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1057 lines
69 KiB
1057 lines
69 KiB
#ifndef STORM_UTILITY_GRAPH_H_
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#define STORM_UTILITY_GRAPH_H_
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#include <set>
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#include <limits>
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#include "utility/OsDetection.h"
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#include "src/storage/sparse/StateType.h"
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#include "src/models/symbolic/DeterministicModel.h"
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#include "src/models/symbolic/NondeterministicModel.h"
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#include "src/models/sparse/DeterministicModel.h"
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#include "src/models/sparse/NondeterministicModel.h"
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#include "src/utility/constants.h"
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#include "src/exceptions/InvalidArgumentException.h"
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#include "log4cplus/logger.h"
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#include "log4cplus/loggingmacros.h"
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extern log4cplus::Logger logger;
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namespace storm {
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namespace utility {
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namespace graph {
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/*!
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* Performs a forward depth-first search through the underlying graph structure to identify the states that
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* are reachable from the given set only passing through a constrained set of states until some target
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* have been reached.
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*
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* @param transitionMatrix The transition relation of the graph structure to search.
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* @param initialStates The set of states from which to start the search.
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* @param constraintStates The set of states that must not be left.
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* @param targetStates The target states that may not be passed.
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*/
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template<typename T>
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storm::storage::BitVector getReachableStates(storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::BitVector const& initialStates, storm::storage::BitVector const& constraintStates, storm::storage::BitVector const& targetStates) {
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storm::storage::BitVector reachableStates(initialStates);
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// Initialize the stack used for the DFS with the states.
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std::vector<uint_fast64_t> stack(initialStates.begin(), initialStates.end());
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// Perform the actual DFS.
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uint_fast64_t currentState = 0;
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while (!stack.empty()) {
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currentState = stack.back();
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stack.pop_back();
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for (auto const& successor : transitionMatrix.getRow(currentState)) {
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// Only explore the state if the transition was actually there and the successor has not yet
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// been visited.
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if (successor.getValue() != storm::utility::zero<T>() && !reachableStates.get(successor.getColumn())) {
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// If the successor is one of the target states, we need to include it, but must not explore
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// it further.
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if (targetStates.get(successor.getColumn())) {
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reachableStates.set(successor.getColumn());
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} else if (constraintStates.get(successor.getColumn())) {
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// However, if the state is in the constrained set of states, we need to follow it.
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reachableStates.set(successor.getColumn());
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stack.push_back(successor.getColumn());
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}
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}
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}
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}
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return reachableStates;
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}
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/*!
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* Performs a breadth-first search through the underlying graph structure to compute the distance from all
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* states to the starting states of the search.
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*
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* @param transitionMatrix The transition relation of the graph structure to search.
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* @param initialStates The set of states from which to start the search.
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* @return The distances of each state to the initial states of the sarch.
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*/
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template<typename T>
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std::vector<std::size_t> getDistances(storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::BitVector const& initialStates) {
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std::vector<std::size_t> distances(transitionMatrix.getRowGroupCount());
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std::vector<std::pair<storm::storage::sparse::state_type, std::size_t>> stateQueue;
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stateQueue.reserve(transitionMatrix.getRowGroupCount());
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storm::storage::BitVector statesInQueue(transitionMatrix.getRowGroupCount());
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storm::storage::sparse::state_type currentPosition = 0;
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for (auto const& initialState : initialStates) {
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stateQueue.emplace_back(initialState, 0);
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statesInQueue.set(initialState);
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}
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// Perform a BFS.
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while (currentPosition < stateQueue.size()) {
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std::pair<storm::storage::sparse::state_type, std::size_t> const& stateDistancePair = stateQueue[currentPosition];
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distances[stateDistancePair.first] = stateDistancePair.second;
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for (auto const& successorEntry : transitionMatrix.getRowGroup(stateDistancePair.first)) {
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if (!statesInQueue.get(successorEntry.getColumn())) {
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stateQueue.emplace_back(successorEntry.getColumn(), stateDistancePair.second + 1);
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statesInQueue.set(successorEntry.getColumn());
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}
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}
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++currentPosition;
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}
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return distances;
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}
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/*!
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* Performs a backward depth-first search trough the underlying graph structure
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* of the given model to determine which states of the model have a positive probability
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* of satisfying phi until psi. The resulting states are written to the given bit vector.
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*
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* @param backwardTransitions The reversed transition relation of the graph structure to search.
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* @param phiStates A bit vector of all states satisfying phi.
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* @param psiStates A bit vector of all states satisfying psi.
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* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
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* @param maximalSteps The maximal number of steps to reach the psi states.
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* @return A bit vector with all indices of states that have a probability greater than 0.
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*/
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template <typename T>
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storm::storage::BitVector performProbGreater0(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0) {
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// Prepare the resulting bit vector.
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uint_fast64_t numberOfStates = phiStates.size();
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storm::storage::BitVector statesWithProbabilityGreater0(numberOfStates);
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// Add all psi states as they already satisfy the condition.
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statesWithProbabilityGreater0 |= psiStates;
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// Initialize the stack used for the DFS with the states.
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std::vector<uint_fast64_t> stack(psiStates.begin(), psiStates.end());
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// Initialize the stack for the step bound, if the number of steps is bounded.
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std::vector<uint_fast64_t> stepStack;
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std::vector<uint_fast64_t> remainingSteps;
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if (useStepBound) {
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stepStack.reserve(numberOfStates);
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stepStack.insert(stepStack.begin(), psiStates.getNumberOfSetBits(), maximalSteps);
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remainingSteps.resize(numberOfStates);
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for (auto state : psiStates) {
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remainingSteps[state] = maximalSteps;
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}
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}
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// Perform the actual DFS.
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uint_fast64_t currentState, currentStepBound;
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while (!stack.empty()) {
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currentState = stack.back();
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stack.pop_back();
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if (useStepBound) {
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currentStepBound = stepStack.back();
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stepStack.pop_back();
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}
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for (typename storm::storage::SparseMatrix<T>::const_iterator entryIt = backwardTransitions.begin(currentState), entryIte = backwardTransitions.end(currentState); entryIt != entryIte; ++entryIt) {
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if (phiStates[entryIt->getColumn()] && (!statesWithProbabilityGreater0.get(entryIt->getColumn()) || (useStepBound && remainingSteps[entryIt->getColumn()] < currentStepBound - 1))) {
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// If we don't have a bound on the number of steps to take, just add the state to the stack.
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if (!useStepBound) {
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statesWithProbabilityGreater0.set(entryIt->getColumn(), true);
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stack.push_back(entryIt->getColumn());
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} else if (currentStepBound > 0) {
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// If there is at least one more step to go, we need to push the state and the new number of steps.
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remainingSteps[entryIt->getColumn()] = currentStepBound - 1;
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statesWithProbabilityGreater0.set(entryIt->getColumn(), true);
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stack.push_back(entryIt->getColumn());
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stepStack.push_back(currentStepBound - 1);
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}
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}
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}
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}
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// Return result.
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return statesWithProbabilityGreater0;
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}
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/*!
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* Computes the set of states of the given model for which all paths lead to
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* the given set of target states and only visit states from the filter set
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* before. In order to do this, it uses the given set of states that
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* characterizes the states that possess at least one path to a target state.
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* The results are written to the given bit vector.
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*
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* @param backwardTransitions The reversed transition relation of the graph structure to search.
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* @param phiStates A bit vector of all states satisfying phi.
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* @param psiStates A bit vector of all states satisfying psi.
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* @param statesWithProbabilityGreater0 A reference to a bit vector of states that possess a positive
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* probability mass of satisfying phi until psi.
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* @return A bit vector with all indices of states that have a probability greater than 1.
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*/
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template <typename T>
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storm::storage::BitVector performProb1(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::BitVector const& statesWithProbabilityGreater0) {
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storm::storage::BitVector statesWithProbability1 = performProbGreater0(backwardTransitions, ~psiStates, ~statesWithProbabilityGreater0);
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statesWithProbability1.complement();
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return statesWithProbability1;
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}
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/*!
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* Computes the set of states of the given model for which all paths lead to
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* the given set of target states and only visit states from the filter set
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* before. In order to do this, it uses the given set of states that
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* characterizes the states that possess at least one path to a target state.
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* The results are written to the given bit vector.
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*
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* @param backwardTransitions The reversed transition relation of the graph structure to search.
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* @param phiStates A bit vector of all states satisfying phi.
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* @param psiStates A bit vector of all states satisfying psi.
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* @return A bit vector with all indices of states that have a probability greater than 1.
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*/
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template <typename T>
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storm::storage::BitVector performProb1(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
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storm::storage::BitVector statesWithProbabilityGreater0 = performProbGreater0(backwardTransitions, phiStates, psiStates);
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storm::storage::BitVector statesWithProbability1 = performProbGreater0(backwardTransitions, ~psiStates, ~(statesWithProbabilityGreater0));
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statesWithProbability1.complement();
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return statesWithProbability1;
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}
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/*!
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* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi until psi in a
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* deterministic model.
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*
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* @param model The model whose graph structure to search.
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* @param phiStates The set of all states satisfying phi.
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* @param psiStates The set of all states satisfying psi.
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* @return A pair of bit vectors such that the first bit vector stores the indices of all states
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* with probability 0 and the second stores all indices of states with probability 1.
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*/
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template <typename T>
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static std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::models::sparse::DeterministicModel<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
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std::pair<storm::storage::BitVector, storm::storage::BitVector> result;
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storm::storage::SparseMatrix<T> backwardTransitions = model.getBackwardTransitions();
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result.first = performProbGreater0(backwardTransitions, phiStates, psiStates);
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result.second = performProb1(backwardTransitions, phiStates, psiStates, result.first);
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result.first.complement();
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return result;
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}
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/*!
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* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi until psi in a
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* deterministic model.
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*
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* @param backwardTransitions The backward transitions of the model whose graph structure to search.
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* @param phiStates The set of all states satisfying phi.
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* @param psiStates The set of all states satisfying psi.
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* @return A pair of bit vectors such that the first bit vector stores the indices of all states
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* with probability 0 and the second stores all indices of states with probability 1.
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*/
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template <typename T>
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static std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::storage::SparseMatrix<T> backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
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std::pair<storm::storage::BitVector, storm::storage::BitVector> result;
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result.first = performProbGreater0(backwardTransitions, phiStates, psiStates);
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result.second = performProb1(backwardTransitions, phiStates, psiStates, result.first);
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result.first.complement();
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return result;
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}
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/*!
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* Computes the set of states that has a positive probability of reaching psi states after only passing
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* through phi states before.
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*
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* @param model The (symbolic) model for which to compute the set of states.
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* @param transitionMatrixBdd The transition matrix of the model as a BDD.
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* @param phiStatesBdd The BDD containing all phi states of the model.
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* @param psiStatesBdd The BDD containing all psi states of the model.
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* @return All states with positive probability.
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*/
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template <storm::dd::DdType Type>
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storm::dd::Dd<Type> performProbGreater0(storm::models::symbolic::DeterministicModel<Type> const& model, storm::dd::Dd<Type> const& transitionMatrixBdd, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd) {
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// Initialize environment for backward search.
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storm::dd::DdManager<Type> const& manager = model.getManager();
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storm::dd::Dd<Type> lastIterationStates = manager.getZero();
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storm::dd::Dd<Type> statesWithProbabilityGreater0 = psiStatesBdd;
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uint_fast64_t iterations = 0;
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while (lastIterationStates != statesWithProbabilityGreater0) {
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lastIterationStates = statesWithProbabilityGreater0;
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statesWithProbabilityGreater0 = statesWithProbabilityGreater0.swapVariables(model.getRowColumnMetaVariablePairs());
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statesWithProbabilityGreater0 &= transitionMatrixBdd;
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statesWithProbabilityGreater0 = statesWithProbabilityGreater0.existsAbstract(model.getColumnVariables());
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statesWithProbabilityGreater0 &= phiStatesBdd;
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statesWithProbabilityGreater0 |= lastIterationStates;
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++iterations;
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}
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return statesWithProbabilityGreater0;
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}
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/*!
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* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi until psi in a
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* deterministic model.
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*
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* @param model The (symbolic) model for which to compute the set of states.
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* @param transitionMatrixBdd The transition matrix of the model as a BDD.
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* @param phiStatesBdd The BDD containing all phi states of the model.
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* @param psiStatesBdd The BDD containing all psi states of the model.
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* @return A pair of DDs that represent all states with probability 0 and 1, respectively.
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*/
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template <storm::dd::DdType Type>
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static std::pair<storm::dd::Dd<Type>, storm::dd::Dd<Type>> performProb01(storm::models::symbolic::DeterministicModel<Type> const& model, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd) {
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std::pair<storm::dd::Dd<Type>, storm::dd::Dd<Type>> result;
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storm::dd::Dd<Type> transitionMatrixBdd = model.getTransitionMatrix().notZero();
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result.first = performProbGreater0(model, transitionMatrixBdd, phiStatesBdd, psiStatesBdd);
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result.second = !performProbGreater0(model, transitionMatrixBdd, !psiStatesBdd && model.getReachableStates(), !result.first && model.getReachableStates()) && model.getReachableStates();
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result.first = !result.first && model.getReachableStates();
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return result;
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}
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/*!
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* Computes the sets of states that have probability greater 0 of satisfying phi until psi under at least
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* one possible resolution of non-determinism in a non-deterministic model. Stated differently,
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* this means that these states have a probability greater 0 of satisfying phi until psi if the
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* scheduler tries to minimize this probability.
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*
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* @param model The model whose graph structure to search.
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* @param backwardTransitions The reversed transition relation of the model.
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* @param phiStates The set of all states satisfying phi.
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* @param psiStates The set of all states satisfying psi.
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* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
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* @param maximalSteps The maximal number of steps to reach the psi states.
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* @return A bit vector that represents all states with probability 0.
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*/
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template <typename T>
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storm::storage::BitVector performProbGreater0E(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0) {
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size_t numberOfStates = phiStates.size();
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// Prepare resulting bit vector.
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storm::storage::BitVector statesWithProbabilityGreater0(numberOfStates);
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// Add all psi states as the already satisfy the condition.
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statesWithProbabilityGreater0 |= psiStates;
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// Initialize the stack used for the DFS with the states
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std::vector<uint_fast64_t> stack(psiStates.begin(), psiStates.end());
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// Initialize the stack for the step bound, if the number of steps is bounded.
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std::vector<uint_fast64_t> stepStack;
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std::vector<uint_fast64_t> remainingSteps;
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if (useStepBound) {
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stepStack.reserve(numberOfStates);
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stepStack.insert(stepStack.begin(), psiStates.getNumberOfSetBits(), maximalSteps);
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remainingSteps.resize(numberOfStates);
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for (auto state : psiStates) {
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remainingSteps[state] = maximalSteps;
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}
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}
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// Perform the actual DFS.
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uint_fast64_t currentState, currentStepBound;
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while (!stack.empty()) {
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currentState = stack.back();
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stack.pop_back();
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if (useStepBound) {
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currentStepBound = stepStack.back();
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stepStack.pop_back();
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}
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for (typename storm::storage::SparseMatrix<T>::const_iterator entryIt = backwardTransitions.begin(currentState), entryIte = backwardTransitions.end(currentState); entryIt != entryIte; ++entryIt) {
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if (phiStates.get(entryIt->getColumn()) && (!statesWithProbabilityGreater0.get(entryIt->getColumn()) || (useStepBound && remainingSteps[entryIt->getColumn()] < currentStepBound - 1))) {
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// If we don't have a bound on the number of steps to take, just add the state to the stack.
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if (!useStepBound) {
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statesWithProbabilityGreater0.set(entryIt->getColumn(), true);
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stack.push_back(entryIt->getColumn());
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} else if (currentStepBound > 0) {
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// If there is at least one more step to go, we need to push the state and the new number of steps.
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remainingSteps[entryIt->getColumn()] = currentStepBound - 1;
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statesWithProbabilityGreater0.set(entryIt->getColumn(), true);
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stack.push_back(entryIt->getColumn());
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stepStack.push_back(currentStepBound - 1);
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}
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}
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}
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}
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return statesWithProbabilityGreater0;
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}
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template <typename T>
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storm::storage::BitVector performProb0A(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
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storm::storage::BitVector statesWithProbability0 = performProbGreater0E(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
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statesWithProbability0.complement();
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return statesWithProbability0;
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}
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/*!
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* Computes the sets of states that have probability 0 of satisfying phi until psi under all
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* possible resolutions of non-determinism in a non-deterministic model. Stated differently,
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* this means that these states have probability 0 of satisfying phi until psi even if the
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* scheduler tries to maximize this probability.
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*
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* @param model The model whose graph structure to search.
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* @param backwardTransitions The reversed transition relation of the model.
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* @param phiStates The set of all states satisfying phi.
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* @param psiStates The set of all states satisfying psi.
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* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
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* @param maximalSteps The maximal number of steps to reach the psi states.
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* @return A bit vector that represents all states with probability 0.
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*/
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template <typename T>
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|
storm::storage::BitVector performProb0A(storm::models::sparse::NondeterministicModel<T> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
return performProb0A(model.getTransitionMatrix(), model.getNondeterministicChoiceIndices(), backwardTransitions, phiStates, psiStates);
|
|
}
|
|
|
|
/*!
|
|
* Computes the sets of states that have probability 1 of satisfying phi until psi under at least
|
|
* one possible resolution of non-determinism in a non-deterministic model. Stated differently,
|
|
* this means that these states have probability 1 of satisfying phi until psi if the
|
|
* scheduler tries to maximize this probability.
|
|
*
|
|
* @param model The model whose graph structure to search.
|
|
* @param backwardTransitions The reversed transition relation of the model.
|
|
* @param phiStates The set of all states satisfying phi.
|
|
* @param psiStates The set of all states satisfying psi.
|
|
* @return A bit vector that represents all states with probability 1.
|
|
*/
|
|
template <typename T>
|
|
storm::storage::BitVector performProb1E(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
size_t numberOfStates = phiStates.size();
|
|
|
|
// Initialize the environment for the iterative algorithm.
|
|
storm::storage::BitVector currentStates(numberOfStates, true);
|
|
std::vector<uint_fast64_t> stack;
|
|
stack.reserve(numberOfStates);
|
|
|
|
// Perform the loop as long as the set of states gets larger.
|
|
bool done = false;
|
|
uint_fast64_t currentState;
|
|
while (!done) {
|
|
stack.clear();
|
|
storm::storage::BitVector nextStates(psiStates);
|
|
stack.insert(stack.end(), psiStates.begin(), psiStates.end());
|
|
|
|
while (!stack.empty()) {
|
|
currentState = stack.back();
|
|
stack.pop_back();
|
|
|
|
for (typename storm::storage::SparseMatrix<T>::const_iterator predecessorEntryIt = backwardTransitions.begin(currentState), predecessorEntryIte = backwardTransitions.end(currentState); predecessorEntryIt != predecessorEntryIte; ++predecessorEntryIt) {
|
|
if (phiStates.get(predecessorEntryIt->getColumn()) && !nextStates.get(predecessorEntryIt->getColumn())) {
|
|
// Check whether the predecessor has only successors in the current state set for one of the
|
|
// nondeterminstic choices.
|
|
for (uint_fast64_t row = nondeterministicChoiceIndices[predecessorEntryIt->getColumn()]; row < nondeterministicChoiceIndices[predecessorEntryIt->getColumn() + 1]; ++row) {
|
|
bool allSuccessorsInCurrentStates = true;
|
|
for (typename storm::storage::SparseMatrix<T>::const_iterator successorEntryIt = transitionMatrix.begin(row), successorEntryIte = transitionMatrix.end(row); successorEntryIt != successorEntryIte; ++successorEntryIt) {
|
|
if (!currentStates.get(successorEntryIt->getColumn())) {
|
|
allSuccessorsInCurrentStates = false;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// If all successors for a given nondeterministic choice are in the current state set, we
|
|
// add it to the set of states for the next iteration and perform a backward search from
|
|
// that state.
|
|
if (allSuccessorsInCurrentStates) {
|
|
nextStates.set(predecessorEntryIt->getColumn(), true);
|
|
stack.push_back(predecessorEntryIt->getColumn());
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Check whether we need to perform an additional iteration.
|
|
if (currentStates == nextStates) {
|
|
done = true;
|
|
} else {
|
|
currentStates = std::move(nextStates);
|
|
}
|
|
}
|
|
|
|
return currentStates;
|
|
}
|
|
|
|
template <typename T>
|
|
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
std::pair<storm::storage::BitVector, storm::storage::BitVector> result;
|
|
|
|
result.first = performProb0A(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
|
|
result.second = performProb1E(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
|
|
return result;
|
|
}
|
|
|
|
/*!
|
|
* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi
|
|
* until psi in a non-deterministic model in which all non-deterministic choices are resolved
|
|
* such that the probability is maximized.
|
|
*
|
|
* @param model The model whose graph structure to search.
|
|
* @param phiStates The set of all states satisfying phi.
|
|
* @param psiStates The set of all states satisfying psi.
|
|
* @return A pair of bit vectors that represent all states with probability 0 and 1, respectively.
|
|
*/
|
|
template <typename T>
|
|
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::models::sparse::NondeterministicModel<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
return performProb01Max(model.getTransitionMatrix(), model.getTransitionMatrix().getRowGroupIndices(), model.getBackwardTransitions(), phiStates, psiStates);
|
|
}
|
|
|
|
/*!
|
|
* Computes the sets of states that have probability greater 0 of satisfying phi until psi under any
|
|
* possible resolution of non-determinism in a non-deterministic model. Stated differently,
|
|
* this means that these states have a probability greater 0 of satisfying phi until psi if the
|
|
* scheduler tries to maximize this probability.
|
|
*
|
|
* @param model The model whose graph structure to search.
|
|
* @param backwardTransitions The reversed transition relation of the model.
|
|
* @param phiStates The set of all states satisfying phi.
|
|
* @param psiStates The set of all states satisfying psi.
|
|
* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
|
|
* @param maximalSteps The maximal number of steps to reach the psi states.
|
|
* @return A bit vector that represents all states with probability 0.
|
|
*/
|
|
template <typename T>
|
|
storm::storage::BitVector performProbGreater0A(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0) {
|
|
size_t numberOfStates = phiStates.size();
|
|
|
|
// Prepare resulting bit vector.
|
|
storm::storage::BitVector statesWithProbabilityGreater0(numberOfStates);
|
|
|
|
// Add all psi states as the already satisfy the condition.
|
|
statesWithProbabilityGreater0 |= psiStates;
|
|
|
|
// Initialize the stack used for the DFS with the states
|
|
std::vector<uint_fast64_t> stack(psiStates.begin(), psiStates.end());
|
|
|
|
// Initialize the stack for the step bound, if the number of steps is bounded.
|
|
std::vector<uint_fast64_t> stepStack;
|
|
std::vector<uint_fast64_t> remainingSteps;
|
|
if (useStepBound) {
|
|
stepStack.reserve(numberOfStates);
|
|
stepStack.insert(stepStack.begin(), psiStates.getNumberOfSetBits(), maximalSteps);
|
|
remainingSteps.resize(numberOfStates);
|
|
for (auto state : psiStates) {
|
|
remainingSteps[state] = maximalSteps;
|
|
}
|
|
}
|
|
|
|
// Perform the actual DFS.
|
|
uint_fast64_t currentState, currentStepBound;
|
|
while(!stack.empty()) {
|
|
currentState = stack.back();
|
|
stack.pop_back();
|
|
|
|
if (useStepBound) {
|
|
currentStepBound = stepStack.back();
|
|
stepStack.pop_back();
|
|
}
|
|
|
|
for(typename storm::storage::SparseMatrix<T>::const_iterator predecessorEntryIt = backwardTransitions.begin(currentState), predecessorEntryIte = backwardTransitions.end(currentState); predecessorEntryIt != predecessorEntryIte; ++predecessorEntryIt) {
|
|
if (phiStates.get(predecessorEntryIt->getColumn()) && (!statesWithProbabilityGreater0.get(predecessorEntryIt->getColumn()) || (useStepBound && remainingSteps[predecessorEntryIt->getColumn()] < currentStepBound - 1))) {
|
|
// Check whether the predecessor has at least one successor in the current state set for every
|
|
// nondeterministic choice.
|
|
bool addToStatesWithProbabilityGreater0 = true;
|
|
for (uint_fast64_t row = nondeterministicChoiceIndices[predecessorEntryIt->getColumn()]; row < nondeterministicChoiceIndices[predecessorEntryIt->getColumn() + 1]; ++row) {
|
|
bool hasAtLeastOneSuccessorWithProbabilityGreater0 = false;
|
|
for (typename storm::storage::SparseMatrix<T>::const_iterator successorEntryIt = transitionMatrix.begin(row), successorEntryIte = transitionMatrix.end(row); successorEntryIt != successorEntryIte; ++successorEntryIt) {
|
|
if (statesWithProbabilityGreater0.get(successorEntryIt->getColumn())) {
|
|
hasAtLeastOneSuccessorWithProbabilityGreater0 = true;
|
|
break;
|
|
}
|
|
}
|
|
|
|
if (!hasAtLeastOneSuccessorWithProbabilityGreater0) {
|
|
addToStatesWithProbabilityGreater0 = false;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// If we need to add the state, then actually add it and perform further search from the state.
|
|
if (addToStatesWithProbabilityGreater0) {
|
|
// If we don't have a bound on the number of steps to take, just add the state to the stack.
|
|
if (!useStepBound) {
|
|
statesWithProbabilityGreater0.set(predecessorEntryIt->getColumn(), true);
|
|
stack.push_back(predecessorEntryIt->getColumn());
|
|
} else if (currentStepBound > 0) {
|
|
// If there is at least one more step to go, we need to push the state and the new number of steps.
|
|
remainingSteps[predecessorEntryIt->getColumn()] = currentStepBound - 1;
|
|
statesWithProbabilityGreater0.set(predecessorEntryIt->getColumn(), true);
|
|
stack.push_back(predecessorEntryIt->getColumn());
|
|
stepStack.push_back(currentStepBound - 1);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return statesWithProbabilityGreater0;
|
|
}
|
|
|
|
/*!
|
|
* Computes the sets of states that have probability 0 of satisfying phi until psi under at least
|
|
* one possible resolution of non-determinism in a non-deterministic model. Stated differently,
|
|
* this means that these states have probability 0 of satisfying phi until psi if the
|
|
* scheduler tries to minimize this probability.
|
|
*
|
|
* @param model The model whose graph structure to search.
|
|
* @param backwardTransitions The reversed transition relation of the model.
|
|
* @param phiStates The set of all states satisfying phi.
|
|
* @param psiStates The set of all states satisfying psi.
|
|
* @return A bit vector that represents all states with probability 0.
|
|
*/
|
|
template <typename T>
|
|
storm::storage::BitVector performProb0E(storm::models::sparse::NondeterministicModel<T> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
storm::storage::BitVector statesWithProbability0 = performProbGreater0A(model.getTransitionMatrix(), model.getNondeterministicChoiceIndices(), backwardTransitions, phiStates, psiStates);
|
|
statesWithProbability0.complement();
|
|
return statesWithProbability0;
|
|
}
|
|
|
|
template <typename T>
|
|
storm::storage::BitVector performProb0E(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
storm::storage::BitVector statesWithProbability0 = performProbGreater0A(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
|
|
statesWithProbability0.complement();
|
|
return statesWithProbability0;
|
|
}
|
|
|
|
/*!
|
|
* Computes the sets of states that have probability 1 of satisfying phi until psi under all
|
|
* possible resolutions of non-determinism in a non-deterministic model. Stated differently,
|
|
* this means that these states have probability 1 of satisfying phi until psi even if the
|
|
* scheduler tries to minimize this probability.
|
|
*
|
|
* @param model The model whose graph structure to search.
|
|
* @param backwardTransitions The reversed transition relation of the model.
|
|
* @param phiStates The set of all states satisfying phi.
|
|
* @param psiStates The set of all states satisfying psi.
|
|
* @return A bit vector that represents all states with probability 0.
|
|
*/
|
|
template <typename T>
|
|
storm::storage::BitVector performProb1A( storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
size_t numberOfStates = phiStates.size();
|
|
|
|
// Initialize the environment for the iterative algorithm.
|
|
storm::storage::BitVector currentStates(numberOfStates, true);
|
|
std::vector<uint_fast64_t> stack;
|
|
stack.reserve(numberOfStates);
|
|
|
|
// Perform the loop as long as the set of states gets smaller.
|
|
bool done = false;
|
|
uint_fast64_t currentState;
|
|
while (!done) {
|
|
stack.clear();
|
|
storm::storage::BitVector nextStates(psiStates);
|
|
stack.insert(stack.end(), psiStates.begin(), psiStates.end());
|
|
|
|
while (!stack.empty()) {
|
|
currentState = stack.back();
|
|
stack.pop_back();
|
|
|
|
for(typename storm::storage::SparseMatrix<T>::const_iterator predecessorEntryIt = backwardTransitions.begin(currentState), predecessorEntryIte = backwardTransitions.end(currentState); predecessorEntryIt != predecessorEntryIte; ++predecessorEntryIt) {
|
|
if (phiStates.get(predecessorEntryIt->getColumn()) && !nextStates.get(predecessorEntryIt->getColumn())) {
|
|
// Check whether the predecessor has only successors in the current state set for all of the
|
|
// nondeterminstic choices.
|
|
bool allSuccessorsInCurrentStatesForAllChoices = true;
|
|
for (typename storm::storage::SparseMatrix<T>::const_iterator successorEntryIt = transitionMatrix.begin(nondeterministicChoiceIndices[predecessorEntryIt->getColumn()]), successorEntryIte = transitionMatrix.begin(nondeterministicChoiceIndices[predecessorEntryIt->getColumn() + 1]); successorEntryIt != successorEntryIte; ++successorEntryIt) {
|
|
if (!currentStates.get(successorEntryIt->getColumn())) {
|
|
allSuccessorsInCurrentStatesForAllChoices = false;
|
|
goto afterCheckLoop;
|
|
}
|
|
}
|
|
|
|
afterCheckLoop:
|
|
// If all successors for all nondeterministic choices are in the current state set, we
|
|
// add it to the set of states for the next iteration and perform a backward search from
|
|
// that state.
|
|
if (allSuccessorsInCurrentStatesForAllChoices) {
|
|
nextStates.set(predecessorEntryIt->getColumn(), true);
|
|
stack.push_back(predecessorEntryIt->getColumn());
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Check whether we need to perform an additional iteration.
|
|
if (currentStates == nextStates) {
|
|
done = true;
|
|
} else {
|
|
currentStates = std::move(nextStates);
|
|
}
|
|
}
|
|
return currentStates;
|
|
}
|
|
|
|
template <typename T>
|
|
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
std::pair<storm::storage::BitVector, storm::storage::BitVector> result;
|
|
result.first = performProb0E(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
|
|
result.second = performProb1A(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
|
|
return result;
|
|
}
|
|
|
|
/*!
|
|
* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi
|
|
* until psi in a non-deterministic model in which all non-deterministic choices are resolved
|
|
* such that the probability is minimized.
|
|
*
|
|
* @param model The model whose graph structure to search.
|
|
* @param phiStates The set of all states satisfying phi.
|
|
* @param psiStates The set of all states satisfying psi.
|
|
* @return A pair of bit vectors that represent all states with probability 0 and 1, respectively.
|
|
*/
|
|
template <typename T>
|
|
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::models::sparse::NondeterministicModel<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
return performProb01Min(model.getTransitionMatrix(), model.getTransitionMatrix().getRowGroupIndices(), model.getBackwardTransitions(), phiStates, psiStates);
|
|
}
|
|
|
|
/*!
|
|
* Computes the set of states for which there exists a scheduler that achieves a probability greater than
|
|
* zero of satisfying phi until psi.
|
|
*
|
|
* @param model The (symbolic) model for which to compute the set of states.
|
|
* @param transitionMatrixBdd The transition matrix of the model as a BDD.
|
|
* @param phiStatesBdd The BDD containing all phi states of the model.
|
|
* @param psiStatesBdd The BDD containing all psi states of the model.
|
|
* @return A DD representing all such states.
|
|
*/
|
|
template <storm::dd::DdType Type>
|
|
storm::dd::Dd<Type> performProbGreater0E(storm::models::symbolic::NondeterministicModel<Type> const& model, storm::dd::Dd<Type> const& transitionMatrixBdd, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd) {
|
|
// Initialize environment for backward search.
|
|
storm::dd::DdManager<Type> const& manager = model.getManager();
|
|
storm::dd::Dd<Type> lastIterationStates = manager.getZero();
|
|
storm::dd::Dd<Type> statesWithProbabilityGreater0E = psiStatesBdd;
|
|
|
|
uint_fast64_t iterations = 0;
|
|
storm::dd::Dd<Type> abstractedTransitionMatrixBdd = transitionMatrixBdd.existsAbstract(model.getNondeterminismVariables());
|
|
while (lastIterationStates != statesWithProbabilityGreater0E) {
|
|
lastIterationStates = statesWithProbabilityGreater0E;
|
|
statesWithProbabilityGreater0E = statesWithProbabilityGreater0E.swapVariables(model.getRowColumnMetaVariablePairs());
|
|
statesWithProbabilityGreater0E = statesWithProbabilityGreater0E.andExists(abstractedTransitionMatrixBdd, model.getColumnVariables());
|
|
statesWithProbabilityGreater0E &= phiStatesBdd;
|
|
statesWithProbabilityGreater0E |= lastIterationStates;
|
|
++iterations;
|
|
}
|
|
|
|
return statesWithProbabilityGreater0E;
|
|
}
|
|
|
|
/*!
|
|
* Computes the set of states for which there does not exist a scheduler that achieves a probability greater
|
|
* than zero of satisfying phi until psi.
|
|
*
|
|
* @param model The (symbolic) model for which to compute the set of states.
|
|
* @param transitionMatrixBdd The transition matrix of the model as a BDD.
|
|
* @param phiStates The phi states of the model.
|
|
* @param psiStates The psi states of the model.
|
|
* @return A DD representing all such states.
|
|
*/
|
|
template <storm::dd::DdType Type>
|
|
storm::dd::Dd<Type> performProb0A(storm::models::symbolic::NondeterministicModel<Type> const& model, storm::dd::Dd<Type> const& transitionMatrixBdd, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd) {
|
|
return !performProbGreater0E(model, transitionMatrixBdd, phiStatesBdd, psiStatesBdd) && model.getReachableStates();
|
|
}
|
|
|
|
/*!
|
|
* Computes the set of states for which all schedulers achieve a probability greater than zero of satisfying
|
|
* phi until psi.
|
|
*
|
|
* @param model The (symbolic) model for which to compute the set of states.
|
|
* @param transitionMatrixBdd The transition matrix of the model as a BDD.
|
|
* @param phiStatesBdd The BDD containing all phi states of the model.
|
|
* @param psiStatesBdd The BDD containing all psi states of the model.
|
|
* @return A DD representing all such states.
|
|
*/
|
|
template <storm::dd::DdType Type>
|
|
storm::dd::Dd<Type> performProbGreater0A(storm::models::symbolic::NondeterministicModel<Type> const& model, storm::dd::Dd<Type> const& transitionMatrixBdd, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd) {
|
|
// Initialize environment for backward search.
|
|
storm::dd::DdManager<Type> const& manager = model.getManager();
|
|
storm::dd::Dd<Type> lastIterationStates = manager.getZero();
|
|
storm::dd::Dd<Type> statesWithProbabilityGreater0A = psiStatesBdd;
|
|
|
|
uint_fast64_t iterations = 0;
|
|
while (lastIterationStates != statesWithProbabilityGreater0A) {
|
|
lastIterationStates = statesWithProbabilityGreater0A;
|
|
statesWithProbabilityGreater0A = statesWithProbabilityGreater0A.swapVariables(model.getRowColumnMetaVariablePairs());
|
|
statesWithProbabilityGreater0A = statesWithProbabilityGreater0A.andExists(transitionMatrixBdd, model.getColumnVariables());
|
|
statesWithProbabilityGreater0A |= model.getIllegalMask();
|
|
statesWithProbabilityGreater0A = statesWithProbabilityGreater0A.universalAbstract(model.getNondeterminismVariables());
|
|
statesWithProbabilityGreater0A &= phiStatesBdd;
|
|
statesWithProbabilityGreater0A |= psiStatesBdd;
|
|
++iterations;
|
|
}
|
|
|
|
return statesWithProbabilityGreater0A;
|
|
}
|
|
|
|
/*!
|
|
* Computes the set of states for which there exists a scheduler that achieves probability zero of satisfying
|
|
* phi until psi.
|
|
*
|
|
* @param model The (symbolic) model for which to compute the set of states.
|
|
* @param transitionMatrixBdd The transition matrix of the model as a BDD.
|
|
* @param phiStatesBdd The BDD containing all phi states of the model.
|
|
* @param psiStatesBdd The BDD containing all psi states of the model.
|
|
* @return A DD representing all such states.
|
|
*/
|
|
template <storm::dd::DdType Type>
|
|
storm::dd::Dd<Type> performProb0E(storm::models::symbolic::NondeterministicModel<Type> const& model, storm::dd::Dd<Type> const& transitionMatrixBdd, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd) {
|
|
return !performProbGreater0A(model, transitionMatrixBdd, phiStatesBdd, psiStatesBdd) && model.getReachableStates();
|
|
}
|
|
|
|
/*!
|
|
* Computes the set of states for which all schedulers achieve probability one of satisfying phi until psi.
|
|
*
|
|
* @param model The (symbolic) model for which to compute the set of states.
|
|
* @param transitionMatrixBdd The transition matrix of the model as a BDD.
|
|
* @param phiStatesBdd The BDD containing all phi states of the model.
|
|
* @param psiStatesBdd The BDD containing all psi states of the model.
|
|
* @param statesWithProbabilityGreater0A The states of the model that have a probability greater zero under
|
|
* all schedulers.
|
|
* @return A DD representing all such states.
|
|
*/
|
|
template <storm::dd::DdType Type>
|
|
storm::dd::Dd<Type> performProb1A(storm::models::symbolic::NondeterministicModel<Type> const& model, storm::dd::Dd<Type> const& transitionMatrixBdd, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd, storm::dd::Dd<Type> const& statesWithProbabilityGreater0A) {
|
|
// Initialize environment for backward search.
|
|
storm::dd::DdManager<Type> const& manager = model.getManager();
|
|
storm::dd::Dd<Type> lastIterationStates = manager.getZero();
|
|
storm::dd::Dd<Type> statesWithProbability1A = psiStatesBdd || statesWithProbabilityGreater0A;
|
|
|
|
uint_fast64_t iterations = 0;
|
|
while (lastIterationStates != statesWithProbability1A) {
|
|
lastIterationStates = statesWithProbability1A;
|
|
statesWithProbability1A = statesWithProbability1A.swapVariables(model.getRowColumnMetaVariablePairs());
|
|
statesWithProbability1A = transitionMatrixBdd.implies(statesWithProbability1A).universalAbstract(model.getColumnVariables());
|
|
statesWithProbability1A |= model.getIllegalMask();
|
|
statesWithProbability1A = statesWithProbability1A.universalAbstract(model.getNondeterminismVariables());
|
|
statesWithProbability1A &= statesWithProbabilityGreater0A;
|
|
statesWithProbability1A |= psiStatesBdd;
|
|
++iterations;
|
|
}
|
|
|
|
return statesWithProbability1A;
|
|
}
|
|
|
|
/*!
|
|
* Computes the set of states for which there exists a scheduler that achieves probability one of satisfying
|
|
* phi until psi.
|
|
*
|
|
* @param model The (symbolic) model for which to compute the set of states.
|
|
* @param transitionMatrixBdd The transition matrix of the model as a BDD.
|
|
* @param phiStatesBdd The BDD containing all phi states of the model.
|
|
* @param psiStatesBdd The BDD containing all psi states of the model.
|
|
* @param statesWithProbabilityGreater0E The states of the model that have a scheduler that achieves a value
|
|
* greater than zero.
|
|
* @return A DD representing all such states.
|
|
*/
|
|
template <storm::dd::DdType Type>
|
|
storm::dd::Dd<Type> performProb1E(storm::models::symbolic::NondeterministicModel<Type> const& model, storm::dd::Dd<Type> const& transitionMatrixBdd, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd, storm::dd::Dd<Type> const& statesWithProbabilityGreater0E) {
|
|
// Initialize environment for backward search.
|
|
storm::dd::DdManager<Type> const& manager = model.getManager();
|
|
storm::dd::Dd<Type> statesWithProbability1E = statesWithProbabilityGreater0E;
|
|
|
|
uint_fast64_t iterations = 0;
|
|
bool outerLoopDone = false;
|
|
while (!outerLoopDone) {
|
|
storm::dd::Dd<Type> innerStates = manager.getZero();
|
|
|
|
bool innerLoopDone = false;
|
|
while (!innerLoopDone) {
|
|
storm::dd::Dd<Type> temporary = statesWithProbability1E.swapVariables(model.getRowColumnMetaVariablePairs());
|
|
temporary = transitionMatrixBdd.implies(temporary).universalAbstract(model.getColumnVariables());
|
|
|
|
storm::dd::Dd<Type> temporary2 = innerStates.swapVariables(model.getRowColumnMetaVariablePairs());
|
|
temporary2 = transitionMatrixBdd.andExists(temporary2, model.getColumnVariables());
|
|
|
|
temporary = temporary.andExists(temporary2, model.getNondeterminismVariables());
|
|
temporary &= phiStatesBdd;
|
|
temporary |= psiStatesBdd;
|
|
|
|
if (innerStates == temporary) {
|
|
innerLoopDone = true;
|
|
} else {
|
|
innerStates = temporary;
|
|
}
|
|
}
|
|
|
|
if (statesWithProbability1E == innerStates) {
|
|
outerLoopDone = true;
|
|
} else {
|
|
statesWithProbability1E = innerStates;
|
|
}
|
|
++iterations;
|
|
}
|
|
|
|
return statesWithProbability1E;
|
|
}
|
|
|
|
template <storm::dd::DdType Type>
|
|
std::pair<storm::dd::Dd<Type>, storm::dd::Dd<Type>> performProb01Max(storm::models::symbolic::NondeterministicModel<Type> const& model, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd) {
|
|
std::pair<storm::dd::Dd<Type>, storm::dd::Dd<Type>> result;
|
|
storm::dd::Dd<Type> transitionMatrixBdd = model.getTransitionMatrix().notZero();
|
|
result.first = performProb0A(model, transitionMatrixBdd, phiStatesBdd, psiStatesBdd);
|
|
result.second = performProb1E(model, transitionMatrixBdd, phiStatesBdd, psiStatesBdd, !result.first && model.getReachableStates());
|
|
return result;
|
|
}
|
|
|
|
template <storm::dd::DdType Type>
|
|
std::pair<storm::dd::Dd<Type>, storm::dd::Dd<Type>> performProb01Min(storm::models::symbolic::NondeterministicModel<Type> const& model, storm::dd::Dd<Type> const& phiStatesBdd, storm::dd::Dd<Type> const& psiStatesBdd) {
|
|
std::pair<storm::dd::Dd<Type>, storm::dd::Dd<Type>> result;
|
|
storm::dd::Dd<Type> transitionMatrixBdd = model.getTransitionMatrix().notZero();
|
|
result.first = performProb0E(model, transitionMatrixBdd, phiStatesBdd, psiStatesBdd);
|
|
result.second = performProb1A(model, transitionMatrixBdd, phiStatesBdd, psiStatesBdd, !result.first && model.getReachableStates());
|
|
return result;
|
|
}
|
|
|
|
/*!
|
|
* Performs a topological sort of the states of the system according to the given transitions.
|
|
*
|
|
* @param matrix A square matrix representing the transition relation of the system.
|
|
* @return A vector of indices that is a topological sort of the states.
|
|
*/
|
|
template <typename T>
|
|
std::vector<uint_fast64_t> getTopologicalSort(storm::storage::SparseMatrix<T> const& matrix) {
|
|
if (matrix.getRowCount() != matrix.getColumnCount()) {
|
|
LOG4CPLUS_ERROR(logger, "Provided matrix is required to be square.");
|
|
throw storm::exceptions::InvalidArgumentException() << "Provided matrix is required to be square.";
|
|
}
|
|
|
|
uint_fast64_t numberOfStates = matrix.getRowCount();
|
|
|
|
// Prepare the result. This relies on the matrix being square.
|
|
std::vector<uint_fast64_t> topologicalSort;
|
|
topologicalSort.reserve(numberOfStates);
|
|
|
|
// Prepare the stacks needed for recursion.
|
|
std::vector<uint_fast64_t> recursionStack;
|
|
recursionStack.reserve(matrix.getRowCount());
|
|
std::vector<typename storm::storage::SparseMatrix<T>::const_iterator> iteratorRecursionStack;
|
|
iteratorRecursionStack.reserve(numberOfStates);
|
|
|
|
// Perform a depth-first search over the given transitions and record states in the reverse order they were visited.
|
|
storm::storage::BitVector visitedStates(numberOfStates);
|
|
for (uint_fast64_t state = 0; state < numberOfStates; ++state) {
|
|
if (!visitedStates.get(state)) {
|
|
recursionStack.push_back(state);
|
|
iteratorRecursionStack.push_back(matrix.begin(state));
|
|
|
|
recursionStepForward:
|
|
while (!recursionStack.empty()) {
|
|
uint_fast64_t currentState = recursionStack.back();
|
|
typename storm::storage::SparseMatrix<T>::const_iterator successorIterator = iteratorRecursionStack.back();
|
|
|
|
visitedStates.set(currentState, true);
|
|
|
|
recursionStepBackward:
|
|
for (; successorIterator != matrix.end(currentState); ++successorIterator) {
|
|
if (!visitedStates.get(successorIterator->getColumn())) {
|
|
// Put unvisited successor on top of our recursion stack and remember that.
|
|
recursionStack.push_back(successorIterator->getColumn());
|
|
|
|
// Also, put initial value for iterator on corresponding recursion stack.
|
|
iteratorRecursionStack.push_back(matrix.begin(successorIterator->getColumn()));
|
|
|
|
goto recursionStepForward;
|
|
}
|
|
}
|
|
|
|
topologicalSort.push_back(currentState);
|
|
|
|
// If we reach this point, we have completed the recursive descent for the current state.
|
|
// That is, we need to pop it from the recursion stacks.
|
|
recursionStack.pop_back();
|
|
iteratorRecursionStack.pop_back();
|
|
|
|
// If there is at least one state under the current one in our recursion stack, we need
|
|
// to restore the topmost state as the current state and jump to the part after the
|
|
// original recursive call.
|
|
if (recursionStack.size() > 0) {
|
|
currentState = recursionStack.back();
|
|
successorIterator = iteratorRecursionStack.back();
|
|
|
|
goto recursionStepBackward;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return topologicalSort;
|
|
}
|
|
|
|
/*!
|
|
* A class needed to compare the distances for two states in the Dijkstra search.
|
|
*/
|
|
template<typename T>
|
|
struct DistanceCompare {
|
|
bool operator()(std::pair<T, uint_fast64_t> const& lhs, std::pair<T, uint_fast64_t> const& rhs) const {
|
|
return lhs.first > rhs.first || (lhs.first == rhs.first && lhs.second > rhs.second);
|
|
}
|
|
};
|
|
|
|
/*!
|
|
* Performs a Dijkstra search from the given starting states to determine the most probable paths to all other states
|
|
* by only passing through the given state set.
|
|
*
|
|
* @param model The model whose state space is to be searched.
|
|
* @param transitions The transitions wrt to which to compute the most probable paths.
|
|
* @param startingStates The starting states of the Dijkstra search.
|
|
* @param filterStates A set of states that must not be left on any path.
|
|
*/
|
|
template <typename T>
|
|
std::pair<std::vector<T>, std::vector<uint_fast64_t>> performDijkstra(storm::models::sparse::Model<T> const& model,
|
|
storm::storage::SparseMatrix<T> const& transitions,
|
|
storm::storage::BitVector const& startingStates,
|
|
storm::storage::BitVector const* filterStates = nullptr) {
|
|
|
|
LOG4CPLUS_INFO(logger, "Performing Dijkstra search.");
|
|
|
|
const uint_fast64_t noPredecessorValue = storm::utility::zero<uint_fast64_t>();
|
|
std::vector<T> probabilities(model.getNumberOfStates(), storm::utility::zero<T>());
|
|
std::vector<uint_fast64_t> predecessors(model.getNumberOfStates(), noPredecessorValue);
|
|
|
|
// Set the probability to 1 for all starting states.
|
|
std::set<std::pair<T, uint_fast64_t>, DistanceCompare<T>> probabilityStateSet;
|
|
|
|
for (auto state : startingStates) {
|
|
probabilityStateSet.emplace(storm::utility::one<T>(), state);
|
|
probabilities[state] = storm::utility::one<T>();
|
|
}
|
|
|
|
// As long as there is one reachable state, we need to consider it.
|
|
while (!probabilityStateSet.empty()) {
|
|
// Get the state with the least distance from the set and remove it.
|
|
std::pair<T, uint_fast64_t> probabilityStatePair = *probabilityStateSet.begin();
|
|
probabilityStateSet.erase(probabilityStateSet.begin());
|
|
|
|
// Now check the new distances for all successors of the current state.
|
|
typename storm::storage::SparseMatrix<T>::Rows row = transitions.getRow(probabilityStatePair.second);
|
|
for (auto const& transition : row) {
|
|
// Only follow the transition if it lies within the filtered states.
|
|
if (filterStates != nullptr && filterStates->get(transition.first)) {
|
|
// Calculate the distance we achieve when we take the path to the successor via the current state.
|
|
T newDistance = probabilityStatePair.first * transition.second;
|
|
|
|
// We found a cheaper way to get to the target state of the transition.
|
|
if (newDistance > probabilities[transition.first]) {
|
|
// Remove the old distance.
|
|
if (probabilities[transition.first] != noPredecessorValue) {
|
|
probabilityStateSet.erase(std::make_pair(probabilities[transition.first], transition.first));
|
|
}
|
|
|
|
// Set and add the new distance.
|
|
probabilities[transition.first] = newDistance;
|
|
predecessors[transition.first] = probabilityStatePair.second;
|
|
probabilityStateSet.insert(std::make_pair(newDistance, transition.first));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Move the values into the result and return it.
|
|
std::pair<std::vector<T>, std::vector<uint_fast64_t>> result;
|
|
result.first = std::move(probabilities);
|
|
result.second = std::move(predecessors);
|
|
LOG4CPLUS_INFO(logger, "Done performing Dijkstra search.");
|
|
return result;
|
|
}
|
|
|
|
} // namespace graph
|
|
} // namespace utility
|
|
} // namespace storm
|
|
|
|
#endif /* STORM_UTILITY_GRAPH_H_ */
|