVarName,
new PrimitiveApplication(
PrimitiveApplication.MINUS,
new IntConstant(1),
new Variable(newVarName))));
List<CUDDNode> transition1 = transition1Exp.TranslateBoolExpToBDD(model).GuardDDs;
//!guard and (temp' = temp)
Expression transition2Exp = Expression.AND(
Expression.NOT(guard),
new Assignment(newVarName, new Variable(newVarName)));
List<CUDDNode> transition2 = transition2Exp.TranslateBoolExpToBDD(model).GuardDDs;
//transition must happen at both automata1 + negation LTL
List<CUDDNode> bothTransition = CUDD.Function.And(automata1.transitionBDD, automata2.transitionBDD);
CUDD.Ref(bothTransition);
transition1 = CUDD.Function.And(transition1, bothTransition);
result.transitionBDD.AddRange(transition1);
transition2 = CUDD.Function.And(transition2, bothTransition);
result.transitionBDD.AddRange(transition2);
//
CUDD.Deref(automata1.channelInTransitionBDD, automata1.channelOutTransitionBDD, automata2.channelInTransitionBDD, automata2.channelOutTransitionBDD);
return result;
}
/// <summary>
/// P.var : P1.var ∪ P2.var ∪{isP1Terminate}
/// </summary>
public static List<string> SequenceSetVariable(AutomataBDD P1, AutomataBDD P2, Model model, AutomataBDD result)
{
//
result.variableIndex.AddRange(P1.variableIndex);
result.variableIndex.AddRange(P2.variableIndex);
string isP1Terminate = Model.GetNewTempVarName();
model.AddLocalVar(isP1Terminate, 0, 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
return new List<string>() { isP1Terminate };
}
/// <summary>
/// P.var = {temp}
/// </summary>
private static void SkipSetVariable(Model model, AutomataBDD result)
{
result.newLocalVarName = Model.GetNewTempVarName();
model.AddLocalVar(result.newLocalVarName, 0, 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
}
/// <summary>
/// P.var : [∪ {i = 1..n}Pi.var] ∪ {temp}
/// </summary>
private static void ExternalChoiceSetVariable(List<AutomataBDD> choices, Model model, AutomataBDD result)
{
foreach (AutomataBDD choice in choices)
{
result.variableIndex.AddRange(choice.variableIndex);
}
result.newLocalVarName = Model.GetNewTempVarName();
model.AddLocalVar(result.newLocalVarName, -1, choices.Count - 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
}
/// <summary>
/// P.var : 0 <= state <= t + 1
/// </summary>
/// <param name="t"></param>
/// <param name="model"></param>
/// <param name="result"></param>
/// <returns></returns>
private static List<string> WaitSetVariable(int t, Model model, AutomataBDD result)
{
string state = Model.GetNewTempVarName();
model.AddLocalVar(state, 0, t + 1);
result.variableIndex.Add(model.GetNumberOfVars() - 1);
return new List<string>() { state };
}
