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728 lines
46 KiB
728 lines
46 KiB
/*
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* graph.h
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*
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* Created on: 28.11.2012
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* Author: Christian Dehnert
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*/
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#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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//GCC 4.7 does not support method emplace yet, therefore use boost map on Linux
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#ifdef LINUX
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#include <boost/container/set.hpp>
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#endif
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#include "src/models/AbstractDeterministicModel.h"
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#include "src/models/AbstractNondeterministicModel.h"
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#include "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 backwards breadt-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 model The model whose 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::models::AbstractDeterministicModel<T> const& model, 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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storm::storage::BitVector statesWithProbabilityGreater0(model.getNumberOfStates());
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// Get the backwards transition relation from the model to ease the search.
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storm::storage::SparseMatrix<T> backwardTransitions = model.getBackwardTransitions();
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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(model.getNumberOfStates());
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stepStack.insert(stepStack.begin(), psiStates.getNumberOfSetBits(), maximalSteps);
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remainingSteps.resize(model.getNumberOfStates());
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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 (auto predecessorIt = backwardTransitions.constColumnIteratorBegin(currentState), predecessorIte = backwardTransitions.constColumnIteratorEnd(currentState); predecessorIt != predecessorIte; ++predecessorIt) {
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if (phiStates.get(*predecessorIt) && (!statesWithProbabilityGreater0.get(*predecessorIt) || (useStepBound && remainingSteps[*predecessorIt] < 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(*predecessorIt, true);
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stack.push_back(*predecessorIt);
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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[*predecessorIt] = currentStepBound - 1;
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statesWithProbabilityGreater0.set(*predecessorIt, true);
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stack.push_back(*predecessorIt);
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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 model The model whose 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::models::AbstractDeterministicModel<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::BitVector const& statesWithProbabilityGreater0) {
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storm::storage::BitVector statesWithProbability1 = performProbGreater0(model, ~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 model The model whose 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::models::AbstractDeterministicModel<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
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storm::storage::BitVector statesWithProbabilityGreater0 = performProbGreater0(model, phiStates, psiStates);
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storm::storage::BitVector statesWithProbability1 = performProbGreater0(model, ~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::AbstractDeterministicModel<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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result.first = performProbGreater0(model, phiStates, psiStates);
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result.second = performProb1(model, 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 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 (auto predecessorIt = backwardTransitions.constColumnIteratorBegin(currentState), predecessorIte = backwardTransitions.constColumnIteratorEnd(currentState); predecessorIt != predecessorIte; ++predecessorIt) {
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if (phiStates.get(*predecessorIt) && (!statesWithProbabilityGreater0.get(*predecessorIt) || (useStepBound && remainingSteps[*predecessorIt] < 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(*predecessorIt, true);
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stack.push_back(*predecessorIt);
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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[*predecessorIt] = currentStepBound - 1;
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statesWithProbabilityGreater0.set(*predecessorIt, true);
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stack.push_back(*predecessorIt);
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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::AbstractNondeterministicModel<T> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
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return performProb0A(model.getTransitionMatrix(), model.getNondeterministicChoiceIndices(), backwardTransitions, phiStates, psiStates);
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}
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/*!
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* Computes the sets of states that have probability 1 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 probability 1 of satisfying phi until psi 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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* @return A bit vector that represents all states with probability 1.
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*/
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template <typename T>
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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) {
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size_t numberOfStates = phiStates.size();
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// Initialize the environment for the iterative algorithm.
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storm::storage::BitVector currentStates(numberOfStates, true);
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std::vector<uint_fast64_t> stack;
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stack.reserve(numberOfStates);
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// Perform the loop as long as the set of states gets larger.
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bool done = false;
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uint_fast64_t currentState;
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while (!done) {
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stack.clear();
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storm::storage::BitVector nextStates(psiStates);
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stack.insert(stack.end(), psiStates.begin(), psiStates.end());
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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 predecessorIt = backwardTransitions.constColumnIteratorBegin(currentState), predecessorIte = backwardTransitions.constColumnIteratorEnd(currentState); predecessorIt != predecessorIte; ++predecessorIt) {
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if (phiStates.get(*predecessorIt) && !nextStates.get(*predecessorIt)) {
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// Check whether the predecessor has only successors in the current state set for one of the
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// nondeterminstic choices.
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for (auto row = nondeterministicChoiceIndices[*predecessorIt]; row < nondeterministicChoiceIndices[*predecessorIt + 1]; ++row) {
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bool allSuccessorsInCurrentStates = true;
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for (auto targetIt = transitionMatrix.constColumnIteratorBegin(row), targetIte = transitionMatrix.constColumnIteratorEnd(row); targetIt != targetIte; ++targetIt) {
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if (!currentStates.get(*targetIt)) {
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allSuccessorsInCurrentStates = false;
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break;
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}
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}
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// If all successors for a given nondeterministic choice are in the current state set, we
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// add it to the set of states for the next iteration and perform a backward search from
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// that state.
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if (allSuccessorsInCurrentStates) {
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nextStates.set(*predecessorIt, true);
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stack.push_back(*predecessorIt);
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break;
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}
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}
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}
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}
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}
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// Check whether we need to perform an additional iteration.
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if (currentStates == nextStates) {
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done = true;
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} else {
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currentStates = std::move(nextStates);
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}
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}
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return currentStates;
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}
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template <typename T>
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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) {
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std::pair<storm::storage::BitVector, storm::storage::BitVector> result;
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result.first = performProb0A(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
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result.second = performProb1E(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
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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
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* until psi in a non-deterministic model in which all non-deterministic choices are resolved
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* such that the probability is maximized.
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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 that represent all states with probability 0 and 1, respectively.
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*/
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template <typename T>
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std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::models::AbstractNondeterministicModel<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
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return performProb01Max(model.getTransitionMatrix(), model.getNondeterministicChoiceIndices(), model.getBackwardTransitions(), phiStates, psiStates);
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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 any
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* 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 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 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) {
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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(auto predecessorIt = backwardTransitions.constColumnIteratorBegin(currentState), predecessorIte = backwardTransitions.constColumnIteratorEnd(currentState); predecessorIt != predecessorIte; ++predecessorIt) {
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if (phiStates.get(*predecessorIt) && (!statesWithProbabilityGreater0.get(*predecessorIt) || (useStepBound && remainingSteps[*predecessorIt] < currentStepBound - 1))) {
|
|
// Check whether the predecessor has at least one successor in the current state set for every
|
|
// nondeterministic choice.
|
|
bool addToStatesWithProbabilityGreater0 = true;
|
|
for (auto row = nondeterministicChoiceIndices[*predecessorIt]; row < nondeterministicChoiceIndices[*predecessorIt + 1]; ++row) {
|
|
bool hasAtLeastOneSuccessorWithProbabilityGreater0 = false;
|
|
for (auto successorIt = transitionMatrix.constColumnIteratorBegin(row), successorIte = transitionMatrix.constColumnIteratorEnd(row); successorIt != successorIte; ++successorIt) {
|
|
if (statesWithProbabilityGreater0.get(*successorIt)) {
|
|
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(*predecessorIt, true);
|
|
stack.push_back(*predecessorIt);
|
|
} 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[*predecessorIt] = currentStepBound - 1;
|
|
statesWithProbabilityGreater0.set(*predecessorIt, true);
|
|
stack.push_back(*predecessorIt);
|
|
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::AbstractNondeterministicModel<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(auto predecessorIt = backwardTransitions.constColumnIteratorBegin(currentState), predecessorIte = backwardTransitions.constColumnIteratorEnd(currentState); predecessorIt != predecessorIte; ++predecessorIt) {
|
|
if (phiStates.get(*predecessorIt) && !nextStates.get(*predecessorIt)) {
|
|
// Check whether the predecessor has only successors in the current state set for all of the
|
|
// nondeterminstic choices.
|
|
bool allSuccessorsInCurrentStatesForAllChoices = true;
|
|
for (auto row = nondeterministicChoiceIndices[*predecessorIt]; row < nondeterministicChoiceIndices[*predecessorIt + 1]; ++row) {
|
|
for (auto successorIt = transitionMatrix.constColumnIteratorBegin(row), successorIte = transitionMatrix.constColumnIteratorEnd(row); successorIt != successorIte; ++successorIt) {
|
|
if (!currentStates.get(*successorIt)) {
|
|
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(*predecessorIt, true);
|
|
stack.push_back(*predecessorIt);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// 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::AbstractNondeterministicModel<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
return performProb01Min(model.getTransitionMatrix(), model.getNondeterministicChoiceIndices(), model.getBackwardTransitions(), phiStates, psiStates);
|
|
}
|
|
|
|
/*!
|
|
* 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>::ConstIndexIterator> 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.constColumnIteratorBegin(state));
|
|
|
|
recursionStepForward:
|
|
while (!recursionStack.empty()) {
|
|
uint_fast64_t currentState = recursionStack.back();
|
|
typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = iteratorRecursionStack.back();
|
|
|
|
visitedStates.set(currentState, true);
|
|
|
|
recursionStepBackward:
|
|
for (; successorIt != matrix.constColumnIteratorEnd(currentState); ++successorIt) {
|
|
if (!visitedStates.get(*successorIt)) {
|
|
// Put unvisited successor on top of our recursion stack and remember that.
|
|
recursionStack.push_back(*successorIt);
|
|
|
|
// Save current iterator position so we can continue where we left off later.
|
|
iteratorRecursionStack.pop_back();
|
|
iteratorRecursionStack.push_back(successorIt + 1);
|
|
|
|
// Also, put initial value for iterator on corresponding recursion stack.
|
|
iteratorRecursionStack.push_back(matrix.constColumnIteratorBegin(*successorIt));
|
|
|
|
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();
|
|
successorIt = 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::AbstractModel<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::constantZero<uint_fast64_t>();
|
|
std::vector<T> probabilities(model.getNumberOfStates(), storm::utility::constantZero<T>());
|
|
std::vector<uint_fast64_t> predecessors(model.getNumberOfStates(), noPredecessorValue);
|
|
|
|
// Set the probability to 1 for all starting states.
|
|
#ifdef LINUX
|
|
boost::container::set<std::pair<T, uint_fast64_t>, DistanceCompare<T>> probabilityStateSet;
|
|
#else
|
|
std::set<std::pair<T, uint_fast64_t>, DistanceCompare<T>> probabilityStateSet;
|
|
#endif
|
|
for (auto state : startingStates) {
|
|
probabilityStateSet.emplace(storm::utility::constantOne<T>(), state);
|
|
probabilities[state] = storm::utility::constantOne<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.getRows(probabilityStatePair.second, probabilityStatePair.second);
|
|
for (auto& transition : row) {
|
|
// Only follow the transition if it lies within the filtered states.
|
|
if (filterStates != nullptr && filterStates->get(transition.column())) {
|
|
// Calculate the distance we achieve when we take the path to the successor via the current state.
|
|
T newDistance = probabilityStatePair.first * transition.value();
|
|
|
|
// We found a cheaper way to get to the target state of the transition.
|
|
if (newDistance > probabilities[transition.column()]) {
|
|
// Remove the old distance.
|
|
if (probabilities[transition.column()] != noPredecessorValue) {
|
|
probabilityStateSet.erase(std::make_pair(probabilities[transition.column()], transition.column()));
|
|
}
|
|
|
|
// Set and add the new distance.
|
|
probabilities[transition.column()] = newDistance;
|
|
predecessors[transition.column()] = probabilityStatePair.second;
|
|
probabilityStateSet.insert(std::make_pair(newDistance, transition.column()));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// 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_ */
|