public MDP ComputeGCPP(VerificationOutput VerificationOutput)
{
MDP toReturn = new MDP(Precision, MAX_DIFFERENCE);
//add Initial
MDPState Initial = new MDPState(InitState.ID);
toReturn.AddState(Initial);
toReturn.SetInit(Initial);
//add target
foreach (MDPState targetstate in this.TargetStates)
{
AddTargetStates(targetstate);
}
//note here remaining doesn't include the target states and initial states
HashSet<MDPState> remaining = new HashSet<MDPState>();
foreach (MDPState mdpState in States.Values)
{
if (!TargetStates.Contains(mdpState) && InitState != mdpState)
{
remaining.Add(mdpState);
}
}
//instantiate GCPP
GCPP gcpp = new GCPP();
Dictionary<string, int> table = new Dictionary<string, int>();
foreach (MDPState mdpState in remaining)
{
gcpp.MDPTable.Add(mdpState.ID, mdpState);
table.Add(mdpState.ID, 0);
}
int n = 0;
foreach (MDPState mdpState1 in remaining)
{
foreach (MDPState mdpState2 in remaining)
{
List<MDPState> list = new List<MDPState>();
if (mdpState1 != mdpState2 && table[mdpState1.ID] == table[mdpState2.ID] && PropositionEquals(mdpState1, mdpState2))
{
list.Add(mdpState1);
list.Add(mdpState2);
table[mdpState1.ID] = 1;
table[mdpState2.ID] = 1;
gcpp.PartOrder.Add(n, n);
gcpp.Partition.Add(n, list);
gcpp.PartitionGetKey.Add(list, n++);
}
}
}
gcpp.partition = null;
gcpp.partorder = null;
while (gcpp.Partition != gcpp.partition || gcpp.PartOrder != gcpp.partorder)
{
gcpp.partition = gcpp.Partition;
gcpp.partorder = gcpp.PartOrder;
foreach (List<MDPState> B in gcpp.partition.Values)
{
//GCPP item = new GCPP();
gcpp = Split(gcpp, B);
//∑:=∑\{B}∪{∑B}
gcpp.Partition.Remove(gcpp.PartitionGetKey[B]);
foreach (KeyValuePair<int, List<MDPState>> pair in gcpp.partition)
{
gcpp.Partition.Add(n, pair.Value);
gcpp.PartitionGetKey.Add(pair.Value, n);
}
//≤:=≤∪≤B
// ∪{(B',X)|X∈∑:B'∈∑B:(B,X)∈≤}
// ∪{(X,B')|X∈∑:B'∈∑B:(X,B)∈≤}
// \{(B,X),(X,B)|X∈∑:(X,B),(B,X)∈≤}
foreach (KeyValuePair<int, int> pair in gcpp.partorder)
{
gcpp.PartOrder.Add(pair.Key, pair.Value);
}
foreach (List<MDPState> X in gcpp.Partition.Values)
{
if (SamePartOrder(X, B, gcpp.PartOrder, gcpp.PartitionGetKey) && SamePartOrder(B, X, gcpp.PartOrder, gcpp.PartitionGetKey))
{
var query1 = from p in gcpp.PartOrder
where p.Key == gcpp.PartitionGetKey[B] && p.Value == gcpp.PartitionGetKey[X]
select p.Key;
gcpp.PartOrder.Remove(query1.FirstOrDefault());
var query2 = from p in gcpp.PartOrder
where p.Key == gcpp.PartitionGetKey[X] && p.Value == gcpp.PartitionGetKey[B]
select p.Key;
gcpp.PartOrder.Remove(query2.FirstOrDefault());
}
foreach (List<MDPState> B1 in gcpp.partition.Values)
{
if (SamePartOrder(B, X, gcpp.PartOrder, gcpp.PartitionGetKey))
{
gcpp.PartOrder.Add(gcpp.PartitionGetKey[B1], gcpp.PartitionGetKey[X]);
}
if (SamePartOrder(X, B, gcpp.PartOrder, gcpp.PartitionGetKey))
{
gcpp.PartOrder.Add(gcpp.PartitionGetKey[X], gcpp.PartitionGetKey[B1]);
}
}
}
}
}
return toReturn;
}
//re-calculate the distribution after removing selfloop
//public Distribution DistrbutionReCalculate(List<string> newSCC, MDPState node, Distribution distr)
//{
// double nonSelfLoopProb = 0.0;
// for (int i = 0; i < distr.States.Count; i++)
// {
// KeyValuePair<double, MDPState> pair = distr.States[i];
// if (newSCC.Contains(pair.Value.ID))
// {
// //selfLoopProb += pair.Key;
// //hasSelfLoop = true;
// //the self loop is removed in this distribution
// distr.States.Remove(pair);
// //i-- is used to keep the loop correct after removing one element
// i--;
// }
// else
// {
// nonSelfLoopProb += pair.Key;
// }
// }
// foreach (KeyValuePair<double, MDPState> pair in distr.States)
// {
// //KeyValuePair<double, MDPState> newPair = new KeyValuePair<double, MDPState>(pair.Key / nonSelfLoopProb, pair.Value);
// distr.AddProbStatePair(pair.Key / nonSelfLoopProb, pair.Value);
// distr.States.Remove(pair);
// }
// return distr;
//}
//this method is used to remove all loops in a DTMC.
public MDP BuildQuotientMDPBisimulation(VerificationOutput VerificationOutput)
{
MDP toReturn = new MDP(Precision, MAX_DIFFERENCE);
//calculate the nonsafe states, whose maximal prob is not 0
Stack<MDPState> NonSafe = new Stack<MDPState>(TargetStates);
Stack<MDPState> helper = new Stack<MDPState>(TargetStates);
//backward checking from target states
while (helper.Count != 0)
{
MDPState t = helper.Pop();
foreach (MDPState s in t.Pre)
{
bool addState = false;
//check each distribution; as long as s has a post state in NonSafe, then s should be added.
foreach (Distribution distribution in s.Distributions)
{
foreach (KeyValuePair<double, MDPState> pair in distribution.States)
{
if (NonSafe.Contains(pair.Value))
{
addState = true;
//s.Distributions.Remove(distribution);
break;
}
}
if (addState)
{
break;
}
}
if (addState && !NonSafe.Contains(s))
{
helper.Push(s);
NonSafe.Push(s);
}
}
}
//note here remaining doesn't include the target states and initial states
HashSet<MDPState> remaining = new HashSet<MDPState>();
foreach (MDPState mdpState in NonSafe)
{
if (!TargetStates.Contains(mdpState) && InitState != mdpState)
{
remaining.Add(mdpState);
}
}
//add Initial
MDPState Initial = new MDPState(InitState.ID);
toReturn.AddState(Initial);
toReturn.SetInit(Initial);
//add target
MDPState Target = new MDPState("target");
toReturn.AddState(Target);
toReturn.AddTargetStates(Target);
//add safe
MDPState Safe = new MDPState("safe");
toReturn.AddState(Safe);
//add remaining
//MDPState Remaining = new MDPState("remaining");
//toReturn.AddState(Remaining);
//add selfloop at Target.
//Target.AddDistribution(new Distribution(Constants.TAU, Target));
//add selfloop at Safe.
//Safe.AddDistribution(new Distribution(Constants.TAU, Safe));
//add the group distributions in Remaining
List<HashSet<MDPState>> SeperatingRemaining = new List<HashSet<MDPState>>();
SeperatingRemaining.Add(remaining);
bool refinement = true;
while (refinement)//if the former iteration has splitted some groups
{
refinement = false;
for (int i = 0; i < SeperatingRemaining.Count; i++)
{
HashSet<MDPState> mdpStates = SeperatingRemaining[i];
if (mdpStates.Count > 1)
{
Dictionary<string, HashSet<MDPState>> groups = SeperateGroup(SeperatingRemaining, mdpStates, Initial, Target, Safe);
if (groups.Count > 1)
{
SeperatingRemaining.RemoveAt(i--);
foreach (KeyValuePair<string, HashSet<MDPState>> keyValuePair in groups)
{
SeperatingRemaining.Add(keyValuePair.Value);
}
refinement = true;
}
}
}
//List<HashSet<MDPState>> NewSeperating = new List<HashSet<MDPState>>();
//foreach (HashSet<MDPState> mdpStates in SeperatingRemaining)
//{
// if (mdpStates.Count > 1)
// {
// int counter = 0;
// foreach (HashSet<MDPState> grouped in SeperateGroup(SeperatingRemaining, mdpStates, Initial, Target, Safe).Values)
// {
// counter++;
// NewSeperating.Add(grouped);
// }
// if (counter > 1)
// {
// refinement = true;
// }
// }
// else
// {
// NewSeperating.Add(mdpStates);
// }
// }
////todo: reduce the loop number
//SeperatingRemaining = NewSeperating;
}
//add distributions after all the refinement
foreach (HashSet<MDPState> mdpStates in SeperatingRemaining)
{
//add representative state of each groupd states
MDPState Grouped = StateFromHashset(mdpStates);
toReturn.AddState(new MDPState(Grouped.ID));
}
foreach (MDPState state in toReturn.States.Values)
{
if (state.ID == "target" || state.ID == "safe")
{
continue;
}
HashSet<Distribution> DistrToAdd = new HashSet<Distribution>();
foreach (Distribution Distr in this.States[state.ID].Distributions)
{
Distribution newDistr = calcGroupedDistr(SeperatingRemaining, Distr, Initial, Target, Safe, toReturn);
DistrToAdd.Add(newDistr);
}
foreach (Distribution distribution in DistrToAdd)
{
toReturn.AddDistribution(state.ID, distribution);
}
}
//foreach (HashSet<MDPState> mdpStates in SeperatingRemaining)
//{
// MDPState Grouped = StateFromHashset(mdpStates);
// FinalgroupedDistribution(SeperatingRemaining, Grouped, Target, Safe, toReturn);//calculate the grouped distributions
//}
//note: add initial state's distributions after refinement
//FinalgroupedDistribution(SeperatingRemaining, InitState, Target, Safe, toReturn);
return toReturn;
}
public Distribution calcGroupedDistr(List<HashSet<MDPState>> ListHashMDP, Distribution Distr, MDPState Initial, MDPState Target, MDPState Safe, MDP mdp)
{
Distribution toReturn = new Distribution(Distr.Event);
double toInit = 0;
double toTarget = 0;
double[] combined = new double[ListHashMDP.Count];
//MDPState[] groupstates = new MDPState[seperation.Count];
foreach (KeyValuePair<double, MDPState> transition in Distr.States)
{
if (TargetStates.Contains(transition.Value))
{
toTarget += transition.Key;
}
else if (InitState == transition.Value)
{
toInit += transition.Key;
}
else
{
for (int i = 0; i < ListHashMDP.Count; i++)
{
if (ListHashMDP[i].Contains(transition.Value))
{
combined[i] += transition.Key;
break;
}
}
}
}
double toSafe = 1 - toTarget - toInit;
for (int i = 0; i < ListHashMDP.Count; i++)
{
toSafe -= combined[i];
}
if (toInit != 0)
{
toReturn.AddProbStatePair(Math.Round(toInit, 5), Initial);
}
if (toTarget != 0)
{
toReturn.AddProbStatePair(Math.Round(toTarget, 5), Target);
}
if (toSafe != 0)
{
toReturn.AddProbStatePair(Math.Round(toSafe, 5), Safe);
}
//toReturn.AddProbStatePair(toSafe, Safe);
for (int j = 0; j < ListHashMDP.Count; j++)
{
if (combined[j] != 0)
{
MDPState state = mdp.States[StateFromHashset(ListHashMDP[j]).ID];
toReturn.AddProbStatePair(Math.Round(combined[j], 5), state);
//toReturn.AddProbStatePair(Math.Round(combined[j], 5), StateFromHashset(ListHashMDP[j]));
}
}
return toReturn;
}
public MDP BuildQuotientMDP(VerificationOutput VerificationOutput)
{
//return this;
MDP toReturn = new MDP(Precision, MAX_DIFFERENCE);
//todo change to set
List<KeyValuePair<string, string>> BoundaryOneTransition = new List<KeyValuePair<string, string>>();
//todo change to set
List<Distribution> ProbTransitions = new List<Distribution>();
Dictionary<string, List<Distribution>> GlobalProbTransitions = new Dictionary<string, List<Distribution>>();
StringDictionary<bool> visited = new StringDictionary<bool>(States.Count);
List<KeyValuePair<HashSet<string>, MDPState>> sccs = new List<KeyValuePair<HashSet<string>, MDPState>>();
Dictionary<string, int> preorder = new Dictionary<string, int>();
Dictionary<string, int> lowlink = new Dictionary<string, int>();
//HashSet<string> scc_found = new HashSet<string>();
Stack<MDPState> TaskStack = new Stack<MDPState>();
//Dictionary<string, List<string>> OutgoingTransitionTable = new Dictionary<string, List<string>>();
Stack<MDPState> stepStack = new Stack<MDPState>(1024);
visited.Add(InitState.ID, false);
TaskStack.Push(InitState);
//# Preorder counter
int preor = 0;
do
{
while (TaskStack.Count > 0)
{
MDPState pair = TaskStack.Peek();
string v = pair.ID;
if (visited.GetContainsKey(v) && visited.GetContainsKey(v))
{
TaskStack.Pop();
continue;
}
if (!preorder.ContainsKey(v))
{
preorder.Add(v, preor);
preor++;
}
bool done = true;
List<Distribution> list = pair.Distributions;
List<MDPState> nonProbTrans = new List<MDPState>();
List<Distribution> ProbTrans = new List<Distribution>();
for (int i = 0; i < list.Count; i++)
{
if (list[i].IsTrivial())
{
nonProbTrans.Add(list[i].States[0].Value);
}
else
{
ProbTrans.Add(list[i]);
}
}
if (ProbTrans.Count > 0 && !GlobalProbTransitions.ContainsKey(v))
{
GlobalProbTransitions.Add(v, ProbTrans);
ProbTransitions.AddRange(ProbTrans);
}
for (int k = nonProbTrans.Count - 1; k >= 0; k--)
{
MDPState step = nonProbTrans[k];
string tmp = step.ID;
if (visited.ContainsKey(tmp))
{
//if this node is still not visited
if (!preorder.ContainsKey(tmp))
{
//only put the first one to the work list stack.
//if there are more than one node to be visited,
//simply ignore them and keep its event step in the list.
if (done)
{
TaskStack.Push(step);
done = false;
}
}
}
else
{
visited.Add(tmp, false);
//OutgoingTransitionTable.Add(tmp, new List<string>(8));
//only put the first one into the stack.
if (done)
{
TaskStack.Push(step);
done = false;
}
}
}
if (done)
{
int lowlinkV = preorder[v];
int preorderV = preorder[v];
bool selfLoop = false;
for (int j = 0; j < nonProbTrans.Count; j++)
{
string w = nonProbTrans[j].ID;
if (w == v)
{
selfLoop = true;
}
if (!visited.GetContainsKey(w))
{
if (preorder[w] > preorderV)
{
lowlinkV = Math.Min(lowlinkV, lowlink[w]);
}
else
{
lowlinkV = Math.Min(lowlinkV, preorder[w]);
}
}
else //in this case, there is a tau transition leading to an SCC; must add the transition into the toReturn automaton
{
BoundaryOneTransition.Add(new KeyValuePair<string, string>(v, w));
}
}
lowlink[v] = lowlinkV;
TaskStack.Pop();
HashSet<string> scc = new HashSet<string>();
if (lowlinkV == preorderV)
{
scc.Add(v);
visited.SetValue(v, true);
while (stepStack.Count > 0 && preorder[stepStack.Peek().ID] > preorderV)
{
string s = stepStack.Pop().ID;
scc.Add(s);
visited.SetValue(s, true);
}
MDPState newstate = new MDPState(toReturn.States.Count.ToString());
if (scc.Count > 1 || (scc.Count == 1 && selfLoop))
{
newstate.AddDistribution(new Distribution(Constants.TAU, newstate)); //add self loop: sun jun
}
sccs.Add(new KeyValuePair<HashSet<string>, MDPState>(scc, newstate));
toReturn.AddState(newstate);
if (scc.Contains(InitState.ID))
{
toReturn.SetInit(newstate);
}
foreach (MDPState state in TargetStates)
{
if (scc.Contains(state.ID))
{
toReturn.AddTargetStates(newstate);
}
}
}
else
{
stepStack.Push(pair);
}
}
}
if (ProbTransitions.Count > 0)
{
foreach (Distribution step in ProbTransitions)
{
foreach (KeyValuePair<double, MDPState> pair in step.States)
{
string stateID = pair.Value.ID;
if (!visited.ContainsKey(stateID))
{
TaskStack.Push(pair.Value);
visited.Add(stateID, false);
}
}
}
ProbTransitions.Clear();
}
} while (TaskStack.Count > 0);
foreach (KeyValuePair<string, string> pair in BoundaryOneTransition)
{
MDPState source = null;
MDPState target = null;
foreach (KeyValuePair<HashSet<string>, MDPState> sccstate in sccs)
{
if (sccstate.Key.Contains(pair.Key))
{
source = sccstate.Value;
}
if (sccstate.Key.Contains(pair.Value))
{
target = sccstate.Value;
}
}
toReturn.AddDistribution(source.ID, new Distribution(Constants.TAU, target));
VerificationOutput.ReducedMDPTransitions++;
}
foreach (KeyValuePair<string, List<Distribution>> pair in GlobalProbTransitions)
{
MDPState source = null;
foreach (KeyValuePair<HashSet<string>, MDPState> sccstate in sccs)
{
if (sccstate.Key.Contains(pair.Key))
{
source = sccstate.Value;
break;
}
}
foreach (Distribution distribution in pair.Value)
{
Distribution disNew = new Distribution(distribution.Event);
foreach (KeyValuePair<double, MDPState> state in distribution.States)
{
foreach (KeyValuePair<HashSet<string>, MDPState> sccstate in sccs)
{
if (sccstate.Key.Contains(state.Value.ID))
{
disNew.AddProbStatePair(state.Key, sccstate.Value);
VerificationOutput.ReducedMDPTransitions++;
break;
}
}
}
toReturn.AddDistribution(source.ID, disNew);
}
}
VerificationOutput.ReducedMDPStates = toReturn.States.Count;
return toReturn;
}
protected MDP BuildMDP_SCC_Cut_Mutlicores()
{
Stack<KeyValuePair<MDPConfiguration, MDPState>> working = new Stack<KeyValuePair<MDPConfiguration, MDPState>>(1024);
string initID = InitialStep.GetID();
MDPState init = new MDPState(initID);
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(InitialStep as MDPConfiguration, init));
MDP mdp = new MDP(init, Ultility.Ultility.DEFAULT_PRECISION, Ultility.Ultility.MAX_DIFFERENCE);
Stack<MDPState> stepStack = new Stack<MDPState>(1024);
//MDPState2DRAStateMapping = new Dictionary<string, int>(Common.Classes.Ultility.Ultility.MC_INITIAL_SIZE);
const int VISITED_NOPREORDER = -1;
const int SCC_FOUND = -2;
const int SCCBound = 20;
//DFS data, which mapping each state to an int[] of size 3, first is the pre-order, second is the lowlink, last one is DRAState
Dictionary<string, int[]> DFSData = new Dictionary<string, int[]>(Ultility.Ultility.MC_INITIAL_SIZE);
DFSData.Add(initID, new int[] { VISITED_NOPREORDER, 0 });
//build the MDP while identifying the SCCs
List<List<MDPState>> SCCs = new List<List<MDPState>>(64);
Dictionary<int, List<MDPState>> scc2out = new Dictionary<int, List<MDPState>>();
Dictionary<int, HashSet<MDPState>> scc2input = new Dictionary<int, HashSet<MDPState>>();
//Dictionary<string, int> preorder = new Dictionary<string, int>(Common.Classes.Ultility.Ultility.MC_INITIAL_SIZE);
//Dictionary<string, int> lowlink = new Dictionary<string, int>(Common.Classes.Ultility.Ultility.MC_INITIAL_SIZE);
int preordercounter = 0;
Dictionary<string, List<MDPConfiguration>> ExpendedNode = new Dictionary<string, List<MDPConfiguration>>();
bool reachTarget = true;
do
{
if (CancelRequested)
{
this.VerificationOutput.NoOfStates = this.VerificationOutput.NoOfStates + mdp.States.Count;
return mdp;
}
KeyValuePair<MDPConfiguration, MDPState> pair = working.Peek();
MDPConfiguration evt = pair.Key;
//int DRAState = pair.Key.state;
string currentID = pair.Key.GetID();
MDPState currentState = pair.Value;
List<Distribution> outgoing = currentState.Distributions;
//if (!preorder.ContainsKey(currentID))
//{
// preorder.Add(currentID, preorderCounter);
// preorderCounter++;
//}
int[] nodeData = DFSData[currentID];
if (nodeData[0] == VISITED_NOPREORDER)
{
nodeData[0] = preordercounter;
preordercounter++;
}
bool done = true;
if (ExpendedNode.ContainsKey(currentID))
{
if (reachTarget)
{
currentState.ReachTarget = reachTarget;
}
else
{
reachTarget = currentState.ReachTarget;
}
List<MDPConfiguration> list = ExpendedNode[currentID];
if (list.Count > 0)
{
for (int k = list.Count - 1; k >= 0; k--)
{
MDPConfiguration step = list[k];
string stepID = step.GetID();
//if (!preorder.ContainsKey(stepID))
if (DFSData[stepID][0] == VISITED_NOPREORDER)
{
if (done)
{
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(step, mdp.States[stepID]));
done = false;
list.RemoveAt(k);
}
}
else
{
MDPState s = mdp.States[stepID];
if (s.ReachTarget)
{
reachTarget = true;
currentState.ReachTarget = reachTarget;
if (s.SCCIndex >= 0)
{
scc2input[s.SCCIndex].Add(s);
}
}
list.RemoveAt(k);
}
}
}
}
else
{
reachTarget = false;
int currentDistriIndex = -1;
Distribution newDis = new Distribution(Constants.TAU);
//MDPConfiguration[] steps = evt.MakeOneMoveLocal();
IEnumerable<MDPConfiguration> steps = evt.MakeOneMoveLocal();
//NOTE: here we play a trick for deadlock case: if a deadlock exist in the MDP, we will make a
//self loop transition to remove the deadlock. Deadlock is meaningless in MDP.
if (evt.IsDeadLock)
{
//List<MDPConfiguration> stepsList = new List<MDPConfiguration>(steps);
working.Pop();
nodeData[0] = SCC_FOUND;
continue;
//stepsList.Add(CreateSelfLoopStep(evt));
//steps = stepsList.ToArray();
//HasDeadLock = true;
}
List<MDPConfiguration> stepsList = new List<MDPConfiguration>(steps);
//List<PCSPEventDRAPair> product = Next(steps, DRAState);
this.VerificationOutput.Transitions += stepsList.Count;
for (int k = stepsList.Count - 1; k >= 0; k--)
{
MDPConfiguration step = stepsList[k];
string tmp = step.GetID();
bool target = false;
ExpressionValue v = EvaluatorDenotational.Evaluate(ReachableStateCondition, step.GlobalEnv);
MDPState nextState;
if ((v as BoolConstant).Value)
{
target = true;
if (!DFSData.Keys.Contains(tmp))
{
DFSData.Add(tmp, new int[] { SCC_FOUND, SCC_FOUND });
// nextState = new MDPState(tmp);
// mdp.States.Add(tmp, nextState);
//preordercounter++;
}
//else if(DFSData[tmp][0] == VISITED_NOPREORDER)
//{
// DFSData[tmp][0] = preordercounter;
// preordercounter++;
//}
}
//int nextIndex = VisitedWithID.Count;
int[] data;
if (mdp.States.TryGetValue(tmp, out nextState))
{
DFSData.TryGetValue(tmp, out data);
if (!target && data[0] == VISITED_NOPREORDER)
{
//if (mdp.States.TryGetValue(tmp, out nextState))
//{
// if (!preorder.ContainsKey(tmp))
// {
if (done)
{
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(step, nextState));
done = false;
stepsList.RemoveAt(k);
}
else
{
stepsList[k] = step;
}
}
else
{
stepsList.RemoveAt(k);
MDPState s = mdp.States[tmp];
if (s.ReachTarget)
{
reachTarget = true;
currentState.ReachTarget = reachTarget;
if (s.SCCIndex >= 0)
{
scc2input[s.SCCIndex].Add(s);
}
}
}
}
else
{
if (!target)
{
DFSData.Add(tmp, new int[] { VISITED_NOPREORDER, 0 });
}
nextState = new MDPState(tmp);
mdp.States.Add(tmp, nextState);
if (done)
{
if (target)
{
mdp.AddTargetStates(nextState);
reachTarget = true;
}
else
{
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(step, nextState));
}
done = false;
stepsList.RemoveAt(k);
}
else
{
if (target)
{
stepsList.RemoveAt(k);
mdp.AddTargetStates(nextState);
reachTarget = true;
}
else
{
stepsList[k] = step;
}
}
}
MDPConfiguration pstep = step;
if (pstep.DisIndex == -1)
{
if (currentDistriIndex >= 0)
{
//currentState.AddDistribution(newDis);
//note here no pre is stored
currentState.Distributions.Add(newDis);
newDis = new Distribution(Constants.TAU);
}
Distribution newTrivialDis = new Distribution(pstep.Event, nextState);
//currentState.AddDistribution(newTrivialDis);
currentState.Distributions.Add(newTrivialDis);
}
else if (currentDistriIndex != -1 && pstep.DisIndex != currentDistriIndex)
{
//currentState.AddDistribution(newDis);
currentState.Distributions.Add(newDis);
newDis = new Distribution(Constants.TAU);
newDis.AddProbStatePair(pstep.Probability, nextState);
}
else
{
newDis.AddProbStatePair(pstep.Probability, nextState);
}
currentDistriIndex = pstep.DisIndex;
}
if (currentDistriIndex >= 0)
{
//currentState.AddDistribution(newDis);
currentState.Distributions.Add(newDis);
}
ExpendedNode.Add(currentID, stepsList);
}
if (done)
{
int lowlinkV = nodeData[0];
int preorderV = lowlinkV;
bool selfLoop = false;
foreach (Distribution list in outgoing)
{
foreach (KeyValuePair<double, MDPState> state in list.States)
{
string w = state.Value.ID;
if (w == currentID)
{
selfLoop = true;
}
//if (!MDPState2DRAStateMapping.ContainsKey(w))
//{
// if (preorder[w] > preorderV)
// {
// lowlinkV = Math.Min(lowlinkV, lowlink[w]);
// }
// else
// {
// lowlinkV = Math.Min(lowlinkV, preorder[w]);
// }
//}
int[] wdata = DFSData[w];
if (wdata[0] != SCC_FOUND)
{
if (wdata[0] > preorderV)
{
lowlinkV = Math.Min(lowlinkV, wdata[1]);
}
else
{
lowlinkV = Math.Min(lowlinkV, wdata[0]);
}
}
}
}
nodeData[1] = lowlinkV;
working.Pop();
if (lowlinkV == preorderV)
{
if (currentState.ReachTarget)
{
List<MDPState> SCC = new List<MDPState>();
//List<HashSet<MDPState>> Groupings = new List<HashSet<MDPState>>();
HashSet<MDPState> Grouping = new HashSet<MDPState>();
//bool reduceScc = false;
Grouping.Add(currentState);
SCC.Add(currentState);
//int count = 1;
//dtmcSCCstates.Add(currentID);
nodeData[0] = SCC_FOUND;
while (stepStack.Count > 0 && DFSData[stepStack.Peek().ID][0] > preorderV)
{
MDPState s = stepStack.Pop();
s.ReachTarget = true;
string sID = s.ID;
//Grouping.Add(s);
SCC.Add(s);
//dtmcSCCstates.Add(sID);
DFSData[sID][0] = SCC_FOUND;
//count++;
}
if (SCC.Count > 1 || selfLoop)
{
SCCs.Add(SCC);
HashSet<MDPState> inputs = new HashSet<MDPState>();
inputs.Add(currentState);
int Count = SCCs.Count;
foreach (var state in SCC)
{
state.SCCIndex = Count - 1;
}
scc2input.Add(currentState.SCCIndex, inputs);
HashSet<MDPState> outputs = new HashSet<MDPState>();
//input.Add(currentState);
foreach (MDPState state in SCC)
{
foreach (var distr in state.Distributions)
{
foreach (var KVpair in distr.States)
{
if (!SCC.Contains(KVpair.Value))
{
outputs.Add(KVpair.Value);
}
}
}
}
List<MDPState> outofscc = new List<MDPState>(outputs);
scc2out.Add(SCCs.IndexOf(SCC), outofscc);
}
//}
}
else
{
//dtmcSCCstates.Add(currentID);
nodeData[0] = SCC_FOUND;
while (stepStack.Count > 0 && DFSData[stepStack.Peek().ID][0] > preorderV)
{
string sID = stepStack.Pop().ID;
DFSData[sID][0] = SCC_FOUND;
}
}
}
else
{
stepStack.Push(pair.Value);
}
}
} while (working.Count > 0);
//List<string> EndComponents = new List<string>(SCCs.Count);
//foreach (List<MDPState> scc in SCCs)
var localMapSCCsWithOutputSmallSCC = new Dictionary<List<MDPState>, List<MDPState>>();
while (SCCs.Count > 0)
{
for (int i = SCCs.Count - 1; i >= 0; i--)
{
List<MDPState> SCC = SCCs[i];
int index;
//foreach(var state in SCC)
//{
// index = state.SCCIndex;
// break;
//}
//FindMECDistribution(SCC);
if (SCC.Count <= SCCBound)
{
// SCCReductionGaussianSparseMatrix(new List<MDPState>(SCC), scc2out[index]);
localMapSCCsWithOutputSmallSCC.Add(new List<MDPState>(SCC), scc2out[i]);
SCCs.RemoveAt(i);
}
else
{
List<MDPState> SCCi = new List<MDPState>(SCCs[i]);
int Counter = 0;
var localMapSCCsWithOutputSubCutSCC = new Dictionary<List<MDPState>, List<MDPState>>();
while (Counter < SCCi.Count - SCCBound)
{
List<MDPState> group = SCCi.GetRange(Counter, SCCBound);
HashSet<MDPState> outputs = new HashSet<MDPState>();
//input.Add(currentState);
foreach (MDPState state in group)
{
foreach (var Distr in state.Distributions)
{
foreach (KeyValuePair<double, MDPState> KVpair in Distr.States)
{
MDPState nextState = KVpair.Value;
if (!group.Contains(nextState))
{
outputs.Add(nextState);
}
}
}
}
// List<MDPState> output = new List<MDPState>(outputs);
//SCCReductionGaussianSparseMatrix(group, output);
localMapSCCsWithOutputSubCutSCC.Add(group, new List<MDPState>(outputs));
//SCCReduction(group, output);
Counter += SCCBound;
}
Parallel.ForEach(localMapSCCsWithOutputSubCutSCC,
subscc2Out =>
SCCReductionGaussianSparseMatrix(subscc2Out.Key, subscc2Out.Value, true));
List<MDPState> Group = SCCi.GetRange(Counter, SCCi.Count - Counter);
HashSet<MDPState> Outputs = new HashSet<MDPState>();
//input.Add(currentState);
foreach (MDPState state in Group)
{
foreach (var Distr in state.Distributions)
{
foreach (var KVpair in Distr.States)
{
MDPState nextState = KVpair.Value;
if (!Group.Contains(nextState))
{
Outputs.Add(nextState);
}
}
}
}
List<MDPState> Output = new List<MDPState>(Outputs);
//GL: TODO: this one is not in parallel
SCCReductionGaussianSparseMatrix(Group, Output, true);
//search for the useful subset of SCC that connecting to input states after reduction.
HashSet<MDPState> Working = scc2input[i];
HashSet<MDPState> visited = new HashSet<MDPState>();
do
{
HashSet<MDPState> newWorking = new HashSet<MDPState>();
foreach (var state in Working)
{
visited.Add(state);
foreach (var distr in state.Distributions)
{
foreach (var tran in distr.States)
{
MDPState tranV = tran.Value;
if (!visited.Contains(tranV) && SCCs[i].Contains(tranV))
{
newWorking.Add(tranV);
}
}
}
}
Working = newWorking;
} while (Working.Count > 0);
if (visited.Count > SCCBound && visited.Count < SCCs[i].Count)
{
SCCs[i] = new List<MDPState>(visited);
}
else
{
//List<MDPState> scc = new List<MDPState>(SCCs[i]);
// SCCReductionGaussianSparseMatrix(scc, scc2out[index]);
//SCCReductionMatlab(scc, scc2out[i]);
localMapSCCsWithOutputSmallSCC.Add(new List<MDPState>(visited), scc2out[i]);
SCCs.RemoveAt(i);
}
}
}
}
Parallel.ForEach(localMapSCCsWithOutputSmallSCC,
subscc2Out =>
SCCReductionGaussianSparseMatrix(subscc2Out.Key, subscc2Out.Value, true));
VerificationOutput.NoOfStates = VerificationOutput.NoOfStates + mdp.States.Count;
int counter = 0;
BuildPRE(mdp, ref counter);
return mdp;
}
protected MDP BuildMDP_SCC_Cut()
{
Stack<KeyValuePair<MDPConfiguration, MDPState>> working = new Stack<KeyValuePair<MDPConfiguration, MDPState>>(1024);
string initID = InitialStep.GetID();
MDPState init = new MDPState(initID);
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(InitialStep as MDPConfiguration, init));
MDP mdp = new MDP(init, Ultility.Ultility.DEFAULT_PRECISION, Ultility.Ultility.MAX_DIFFERENCE);
Stack<MDPState> stepStack = new Stack<MDPState>(1024);
//MDPState2DRAStateMapping = new Dictionary<string, int>(Common.Classes.Ultility.Ultility.MC_INITIAL_SIZE);
const int VISITED_NOPREORDER = -1;
const int SCC_FOUND = -2;
//DFS data, which mapping each state to an int[] of size 3, first is the pre-order, second is the lowlink, last one is DRAState
Dictionary<string, int[]> DFSData = new Dictionary<string, int[]>(Ultility.Ultility.MC_INITIAL_SIZE);
DFSData.Add(initID, new int[] { VISITED_NOPREORDER, 0 });
//build the MDP while identifying the SCCs
List<HashSet<MDPState>> SCCs = new List<HashSet<MDPState>>();
//Dictionary<int, List<MDPState>> scc2out = new Dictionary<int, List<MDPState>>();
List<HashSet<MDPState>> scc2out = new List<HashSet<MDPState>>();
List<HashSet<MDPState>> scc2input = new List<HashSet<MDPState>>();
//Dictionary<int, HashSet<MDPState>> scc2input = new Dictionary<int, HashSet<MDPState>>();
//Dictionary<string, int> preorder = new Dictionary<string, int>(Common.Classes.Ultility.Ultility.MC_INITIAL_SIZE);
//Dictionary<string, int> lowlink = new Dictionary<string, int>(Common.Classes.Ultility.Ultility.MC_INITIAL_SIZE);
int preordercounter = 0;
Dictionary<string, List<MDPConfiguration>> ExpendedNode = new Dictionary<string, List<MDPConfiguration>>();
bool reachTarget = true;
do
{
if (CancelRequested)
{
this.VerificationOutput.NoOfStates = this.VerificationOutput.NoOfStates + mdp.States.Count;
return mdp;
}
KeyValuePair<MDPConfiguration, MDPState> pair = working.Peek();
MDPConfiguration evt = pair.Key;
//int DRAState = pair.Key.state;
string currentID = pair.Key.GetID();
MDPState currentState = pair.Value;
List<Distribution> outgoing = currentState.Distributions;
//if (!preorder.ContainsKey(currentID))
//{
// preorder.Add(currentID, preorderCounter);
// preorderCounter++;
//}
int[] nodeData = DFSData[currentID];
if (nodeData[0] == VISITED_NOPREORDER)
{
nodeData[0] = preordercounter;
preordercounter++;
}
bool done = true;
if (ExpendedNode.ContainsKey(currentID))
{
if (reachTarget)
{
currentState.ReachTarget = reachTarget;
}
else
{
reachTarget = currentState.ReachTarget;
}
List<MDPConfiguration> list = ExpendedNode[currentID];
if (list.Count > 0)
{
for (int k = list.Count - 1; k >= 0; k--)
{
MDPConfiguration step = list[k];
string stepID = step.GetID();
//if (!preorder.ContainsKey(stepID))
if (DFSData[stepID][0] == VISITED_NOPREORDER)
{
if (done)
{
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(step, mdp.States[stepID]));
done = false;
list.RemoveAt(k);
}
}
else
{
MDPState s = mdp.States[stepID];
if (s.ReachTarget)
{
reachTarget = true;
currentState.ReachTarget = reachTarget;
if (s.SCCIndex >= 0)
{
scc2input[s.SCCIndex].Add(s);
}
}
list.RemoveAt(k);
}
}
}
}
else
{
reachTarget = false;
int currentDistriIndex = -1;
Distribution newDis = new Distribution(Constants.TAU);
//MDPConfiguration[] steps = evt.MakeOneMoveLocal();
IEnumerable<MDPConfiguration> steps = evt.MakeOneMoveLocal();
//NOTE: here we play a trick for deadlock case: if a deadlock exist in the MDP, we will make a
//self loop transition to remove the deadlock. Deadlock is meaningless in MDP.
if (evt.IsDeadLock)
{
//List<MDPConfiguration> stepsList = new List<MDPConfiguration>(steps);
working.Pop();
nodeData[0] = SCC_FOUND;
continue;
//stepsList.Add(CreateSelfLoopStep(evt));
//steps = stepsList.ToArray();
//HasDeadLock = true;
}
List<MDPConfiguration> stepsList = new List<MDPConfiguration>(steps);
//List<PCSPEventDRAPair> product = Next(steps, DRAState);
this.VerificationOutput.Transitions += stepsList.Count;
for (int k = stepsList.Count - 1; k >= 0; k--)
{
MDPConfiguration step = stepsList[k];
string tmp = step.GetID();
bool target = false;
ExpressionValue v = EvaluatorDenotational.Evaluate(ReachableStateCondition, step.GlobalEnv);
MDPState nextState;
if ((v as BoolConstant).Value)
{
target = true;
if (!DFSData.Keys.Contains(tmp))
{
DFSData.Add(tmp, new int[] { SCC_FOUND, SCC_FOUND });
// nextState = new MDPState(tmp);
// mdp.States.Add(tmp, nextState);
//preordercounter++;
}
//else if(DFSData[tmp][0] == VISITED_NOPREORDER)
//{
// DFSData[tmp][0] = preordercounter;
// preordercounter++;
//}
}
//int nextIndex = VisitedWithID.Count;
int[] data;
if (mdp.States.TryGetValue(tmp, out nextState))
{
nextState.TrivialPre = false;
DFSData.TryGetValue(tmp, out data);
if (!target && data[0] == VISITED_NOPREORDER)
{
//if (mdp.States.TryGetValue(tmp, out nextState))
//{
// if (!preorder.ContainsKey(tmp))
// {
if (done)
{
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(step, nextState));
done = false;
stepsList.RemoveAt(k);
}
else
{
stepsList[k] = step;
}
}
else
{
stepsList.RemoveAt(k);
MDPState s = mdp.States[tmp];
if (s.ReachTarget)
{
reachTarget = true;
currentState.ReachTarget = reachTarget;
if (s.SCCIndex >= 0 && !scc2input[s.SCCIndex].Contains(s))
{
scc2input[s.SCCIndex].Add(s);
}
}
}
}
else
{
if (!target)
{
DFSData.Add(tmp, new int[] { VISITED_NOPREORDER, 0 });
}
nextState = new MDPState(tmp);
mdp.States.Add(tmp, nextState);
if (done)
{
if (target)
{
mdp.AddTargetStates(nextState);
reachTarget = true;
}
else
{
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(step, nextState));
}
done = false;
stepsList.RemoveAt(k);
}
else
{
if (target)
{
stepsList.RemoveAt(k);
mdp.AddTargetStates(nextState);
reachTarget = true;
}
else
{
stepsList[k] = step;
}
}
}
MDPConfiguration pstep = step;
if (pstep.DisIndex == -1)
{
if (currentDistriIndex >= 0)
{
//note here no pre is stored
currentState.Distributions.Add(newDis);
newDis = new Distribution(Constants.TAU);
}
if (nextState.ID != currentID)//note here self loop distribution is removed; so just used for PMAX
{
Distribution newTrivialDis = new Distribution(pstep.Event, nextState);
currentState.Distributions.Add(newTrivialDis);
}
}
else if (currentDistriIndex != -1 && pstep.DisIndex != currentDistriIndex)
{
//note here no pre is stored
currentState.Distributions.Add(newDis);
newDis = new Distribution(Constants.TAU);
newDis.AddProbStatePair(pstep.Probability, nextState);
nextState.TrivialPre = false;
}
else
{
newDis.AddProbStatePair(pstep.Probability, nextState);
nextState.TrivialPre = false;
}
currentDistriIndex = pstep.DisIndex;
}
if (currentDistriIndex >= 0)
{
currentState.Distributions.Add(newDis);
}
ExpendedNode.Add(currentID, stepsList);
}
if (done)
{
int lowlinkV = nodeData[0];
int preorderV = lowlinkV;
bool selfLoop = false;
foreach (Distribution list in outgoing)
{
foreach (KeyValuePair<double, MDPState> state in list.States)
{
string w = state.Value.ID;
if (w == currentID)
{
selfLoop = true;
}
int[] wdata = DFSData[w];
if (wdata[0] != SCC_FOUND)
{
if (wdata[0] > preorderV)
{
lowlinkV = Math.Min(lowlinkV, wdata[1]);
}
else
{
lowlinkV = Math.Min(lowlinkV, wdata[0]);
}
}
}
}
nodeData[1] = lowlinkV;
working.Pop();
if (lowlinkV == preorderV)
{
if (currentState.ReachTarget)
{
HashSet<MDPState> SCC = new HashSet<MDPState>();
//List<HashSet<MDPState>> Groupings = new List<HashSet<MDPState>>();
//HashSet<MDPState> Grouping = new HashSet<MDPState>();
//bool reduceScc = false;
//Grouping.Add(currentState);
SCC.Add(currentState);
//int count = 1;
//dtmcSCCstates.Add(currentID);
nodeData[0] = SCC_FOUND;
while (stepStack.Count > 0 && DFSData[stepStack.Peek().ID][0] > preorderV)
{
MDPState s = stepStack.Pop();
s.ReachTarget = true;
string sID = s.ID;
//Grouping.Add(s);
SCC.Add(s);
//dtmcSCCstates.Add(sID);
DFSData[sID][0] = SCC_FOUND;
//count++;
}
if (SCC.Count > 1 || selfLoop)
{
SCCs.Add(SCC);
HashSet<MDPState> inputs = new HashSet<MDPState>();
inputs.Add(currentState);
int Count = SCCs.Count;
foreach (MDPState state in SCC)
{
state.SCCIndex = Count - 1;
}
scc2input.Add(inputs);
HashSet<MDPState> outputs = new HashSet<MDPState>();
//input.Add(currentState);
foreach (MDPState state in SCC)
{
foreach (Distribution distr in state.Distributions)
{
foreach (KeyValuePair<double, MDPState> KVpair in distr.States)
{
if (!SCC.Contains(KVpair.Value))
{
outputs.Add(KVpair.Value);
}
}
}
}
//List<MDPState> outofscc = new List<MDPState>(outputs);
scc2out.Add(outputs);
}
//}
}
else
{
//dtmcSCCstates.Add(currentID);
nodeData[0] = SCC_FOUND;
while (stepStack.Count > 0 && DFSData[stepStack.Peek().ID][0] > preorderV)
{
string sID = stepStack.Pop().ID;
DFSData[sID][0] = SCC_FOUND;
}
}
}
else
{
stepStack.Push(pair.Value);
}
}
} while (working.Count > 0);
RemoveOneTran(SCCs, scc2input);
for (int i = 0; i < SCCs.Count; i++)
{
FindMECDistribution(SCCs[i]);
}
if(BFS_CUT)
{
BFS_Cut(SCCs, scc2out, scc2input);
}
else
{
//DFS_CutAutoAdjustTreeLike(SCCs, scc2out, scc2input);
DFS_CutAutoAdjust(SCCs, scc2out, scc2input);
//DFS_Cut(SCCs, scc2out, scc2input);
}
VerificationOutput.NoOfStates = VerificationOutput.NoOfStates + mdp.States.Count;
int counter = 0;
BuildPRE(mdp, ref counter);
return mdp;
}
protected MDP BuildMDP()
{
Stack<KeyValuePair<MDPConfiguration, MDPState>> working = new Stack<KeyValuePair<MDPConfiguration, MDPState>>(1024);
string initID = InitialStep.GetID();
MDPState init = new MDPState(initID);
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(InitialStep as MDPConfiguration, init));
MDP mdp = new MDP(init, Ultility.Ultility.DEFAULT_PRECISION, Ultility.Ultility.MAX_DIFFERENCE);
do
{
if (CancelRequested)
{
VerificationOutput.NoOfStates = mdp.States.Count;
return mdp;
}
KeyValuePair<MDPConfiguration, MDPState> current = working.Pop();
IEnumerable<MDPConfiguration> list = current.Key.MakeOneMoveLocal();
VerificationOutput.Transitions += list.Count();
int currentDistriIndex = -1;
Distribution newDis = new Distribution(Constants.TAU);
//for (int i = 0; i < list.Count; i++)
foreach (var step in list)
{
//MDPConfiguration step = list[i];
string stepID = step.GetID();
MDPState nextState;
if (!mdp.States.TryGetValue(stepID, out nextState))
{
nextState = new MDPState(stepID);
mdp.AddState(nextState);
ExpressionValue v = EvaluatorDenotational.Evaluate(ReachableStateCondition, step.GlobalEnv);
if ((v as BoolConstant).Value)
{
mdp.AddTargetStates(nextState);
}
else
{
working.Push(new KeyValuePair<MDPConfiguration, MDPState>(step, nextState));
}
}
if (step.DisIndex == -1)
{
if (currentDistriIndex >= 0)
{
current.Value.AddDistribution(newDis);
newDis = new Distribution(Constants.TAU);
}
Distribution newTrivialDis = new Distribution(step.Event);
newTrivialDis.AddProbStatePair(1, nextState);
current.Value.AddDistribution(newTrivialDis);
}
else if (currentDistriIndex != -1 && step.DisIndex != currentDistriIndex)
{
current.Value.AddDistribution(newDis);
newDis = new Distribution(Constants.TAU);
newDis.AddProbStatePair(step.Probability, nextState);
}
else
{
newDis.AddProbStatePair(step.Probability, nextState);
}
currentDistriIndex = step.DisIndex;
}
if (currentDistriIndex >= 0)
{
current.Value.AddDistribution(newDis);
}
} while (working.Count > 0);
VerificationOutput.NoOfStates = mdp.States.Count;
//mdp.BackUpTargetStates();
return mdp;
}
private void BuildPRE(MDP mdp, ref int counter)
{
HashSet<MDPState> working = new HashSet<MDPState>();
HashSet<MDPState> visited = new HashSet<MDPState>();
working.Add(mdp.InitState);
visited.Add(mdp.InitState);
do
{
HashSet<MDPState> newWorking = new HashSet<MDPState>();
foreach (MDPState state in working)
{
counter++;
foreach (var distr in state.Distributions)
{
foreach (var tran in distr.States)
{
MDPState tranV = tran.Value;
if (tranV.ReachTarget)
{
if (!tranV.Pre.Contains(state))
{
tranV.Pre.Add(state);
}
if (!visited.Contains(tranV))
{
visited.Add(tranV);
newWorking.Add(tranV);
}
}
}
}
}
working = newWorking;
} while (working.Count > 0);
return;
}
