//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 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;
}
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;
}
