//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 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; }