#include "graph.h"
#include "utility/OsDetection.h"
#include "storm-config.h"
#include "storm/adapters/RationalFunctionAdapter.h"
#include "storm/storage/sparse/StateType.h"
#include "storm/storage/dd/Bdd.h"
#include "storm/storage/dd/Add.h"
#include "storm/storage/dd/DdManager.h"
#include "storm/storage/StronglyConnectedComponentDecomposition.h"
#include "storm/models/symbolic/DeterministicModel.h"
#include "storm/models/symbolic/NondeterministicModel.h"
#include "storm/models/symbolic/StandardRewardModel.h"
#include "storm/models/symbolic/StochasticTwoPlayerGame.h"
#include "storm/models/sparse/DeterministicModel.h"
#include "storm/models/sparse/NondeterministicModel.h"
#include "storm/models/sparse/StandardRewardModel.h"
#include "storm/utility/constants.h"
#include "storm/utility/macros.h"
#include "storm/exceptions/InvalidArgumentException.h"
#include <queue>
namespace storm {
namespace utility {
namespace graph {
template<typename T>
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, bool useStepBound, uint_fast64_t maximalSteps) {
storm::storage::BitVector reachableStates(initialStates);
uint_fast64_t numberOfStates = transitionMatrix.getRowGroupCount();
// Initialize the stack used for the DFS with the states.
std::vector<uint_fast64_t> stack(initialStates.begin(), initialStates.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(), initialStates.getNumberOfSetBits(), maximalSteps);
remainingSteps.resize(numberOfStates);
for (auto state : initialStates) {
remainingSteps[state] = maximalSteps;
}
}
// Perform the actual DFS.
uint_fast64_t currentState = 0, currentStepBound = 0;
while (!stack.empty()) {
currentState = stack.back();
stack.pop_back();
if (useStepBound) {
currentStepBound = stepStack.back();
stepStack.pop_back();
if (currentStepBound == 0) {
continue;
}
}
for (auto const& successor : transitionMatrix.getRowGroup(currentState)) {
// Only explore the state if the transition was actually there and the successor has not yet
// been visited.
if (!storm::utility::isZero(successor.getValue()) && (!reachableStates.get(successor.getColumn()) || (useStepBound && remainingSteps[successor.getColumn()] < currentStepBound - 1))) {
// If the successor is one of the target states, we need to include it, but must not explore
// it further.
if (targetStates.get(successor.getColumn())) {
reachableStates.set(successor.getColumn());
} else if (constraintStates.get(successor.getColumn())) {
// However, if the state is in the constrained set of states, we potentially need to follow it.
if (useStepBound) {
// As there is at least one more step to go, we need to push the state and the new number of steps.
remainingSteps[successor.getColumn()] = currentStepBound - 1;
stepStack.push_back(currentStepBound - 1);
}
reachableStates.set(successor.getColumn());
stack.push_back(successor.getColumn());
}
}
}
}
return reachableStates;
}
template<typename T>
storm::storage::BitVector getBsccCover(storm::storage::SparseMatrix<T> const& transitionMatrix) {
storm::storage::BitVector result(transitionMatrix.getRowGroupCount());
storm::storage::StronglyConnectedComponentDecomposition<T> decomposition(transitionMatrix, false, true);
// Take the first state out of each BSCC.
for (auto const& scc : decomposition) {
result.set(*scc.begin());
}
return result;
}
template <typename T>
bool checkIfECWithChoiceExists(storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& subsystem, storm::storage::BitVector const& choices) {
STORM_LOG_THROW(subsystem.size() == transitionMatrix.getRowGroupCount(), storm::exceptions::InvalidArgumentException, "Invalid size of subsystem");
STORM_LOG_THROW(choices.size() == transitionMatrix.getRowCount(), storm::exceptions::InvalidArgumentException, "Invalid size of choice vector");
if (subsystem.empty() || choices.empty()) {
return false;
}
storm::storage::BitVector statesWithChoice(transitionMatrix.getRowGroupCount(), false);
uint_fast64_t state = 0;
for (auto const& choice : choices) {
// Get the correct state
while (choice >= transitionMatrix.getRowGroupIndices()[state + 1]) {
++state;
}
assert(choice >= transitionMatrix.getRowGroupIndices()[state]);
// make sure that the choice originates from the subsystem and also stays within the subsystem
if (subsystem.get(state)) {
bool choiceStaysInSubsys = true;
for (auto const& entry : transitionMatrix.getRow(choice)) {
if (!subsystem.get(entry.getColumn())) {
choiceStaysInSubsys = false;
break;
}
}
if (choiceStaysInSubsys) {
statesWithChoice.set(state, true);
}
}
}
// Initialize candidate states that satisfy some necessary conditions for being part of an EC with a specified choice:
// Get the states for which a policy can enforce that a choice is reached while staying inside the subsystem
storm::storage::BitVector candidateStates = storm::utility::graph::performProb1E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, subsystem, statesWithChoice);
// Only keep the states that can stay in the set of candidates forever
candidateStates = storm::utility::graph::performProb0E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, candidateStates, ~candidateStates);
// Only keep the states that can be reached after performing one of the specified choices
statesWithChoice &= candidateStates;
storm::storage::BitVector choiceTargets(transitionMatrix.getRowGroupCount(), false);
for (auto const& state : statesWithChoice) {
for (uint_fast64_t choice = choices.getNextSetIndex(transitionMatrix.getRowGroupIndices()[state]); choice < transitionMatrix.getRowGroupIndices()[state + 1]; choice = choices.getNextSetIndex(choice + 1)) {
bool choiceStaysInCandidateSet = true;
for (auto const& entry : transitionMatrix.getRow(choice)) {
if (!candidateStates.get(entry.getColumn())) {
choiceStaysInCandidateSet = false;
break;
}
}
if (choiceStaysInCandidateSet) {
for (auto const& entry : transitionMatrix.getRow(choice)) {
choiceTargets.set(entry.getColumn(), true);
}
}
}
}
candidateStates = storm::utility::graph::getReachableStates(transitionMatrix, choiceTargets, candidateStates, storm::storage::BitVector(candidateStates.size(), false));
// At this point we know that every candidate state can reach a state with a choice without leaving the set of candidate states.
// We now compute the states that can reach a choice at least twice, three times, four times, ... until a fixpoint is reached.
while (!candidateStates.empty()) {
// Update the states with a choice that stays within the set of candidates
statesWithChoice &= candidateStates;
for (auto const& state : statesWithChoice) {
bool stateHasChoice = false;
for (uint_fast64_t choice = choices.getNextSetIndex(transitionMatrix.getRowGroupIndices()[state]); choice < transitionMatrix.getRowGroupIndices()[state + 1]; choice = choices.getNextSetIndex(choice + 1)) {
bool choiceStaysInCandidateSet = true;
for (auto const& entry : transitionMatrix.getRow(choice)) {
if (!candidateStates.get(entry.getColumn())) {
choiceStaysInCandidateSet = false;
break;
}
}
if (choiceStaysInCandidateSet) {
stateHasChoice = true;
break;
}
}
if (!stateHasChoice) {
statesWithChoice.set(state, false);
}
}
// Update the candidates
storm::storage::BitVector newCandidates = storm::utility::graph::performProb1E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, candidateStates, statesWithChoice);
// Check if converged
if (newCandidates == candidateStates) {
assert(!candidateStates.empty());
return true;
}
candidateStates = std::move(newCandidates);
}
return false;
}
template<typename T>
std::vector<uint_fast64_t> getDistances(storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::BitVector const& initialStates, boost::optional<storm::storage::BitVector> const& subsystem) {
std::vector<uint_fast64_t> distances(transitionMatrix.getRowGroupCount());
std::vector<std::pair<storm::storage::sparse::state_type, uint_fast64_t>> stateQueue;
stateQueue.reserve(transitionMatrix.getRowGroupCount());
storm::storage::BitVector statesInQueue(transitionMatrix.getRowGroupCount());
storm::storage::sparse::state_type currentPosition = 0;
for (auto const& initialState : initialStates) {
stateQueue.emplace_back(initialState, 0);
statesInQueue.set(initialState);
}
// Perform a BFS.
while (currentPosition < stateQueue.size()) {
std::pair<storm::storage::sparse::state_type, std::size_t> const& stateDistancePair = stateQueue[currentPosition];
distances[stateDistancePair.first] = stateDistancePair.second;
for (auto const& successorEntry : transitionMatrix.getRowGroup(stateDistancePair.first)) {
if (!statesInQueue.get(successorEntry.getColumn())) {
if (!subsystem || subsystem.get()[successorEntry.getColumn()]) {
stateQueue.emplace_back(successorEntry.getColumn(), stateDistancePair.second + 1);
statesInQueue.set(successorEntry.getColumn());
}
}
}
++currentPosition;
}
return distances;
}
template <typename T>
storm::storage::BitVector performProbGreater0(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound, uint_fast64_t maximalSteps) {
// Prepare the resulting bit vector.
uint_fast64_t numberOfStates = phiStates.size();
storm::storage::BitVector statesWithProbabilityGreater0(numberOfStates);
// Add all psi states as they 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();
if(currentStepBound == 0) {
continue;
}
}
for (typename storm::storage::SparseMatrix<T>::const_iterator entryIt = backwardTransitions.begin(currentState), entryIte = backwardTransitions.end(currentState); entryIt != entryIte; ++entryIt) {
if (phiStates[entryIt->getColumn()] && (!statesWithProbabilityGreater0.get(entryIt->getColumn()) || (useStepBound && remainingSteps[entryIt->getColumn()] < currentStepBound - 1))) {
statesWithProbabilityGreater0.set(entryIt->getColumn(), true);
// If we don't have a bound on the number of steps to take, just add the state to the stack.
if (useStepBound) {
// As there is at least one more step to go, we need to push the state and the new number of steps.
remainingSteps[entryIt->getColumn()] = currentStepBound - 1;
stepStack.push_back(currentStepBound - 1);
}
stack.push_back(entryIt->getColumn());
}
}
}
// Return result.
return statesWithProbabilityGreater0;
}
template <typename T>
storm::storage::BitVector performProb1(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const&, storm::storage::BitVector const& psiStates, storm::storage::BitVector const& statesWithProbabilityGreater0) {
storm::storage::BitVector statesWithProbability1 = performProbGreater0(backwardTransitions, ~psiStates, ~statesWithProbabilityGreater0);
statesWithProbability1.complement();
return statesWithProbability1;
}
template <typename T>
storm::storage::BitVector performProb1(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
storm::storage::BitVector statesWithProbabilityGreater0 = performProbGreater0(backwardTransitions, phiStates, psiStates);
storm::storage::BitVector statesWithProbability1 = performProbGreater0(backwardTransitions, ~psiStates, ~(statesWithProbabilityGreater0));
statesWithProbability1.complement();
return statesWithProbability1;
}
template <typename T>
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) {
std::pair<storm::storage::BitVector, storm::storage::BitVector> result;
storm::storage::SparseMatrix<T> backwardTransitions = model.getBackwardTransitions();
result.first = performProbGreater0(backwardTransitions, phiStates, psiStates);
result.second = performProb1(backwardTransitions, phiStates, psiStates, result.first);
result.first.complement();
return result;
}
template <typename T>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(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 = performProbGreater0(backwardTransitions, phiStates, psiStates);
result.second = performProb1(backwardTransitions, phiStates, psiStates, result.first);
result.first.complement();
return result;
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProbGreater0(storm::models::symbolic::Model<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, boost::optional<uint_fast64_t> const& stepBound) {
// Initialize environment for backward search.
storm::dd::DdManager<Type> const& manager = model.getManager();
storm::dd::Bdd<Type> lastIterationStates = manager.getBddZero();
storm::dd::Bdd<Type> statesWithProbabilityGreater0 = psiStates;
uint_fast64_t iterations = 0;
while (lastIterationStates != statesWithProbabilityGreater0) {
if (stepBound && iterations >= stepBound.get()) {
break;
}
lastIterationStates = statesWithProbabilityGreater0;
statesWithProbabilityGreater0 = statesWithProbabilityGreater0.inverseRelationalProduct(transitionMatrix, model.getRowVariables(), model.getColumnVariables());
statesWithProbabilityGreater0 &= phiStates;
statesWithProbabilityGreater0 |= lastIterationStates;
++iterations;
}
return statesWithProbabilityGreater0;
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProb1(storm::models::symbolic::Model<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const&, storm::dd::Bdd<Type> const& psiStates, storm::dd::Bdd<Type> const& statesWithProbabilityGreater0) {
storm::dd::Bdd<Type> statesWithProbability1 = performProbGreater0(model, transitionMatrix, !psiStates && model.getReachableStates(), !statesWithProbabilityGreater0 && model.getReachableStates());
statesWithProbability1 = !statesWithProbability1 && model.getReachableStates();
return statesWithProbability1;
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProb1(storm::models::symbolic::Model<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
storm::dd::Bdd<Type> statesWithProbabilityGreater0 = performProbGreater0(model, transitionMatrix, phiStates, psiStates);
return performProb1(model, transitionMatrix, phiStates, psiStates, statesWithProbabilityGreater0);
}
template <storm::dd::DdType Type, typename ValueType>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01(storm::models::symbolic::DeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> result;
storm::dd::Bdd<Type> transitionMatrix = model.getTransitionMatrix().notZero();
result.first = performProbGreater0(model, transitionMatrix, phiStates, psiStates);
result.second = !performProbGreater0(model, transitionMatrix, !psiStates && model.getReachableStates(), !result.first && model.getReachableStates()) && model.getReachableStates();
result.first = !result.first && model.getReachableStates();
return result;
}
template <storm::dd::DdType Type, typename ValueType>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01(storm::models::symbolic::Model<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> result;
result.first = performProbGreater0(model, transitionMatrix, phiStates, psiStates);
result.second = !performProbGreater0(model, transitionMatrix, !psiStates && model.getReachableStates(), !result.first && model.getReachableStates()) && model.getReachableStates();
result.first = !result.first && model.getReachableStates();
return result;
}
template <typename T>
void computeSchedulerStayingInStates(storm::storage::BitVector const& states, storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::Scheduler<T>& scheduler) {
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
for (auto const& state : states) {
for (uint_fast64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice) {
bool allSuccessorsInStates = true;
for (auto const& element : transitionMatrix.getRow(choice)) {
if (!states.get(element.getColumn())) {
allSuccessorsInStates = false;
break;
}
}
if (allSuccessorsInStates) {
for (uint_fast64_t memState = 0; memState < scheduler.getNumberOfMemoryStates(); ++memState) {
scheduler.setChoice(choice - nondeterministicChoiceIndices[state], state, memState);
}
break;
}
}
}
}
template <typename T>
void computeSchedulerWithOneSuccessorInStates(storm::storage::BitVector const& states, storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::Scheduler<T>& scheduler) {
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
for (auto const& state : states) {
for (uint_fast64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice) {
bool oneSuccessorInStates = false;
for (auto const& element : transitionMatrix.getRow(choice)) {
if (states.get(element.getColumn())) {
oneSuccessorInStates = true;
break;
}
}
if (oneSuccessorInStates) {
for (uint_fast64_t memState = 0; memState < scheduler.getNumberOfMemoryStates(); ++memState) {
scheduler.setChoice(choice - nondeterministicChoiceIndices[state], state, memState);
}
break;
}
}
}
}
template <typename T>
void computeSchedulerProbGreater0E(storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::Scheduler<T>& scheduler, boost::optional<storm::storage::BitVector> const& rowFilter) {
//Perform backwards DFS from psiStates and find a valid choice for each visited state.
std::vector<uint_fast64_t> stack;
storm::storage::BitVector currentStates(psiStates); //the states that are either psiStates or for which we have found a valid choice.
stack.insert(stack.end(), currentStates.begin(), currentStates.end());
uint_fast64_t currentState = 0;
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) {
uint_fast64_t const& predecessor = predecessorEntryIt->getColumn();
if (phiStates.get(predecessor) && !currentStates.get(predecessor)) {
//The predecessor is a probGreater0E state that has not been considered yet. Let's find the right choice that leads to a state in currentStates.
bool foundValidChoice = false;
for (uint_fast64_t row = transitionMatrix.getRowGroupIndices()[predecessor]; row < transitionMatrix.getRowGroupIndices()[predecessor + 1]; ++row) {
if(rowFilter && !rowFilter->get(row)){
continue;
}
for (typename storm::storage::SparseMatrix<T>::const_iterator successorEntryIt = transitionMatrix.begin(row), successorEntryIte = transitionMatrix.end(row); successorEntryIt != successorEntryIte; ++successorEntryIt) {
if(currentStates.get(successorEntryIt->getColumn())){
foundValidChoice = true;
break;
}
}
if(foundValidChoice){
for (uint_fast64_t memState = 0; memState < scheduler.getNumberOfMemoryStates(); ++memState) {
scheduler.setChoice(row - transitionMatrix.getRowGroupIndices()[predecessor], predecessor, memState);
}
currentStates.set(predecessor, true);
stack.push_back(predecessor);
break;
}
}
STORM_LOG_INFO_COND(foundValidChoice, "Could not find a valid choice for ProbGreater0E state " << predecessor << ".");
}
}
}
}
template <typename T>
void computeSchedulerProb0E(storm::storage::BitVector const& prob0EStates, storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::Scheduler<T>& scheduler) {
computeSchedulerStayingInStates(prob0EStates, transitionMatrix, scheduler);
}
template <typename T>
void computeSchedulerProb1E(storm::storage::BitVector const& prob1EStates, storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::Scheduler<T>& scheduler) {
// set an arbitrary choice for the psi states.
for (auto const& psiState : psiStates) {
for (uint_fast64_t memState = 0; memState < scheduler.getNumberOfMemoryStates(); ++memState) {
scheduler.setChoice(0, psiState, memState);
}
}
// Now perform a backwards search from the psi states and store choices with prob. 1
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
std::vector<uint_fast64_t> stack;
storm::storage::BitVector currentStates(psiStates);
stack.insert(stack.end(), currentStates.begin(), currentStates.end());
uint_fast64_t currentState = 0;
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()) && !currentStates.get(predecessorEntryIt->getColumn())) {
// Check whether the predecessor has only successors in the prob1E state set for one of the
// nondeterminstic choices.
for (uint_fast64_t row = nondeterministicChoiceIndices[predecessorEntryIt->getColumn()]; row < nondeterministicChoiceIndices[predecessorEntryIt->getColumn() + 1]; ++row) {
bool allSuccessorsInProb1EStates = true;
bool hasSuccessorInCurrentStates = false;
for (typename storm::storage::SparseMatrix<T>::const_iterator successorEntryIt = transitionMatrix.begin(row), successorEntryIte = transitionMatrix.end(row); successorEntryIt != successorEntryIte; ++successorEntryIt) {
if (!prob1EStates.get(successorEntryIt->getColumn())) {
allSuccessorsInProb1EStates = false;
break;
} else if (currentStates.get(successorEntryIt->getColumn())) {
hasSuccessorInCurrentStates = true;
}
}
// If all successors for a given nondeterministic choice are in the prob1E state set, we
// perform a backward search from that state.
if (allSuccessorsInProb1EStates && hasSuccessorInCurrentStates) {
for (uint_fast64_t memState = 0; memState < scheduler.getNumberOfMemoryStates(); ++memState) {
scheduler.setChoice(row - nondeterministicChoiceIndices[predecessorEntryIt->getColumn()], predecessorEntryIt->getColumn(), memState);
}
currentStates.set(predecessorEntryIt->getColumn(), true);
stack.push_back(predecessorEntryIt->getColumn());
break;
}
}
}
}
}
}
template <typename T>
storm::storage::BitVector performProbGreater0E(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound, uint_fast64_t maximalSteps) {
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();
if (currentStepBound == 0) {
continue;
}
}
for (typename storm::storage::SparseMatrix<T>::const_iterator entryIt = backwardTransitions.begin(currentState), entryIte = backwardTransitions.end(currentState); entryIt != entryIte; ++entryIt) {
if (phiStates.get(entryIt->getColumn()) && (!statesWithProbabilityGreater0.get(entryIt->getColumn()) || (useStepBound && remainingSteps[entryIt->getColumn()] < currentStepBound - 1))) {
// If we don't have a bound on the number of steps to take, just add the state to the stack.
if (useStepBound) {
// If there is at least one more step to go, we need to push the state and the new number of steps.
remainingSteps[entryIt->getColumn()] = currentStepBound - 1;
stepStack.push_back(currentStepBound - 1);
}
statesWithProbabilityGreater0.set(entryIt->getColumn(), true);
stack.push_back(entryIt->getColumn());
}
}
}
return statesWithProbabilityGreater0;
}
template <typename T>
storm::storage::BitVector performProb0A(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
storm::storage::BitVector statesWithProbability0 = performProbGreater0E(backwardTransitions, phiStates, psiStates);
statesWithProbability0.complement();
return statesWithProbability0;
}
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;
bool hasNextStateSuccessor = false;
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;
} else if (nextStates.get(successorEntryIt->getColumn())) {
hasNextStateSuccessor = true;
}
}
// 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 && hasNextStateSuccessor) {
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, typename RM>
storm::storage::BitVector performProb1E(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
return performProb1E(model.getTransitionMatrix(), model.getNondeterministicChoiceIndices(), backwardTransitions, phiStates, psiStates);
}
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(backwardTransitions, phiStates, psiStates);
result.second = performProb1E(transitionMatrix, nondeterministicChoiceIndices, backwardTransitions, phiStates, psiStates);
return result;
}
template <typename T, typename RM>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
return performProb01Max(model.getTransitionMatrix(), model.getTransitionMatrix().getRowGroupIndices(), model.getBackwardTransitions(), phiStates, psiStates);
}
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, uint_fast64_t maximalSteps, boost::optional<storm::storage::BitVector> const& choiceConstraint) {
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();
if (currentStepBound == 0) {
continue;
}
}
for(typename storm::storage::SparseMatrix<T>::const_iterator predecessorEntryIt = backwardTransitions.begin(currentState), predecessorEntryIte = backwardTransitions.end(currentState); predecessorEntryIt != predecessorEntryIte; ++predecessorEntryIt) {
if (phiStates.get(predecessorEntryIt->getColumn())) {
if (!statesWithProbabilityGreater0.get(predecessorEntryIt->getColumn())) {
// Check whether the predecessor has at least one successor in the current state set for every
// nondeterministic choice within the possibly given choiceConstraint.
// Note: The backwards edge might be induced by a choice that violates the choiceConstraint.
// However this is not problematic as long as there is at least one enabled choice for the predecessor.
uint_fast64_t row = nondeterministicChoiceIndices[predecessorEntryIt->getColumn()];
uint_fast64_t const& endOfGroup = nondeterministicChoiceIndices[predecessorEntryIt->getColumn() + 1];
if (!choiceConstraint || choiceConstraint->getNextSetIndex(row) < endOfGroup) {
bool addToStatesWithProbabilityGreater0 = true;
for (; row < endOfGroup; ++row) {
if (!choiceConstraint || choiceConstraint->get(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) {
// 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;
stepStack.push_back(currentStepBound - 1);
}
statesWithProbabilityGreater0.set(predecessorEntryIt->getColumn(), true);
stack.push_back(predecessorEntryIt->getColumn());
}
}
} else if (useStepBound && remainingSteps[predecessorEntryIt->getColumn()] < currentStepBound - 1) {
// We have found a shorter path to the predecessor. Hence, we need to explore it again.
// If there is a choiceConstraint, we still need to check whether the backwards edge was induced by a valid action
bool predecessorIsValid = true;
if (choiceConstraint) {
predecessorIsValid = false;
uint_fast64_t row = choiceConstraint->getNextSetIndex(nondeterministicChoiceIndices[predecessorEntryIt->getColumn()]);
uint_fast64_t const& endOfGroup = nondeterministicChoiceIndices[predecessorEntryIt->getColumn() + 1];
for (; row < endOfGroup && !predecessorIsValid; row = choiceConstraint->getNextSetIndex(row + 1)) {
for (auto const& entry : transitionMatrix.getRow(row)) {
if (entry.getColumn() == currentState) {
predecessorIsValid = true;
break;
}
}
}
}
if (predecessorIsValid) {
remainingSteps[predecessorEntryIt->getColumn()] = currentStepBound - 1;
stepStack.push_back(currentStepBound - 1);
stack.push_back(predecessorEntryIt->getColumn());
}
}
}
}
}
return statesWithProbabilityGreater0;
}
template <typename T, typename RM>
storm::storage::BitVector performProb0E(storm::models::sparse::NondeterministicModel<T, RM> 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;
}
template<typename T, typename RM>
storm::storage::BitVector performProb1A(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
return performProb1A(model.getTransitionMatrix(), model.getNondeterministicChoiceIndices(), backwardTransitions, phiStates, psiStates);
}
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 and that for each choice there exists a successor that is already
// in the next states.
bool addToStatesWithProbability1 = true;
for (uint_fast64_t row = nondeterministicChoiceIndices[predecessorEntryIt->getColumn()]; row < nondeterministicChoiceIndices[predecessorEntryIt->getColumn() + 1]; ++row) {
bool hasAtLeastOneSuccessorWithProbability1 = false;
for (typename storm::storage::SparseMatrix<T>::const_iterator successorEntryIt = transitionMatrix.begin(row), successorEntryIte = transitionMatrix.end(row); successorEntryIt != successorEntryIte; ++successorEntryIt) {
if (!currentStates.get(successorEntryIt->getColumn())) {
addToStatesWithProbability1 = false;
goto afterCheckLoop;
}
if (nextStates.get(successorEntryIt->getColumn())) {
hasAtLeastOneSuccessorWithProbability1 = true;
}
}
if (!hasAtLeastOneSuccessorWithProbability1) {
addToStatesWithProbability1 = false;
break;
}
}
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 (addToStatesWithProbability1) {
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;
}
template <typename T, typename RM>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
return performProb01Min(model.getTransitionMatrix(), model.getTransitionMatrix().getRowGroupIndices(), model.getBackwardTransitions(), phiStates, psiStates);
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> computeSchedulerProbGreater0E(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
// Initialize environment for backward search.
storm::dd::DdManager<Type> const& manager = model.getManager();
storm::dd::Bdd<Type> statesWithProbabilityGreater0E = manager.getBddZero();
storm::dd::Bdd<Type> frontier = psiStates;
storm::dd::Bdd<Type> scheduler = manager.getBddZero();
uint_fast64_t iterations = 0;
while (!frontier.isZero()) {
storm::dd::Bdd<Type> statesAndChoicesWithProbabilityGreater0E = frontier.inverseRelationalProductWithExtendedRelation(transitionMatrix, model.getRowVariables(), model.getColumnVariables());
frontier = phiStates && statesAndChoicesWithProbabilityGreater0E.existsAbstract(model.getNondeterminismVariables()) && !statesWithProbabilityGreater0E;
scheduler = scheduler || (frontier && statesAndChoicesWithProbabilityGreater0E).existsAbstractRepresentative(model.getNondeterminismVariables());
statesWithProbabilityGreater0E |= frontier;
++iterations;
}
return scheduler;
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProbGreater0E(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
// Initialize environment for backward search.
storm::dd::DdManager<Type> const& manager = model.getManager();
storm::dd::Bdd<Type> lastIterationStates = manager.getBddZero();
storm::dd::Bdd<Type> statesWithProbabilityGreater0E = psiStates;
uint_fast64_t iterations = 0;
storm::dd::Bdd<Type> abstractedTransitionMatrix = transitionMatrix.existsAbstract(model.getNondeterminismVariables());
while (lastIterationStates != statesWithProbabilityGreater0E) {
lastIterationStates = statesWithProbabilityGreater0E;
statesWithProbabilityGreater0E = statesWithProbabilityGreater0E.inverseRelationalProduct(abstractedTransitionMatrix, model.getRowVariables(), model.getColumnVariables());
statesWithProbabilityGreater0E &= phiStates;
statesWithProbabilityGreater0E |= lastIterationStates;
++iterations;
}
return statesWithProbabilityGreater0E;
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProb0A(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
return !performProbGreater0E(model, transitionMatrix, phiStates, psiStates) && model.getReachableStates();
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProbGreater0A(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
// Initialize environment for backward search.
storm::dd::DdManager<Type> const& manager = model.getManager();
storm::dd::Bdd<Type> lastIterationStates = manager.getBddZero();
storm::dd::Bdd<Type> statesWithProbabilityGreater0A = psiStates;
uint_fast64_t iterations = 0;
while (lastIterationStates != statesWithProbabilityGreater0A) {
lastIterationStates = statesWithProbabilityGreater0A;
statesWithProbabilityGreater0A = statesWithProbabilityGreater0A.inverseRelationalProductWithExtendedRelation(transitionMatrix, model.getRowVariables(), model.getColumnVariables());
statesWithProbabilityGreater0A |= model.getIllegalMask();
statesWithProbabilityGreater0A = statesWithProbabilityGreater0A.universalAbstract(model.getNondeterminismVariables());
statesWithProbabilityGreater0A &= phiStates;
statesWithProbabilityGreater0A |= psiStates;
++iterations;
}
return statesWithProbabilityGreater0A;
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProb0E(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
return !performProbGreater0A(model, transitionMatrix, phiStates, psiStates) && model.getReachableStates();
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProb1A(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& psiStates, storm::dd::Bdd<Type> const& statesWithProbabilityGreater0A) {
// Initialize environment for backward search.
storm::dd::DdManager<Type> const& manager = model.getManager();
storm::dd::Bdd<Type> lastIterationStates = manager.getBddZero();
storm::dd::Bdd<Type> statesWithProbability1A = psiStates || statesWithProbabilityGreater0A;
uint_fast64_t iterations = 0;
while (lastIterationStates != statesWithProbability1A) {
lastIterationStates = statesWithProbability1A;
statesWithProbability1A = statesWithProbability1A.swapVariables(model.getRowColumnMetaVariablePairs());
statesWithProbability1A = transitionMatrix.implies(statesWithProbability1A).universalAbstract(model.getColumnVariables());
statesWithProbability1A |= model.getIllegalMask();
statesWithProbability1A = statesWithProbability1A.universalAbstract(model.getNondeterminismVariables());
statesWithProbability1A &= statesWithProbabilityGreater0A;
statesWithProbability1A |= psiStates;
++iterations;
}
return statesWithProbability1A;
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProb1E(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::dd::Bdd<Type> const& statesWithProbabilityGreater0E) {
// Initialize environment for backward search.
storm::dd::DdManager<Type> const& manager = model.getManager();
storm::dd::Bdd<Type> statesWithProbability1E = statesWithProbabilityGreater0E;
uint_fast64_t iterations = 0;
bool outerLoopDone = false;
while (!outerLoopDone) {
storm::dd::Bdd<Type> innerStates = manager.getBddZero();
bool innerLoopDone = false;
while (!innerLoopDone) {
storm::dd::Bdd<Type> temporary = statesWithProbability1E.swapVariables(model.getRowColumnMetaVariablePairs());
temporary = transitionMatrix.implies(temporary).universalAbstract(model.getColumnVariables());
storm::dd::Bdd<Type> temporary2 = innerStates.inverseRelationalProductWithExtendedRelation(transitionMatrix, model.getRowVariables(), model.getColumnVariables());
temporary = temporary.andExists(temporary2, model.getNondeterminismVariables());
temporary &= phiStates;
temporary |= psiStates;
if (innerStates == temporary) {
innerLoopDone = true;
} else {
innerStates = temporary;
}
}
if (statesWithProbability1E == innerStates) {
outerLoopDone = true;
} else {
statesWithProbability1E = innerStates;
}
++iterations;
}
return statesWithProbability1E;
}
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> computeSchedulerProb1E(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::dd::Bdd<Type> const& statesWithProbability1E) {
// Initialize environment for backward search.
storm::dd::DdManager<Type> const& manager = model.getManager();
storm::dd::Bdd<Type> scheduler = manager.getBddZero();
storm::dd::Bdd<Type> innerStates = manager.getBddZero();
uint64_t iterations = 0;
bool innerLoopDone = false;
while (!innerLoopDone) {
storm::dd::Bdd<Type> temporary = statesWithProbability1E.swapVariables(model.getRowColumnMetaVariablePairs());
temporary = transitionMatrix.implies(temporary).universalAbstract(model.getColumnVariables());
storm::dd::Bdd<Type> temporary2 = innerStates.inverseRelationalProductWithExtendedRelation(transitionMatrix, model.getRowVariables(), model.getColumnVariables());
temporary &= temporary2;
temporary &= phiStates;
// Extend the scheduler for those states that have not been seen as inner states before.
scheduler |= (temporary && !innerStates).existsAbstractRepresentative(model.getNondeterminismVariables());
temporary = temporary.existsAbstract(model.getNondeterminismVariables());
temporary |= psiStates;
if (innerStates == temporary) {
innerLoopDone = true;
} else {
innerStates = temporary;
}
++iterations;
}
return scheduler;
}
template <storm::dd::DdType Type, typename ValueType>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01Max(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
return performProb01Max(model, model.getTransitionMatrix().notZero(), phiStates, psiStates);
}
template <storm::dd::DdType Type, typename ValueType>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01Max(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> result;
result.first = performProb0A(model, transitionMatrix, phiStates, psiStates);
result.second = performProb1E(model, transitionMatrix, phiStates, psiStates, !result.first && model.getReachableStates());
return result;
}
template <storm::dd::DdType Type, typename ValueType>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01Min(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
return performProb01Min(model, model.getTransitionMatrix().notZero(), phiStates, psiStates);
}
template <storm::dd::DdType Type, typename ValueType>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01Min(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) {
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> result;
result.first = performProb0E(model, transitionMatrix, phiStates, psiStates);
result.second = performProb1A(model, transitionMatrix, psiStates, !result.first && model.getReachableStates());
return result;
}
template <storm::dd::DdType Type, typename ValueType>
GameProb01Result<Type> performProb0(storm::models::symbolic::StochasticTwoPlayerGame<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::OptimizationDirection const& player1Strategy, storm::OptimizationDirection const& player2Strategy, bool producePlayer1Strategy, bool producePlayer2Strategy) {
// The solution sets.
storm::dd::Bdd<Type> player1States = psiStates;
storm::dd::Bdd<Type> player2States = model.getManager().getBddZero();
bool done = false;
uint_fast64_t iterations = 0;
while (!done) {
storm::dd::Bdd<Type> tmp = (transitionMatrix && player1States.swapVariables(model.getRowColumnMetaVariablePairs())).existsAbstract(model.getColumnVariables()) && phiStates;
if (player2Strategy == OptimizationDirection::Minimize) {
tmp = (tmp || model.getIllegalPlayer2Mask()).universalAbstract(model.getPlayer2Variables());
} else {
tmp = tmp.existsAbstract(model.getPlayer2Variables());
}
player2States |= tmp;
if (player1Strategy == OptimizationDirection::Minimize) {
tmp = (tmp || model.getIllegalPlayer1Mask()).universalAbstract(model.getPlayer1Variables());
} else {
tmp = tmp.existsAbstract(model.getPlayer1Variables());
}
// Re-add all previous player 1 states.
tmp |= player1States;
if (tmp == player1States) {
done = true;
}
player1States = tmp;
++iterations;
}
// Since we have determined the complements of the desired sets, we need to complement it now.
player1States = !player1States && model.getReachableStates();
std::set<storm::expressions::Variable> variablesToAbstract(model.getColumnVariables());
variablesToAbstract.insert(model.getPlayer2Variables().begin(), model.getPlayer2Variables().end());
player2States = !player2States && transitionMatrix.existsAbstract(variablesToAbstract);
// Determine all transitions between prob0 states.
storm::dd::Bdd<Type> transitionsBetweenProb0States = player2States && (transitionMatrix && player1States.swapVariables(model.getRowColumnMetaVariablePairs()));
// Determine the distributions that have only successors that are prob0 states.
storm::dd::Bdd<Type> onlyProb0Successors = (transitionsBetweenProb0States || model.getIllegalSuccessorMask()).universalAbstract(model.getColumnVariables());
boost::optional<storm::dd::Bdd<Type>> player2StrategyBdd;
if (producePlayer2Strategy) {
// Pick a distribution that has only prob0 successors.
player2StrategyBdd = onlyProb0Successors.existsAbstractRepresentative(model.getPlayer2Variables());
}
boost::optional<storm::dd::Bdd<Type>> player1StrategyBdd;
if (producePlayer1Strategy) {
// Move from player 2 choices with only prob0 successors to player 1 choices with only prob 0 successors.
onlyProb0Successors = (player1States && onlyProb0Successors).existsAbstract(model.getPlayer2Variables());
// Pick a prob0 player 2 state.
player1StrategyBdd = onlyProb0Successors.existsAbstractRepresentative(model.getPlayer1Variables());
}
return GameProb01Result<Type>(player1States, player2States, player1StrategyBdd, player2StrategyBdd);
}
template <storm::dd::DdType Type, typename ValueType>
GameProb01Result<Type> performProb1(storm::models::symbolic::StochasticTwoPlayerGame<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::OptimizationDirection const& player1Strategy, storm::OptimizationDirection const& player2Strategy, bool producePlayer1Strategy, bool producePlayer2Strategy, boost::optional<storm::dd::Bdd<Type>> const& player1Candidates) {
// Create the potential prob1 states of player 1.
storm::dd::Bdd<Type> maybePlayer1States = model.getReachableStates();
if (player1Candidates) {
maybePlayer1States &= player1Candidates.get();
}
// Initialize potential prob1 states of player 2.
storm::dd::Bdd<Type> maybePlayer2States = model.getManager().getBddZero();
// A flag that governs whether strategies are produced in the current iteration.
bool produceStrategiesInIteration = false;
boost::optional<storm::dd::Bdd<Type>> player1StrategyBdd;
boost::optional<storm::dd::Bdd<Type>> consideredPlayer1States;
boost::optional<storm::dd::Bdd<Type>> player2StrategyBdd;
boost::optional<storm::dd::Bdd<Type>> consideredPlayer2States;
bool maybeStatesDone = false;
uint_fast64_t maybeStateIterations = 0;
while (!maybeStatesDone || produceStrategiesInIteration) {
bool solutionStatesDone = false;
uint_fast64_t solutionStateIterations = 0;
// If we are to produce strategies in this iteration, we prepare some storage.
if (produceStrategiesInIteration) {
if (player1Strategy == storm::OptimizationDirection::Maximize) {
player1StrategyBdd = model.getManager().getBddZero();
consideredPlayer1States = model.getManager().getBddZero();
}
if (player2Strategy == storm::OptimizationDirection::Maximize) {
player2StrategyBdd = model.getManager().getBddZero();
consideredPlayer2States = model.getManager().getBddZero();
}
}
storm::dd::Bdd<Type> player1Solution = psiStates;
storm::dd::Bdd<Type> player2Solution = model.getManager().getBddZero();
while (!solutionStatesDone) {
// Start by computing the transitions that have only maybe states as successors. Note that at
// this point, there may be illegal transitions.
storm::dd::Bdd<Type> distributionsStayingInMaybe = (!transitionMatrix || maybePlayer1States.swapVariables(model.getRowColumnMetaVariablePairs())).universalAbstract(model.getColumnVariables());
// Then, determine all distributions that have at least one successor in the states that have
// probability 1.
storm::dd::Bdd<Type> distributionsWithProb1Successor = (transitionMatrix && player1Solution.swapVariables(model.getRowColumnMetaVariablePairs())).existsAbstract(model.getColumnVariables());
// The valid distributions are then those that emanate from phi states, stay completely in the
// maybe states and have at least one successor with probability 1.
storm::dd::Bdd<Type> valid = phiStates && distributionsStayingInMaybe && distributionsWithProb1Successor;
// Depending on the strategy of player 2, we need to check whether all choices are valid or
// there exists a valid choice.
if (player2Strategy == OptimizationDirection::Minimize) {
valid = (valid || model.getIllegalPlayer2Mask()).universalAbstract(model.getPlayer2Variables());
} else {
if (produceStrategiesInIteration) {
storm::dd::Bdd<Type> newValidDistributions = valid && !consideredPlayer2States.get();
player2StrategyBdd.get() = player2StrategyBdd.get() || newValidDistributions.existsAbstractRepresentative(model.getPlayer2Variables());
}
valid = valid.existsAbstract(model.getPlayer2Variables());
if (produceStrategiesInIteration) {
consideredPlayer2States.get() |= valid;
}
}
player2Solution |= valid;
// And do the same for player 1.
if (player1Strategy == OptimizationDirection::Minimize) {
valid = (valid || model.getIllegalPlayer1Mask()).universalAbstract(model.getPlayer1Variables());
} else {
if (produceStrategiesInIteration) {
storm::dd::Bdd<Type> newValidDistributions = valid && !consideredPlayer1States.get();
player1StrategyBdd.get() = player1StrategyBdd.get() || newValidDistributions.existsAbstractRepresentative(model.getPlayer1Variables());
}
valid = valid.existsAbstract(model.getPlayer1Variables());
if (produceStrategiesInIteration) {
consideredPlayer1States.get() |= valid;
}
}
// Explicitly add psi states to result since they may have transitions going to some state that
// does not have a reachability probability of 1.
valid |= psiStates;
// If no new states were added, we have found the current hypothesis for the states with
// probability 1.
if (valid == player1Solution) {
solutionStatesDone = true;
} else {
player1Solution = valid;
}
++solutionStateIterations;
}
// If the states with probability 1 and the potential probability 1 states coincide, we have found
// the solution.
if (player1Solution == maybePlayer1States) {
maybePlayer2States = player2Solution;
maybeStatesDone = true;
// If we were asked to produce strategies, we propagate that by triggering another iteration.
// We only do this if at least one strategy will be produced.
produceStrategiesInIteration = !produceStrategiesInIteration && ((producePlayer1Strategy && player1Strategy == OptimizationDirection::Maximize) || (producePlayer2Strategy && player2Strategy == OptimizationDirection::Maximize));
} else {
// Otherwise, we use the current hypothesis for the states with probability 1 as the new maybe
// state set.
maybePlayer1States = player1Solution;
}
++maybeStateIterations;
}
// From now on, the solution is stored in maybeStates (as it coincides with the previous solution).
// If we were asked to produce strategies that do not need to pick a certain successor but are
// 'arbitrary', do so now.
bool strategiesToCompute = (producePlayer1Strategy && !player1StrategyBdd) || (producePlayer2Strategy && !player2StrategyBdd);
if (strategiesToCompute) {
storm::dd::Bdd<Type> relevantStates = (transitionMatrix && maybePlayer2States).existsAbstract(model.getColumnVariables());
if (producePlayer2Strategy && !player2StrategyBdd) {
player2StrategyBdd = relevantStates.existsAbstractRepresentative(model.getPlayer2Variables());
}
if (producePlayer1Strategy && !player1StrategyBdd) {
relevantStates = (maybePlayer1States && relevantStates).existsAbstract(model.getPlayer2Variables());
player1StrategyBdd = relevantStates.existsAbstractRepresentative(model.getPlayer1Variables());
}
}
return GameProb01Result<Type>(maybePlayer1States, maybePlayer2States, player1StrategyBdd, player2StrategyBdd);
}
template <typename T>
std::vector<uint_fast64_t> getTopologicalSort(storm::storage::SparseMatrix<T> const& matrix) {
if (matrix.getRowCount() != matrix.getColumnCount()) {
STORM_LOG_ERROR("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;
}
template storm::storage::BitVector getReachableStates(storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::BitVector const& initialStates, storm::storage::BitVector const& constraintStates, storm::storage::BitVector const& targetStates, bool useStepBound, uint_fast64_t maximalSteps);
template storm::storage::BitVector getBsccCover(storm::storage::SparseMatrix<double> const& transitionMatrix);
template bool checkIfECWithChoiceExists(storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& subsystem, storm::storage::BitVector const& choices);
template std::vector<uint_fast64_t> getDistances(storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::BitVector const& initialStates, boost::optional<storm::storage::BitVector> const& subsystem);
template storm::storage::BitVector performProbGreater0(storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0);
template storm::storage::BitVector performProb1(storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::BitVector const& statesWithProbabilityGreater0);
template storm::storage::BitVector performProb1(storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::models::sparse::DeterministicModel<double> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template void computeSchedulerProbGreater0E(storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::Scheduler<double>& scheduler, boost::optional<storm::storage::BitVector> const& rowFilter);
template void computeSchedulerProb0E(storm::storage::BitVector const& prob0EStates, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::Scheduler<double>& scheduler);
template void computeSchedulerProb1E(storm::storage::BitVector const& prob1EStates, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::Scheduler<double>& scheduler);
template storm::storage::BitVector performProbGreater0E(storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0) ;
template storm::storage::BitVector performProb0A(storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb1E(storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb1E(storm::models::sparse::NondeterministicModel<double, storm::models::sparse::StandardRewardModel<double>> const& model, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::models::sparse::NondeterministicModel<double, storm::models::sparse::StandardRewardModel<double>> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template storm::storage::BitVector performProbGreater0A(storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0, boost::optional<storm::storage::BitVector> const& choiceConstraint = boost::none);
template storm::storage::BitVector performProb0E(storm::models::sparse::NondeterministicModel<double, storm::models::sparse::StandardRewardModel<double>> const& model, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
#ifdef STORM_HAVE_CARL
template storm::storage::BitVector performProb0E(storm::models::sparse::NondeterministicModel<double, storm::models::sparse::StandardRewardModel<storm::Interval>> const& model, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
#endif
template storm::storage::BitVector performProb0E(storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template storm::storage::BitVector performProb1A(storm::models::sparse::NondeterministicModel<double, storm::models::sparse::StandardRewardModel<double>> const& model, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
#ifdef STORM_HAVE_CARL
template storm::storage::BitVector performProb1A(storm::models::sparse::NondeterministicModel<double, storm::models::sparse::StandardRewardModel<storm::Interval>> const& model, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
#endif
template storm::storage::BitVector performProb1A( storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::models::sparse::NondeterministicModel<double, storm::models::sparse::StandardRewardModel<double>> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
#ifdef STORM_HAVE_CARL
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::models::sparse::NondeterministicModel<double, storm::models::sparse::StandardRewardModel<storm::Interval>> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
#endif
template std::vector<uint_fast64_t> getTopologicalSort(storm::storage::SparseMatrix<double> const& matrix) ;
// Instantiations for storm::RationalNumber.
#ifdef STORM_HAVE_CARL
template storm::storage::BitVector getReachableStates(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::BitVector const& initialStates, storm::storage::BitVector const& constraintStates, storm::storage::BitVector const& targetStates, bool useStepBound, uint_fast64_t maximalSteps);
template storm::storage::BitVector getBsccCover(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix);
template bool checkIfECWithChoiceExists(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& subsystem, storm::storage::BitVector const& choices);
template std::vector<uint_fast64_t> getDistances(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::BitVector const& initialStates, boost::optional<storm::storage::BitVector> const& subsystem);
template storm::storage::BitVector performProbGreater0(storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0);
template storm::storage::BitVector performProb1(storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::BitVector const& statesWithProbabilityGreater0);
template storm::storage::BitVector performProb1(storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::models::sparse::DeterministicModel<storm::RationalNumber> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template void computeSchedulerProbGreater0E(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::Scheduler<storm::RationalNumber>& scheduler, boost::optional<storm::storage::BitVector> const& rowFilter);
template void computeSchedulerProb0E(storm::storage::BitVector const& prob0EStates, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::Scheduler<storm::RationalNumber>& scheduler);
template void computeSchedulerProb1E(storm::storage::BitVector const& prob1EStates, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::Scheduler<storm::RationalNumber>& scheduler);
template storm::storage::BitVector performProbGreater0E(storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0) ;
template storm::storage::BitVector performProb0A(storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb1E(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb1E(storm::models::sparse::NondeterministicModel<storm::RationalNumber> const& model, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::models::sparse::NondeterministicModel<storm::RationalNumber> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template storm::storage::BitVector performProbGreater0A(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0, boost::optional<storm::storage::BitVector> const& choiceConstraint = boost::none);
template storm::storage::BitVector performProb0E(storm::models::sparse::NondeterministicModel<storm::RationalNumber> const& model, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb0E(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template storm::storage::BitVector performProb1A( storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::models::sparse::NondeterministicModel<storm::RationalNumber> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::vector<uint_fast64_t> getTopologicalSort(storm::storage::SparseMatrix<storm::RationalNumber> const& matrix);
// End of instantiations for storm::RationalNumber.
template storm::storage::BitVector getReachableStates(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, storm::storage::BitVector const& initialStates, storm::storage::BitVector const& constraintStates, storm::storage::BitVector const& targetStates, bool useStepBound, uint_fast64_t maximalSteps);
template storm::storage::BitVector getBsccCover(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix);
template bool checkIfECWithChoiceExists(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& subsystem, storm::storage::BitVector const& choices);
template std::vector<uint_fast64_t> getDistances(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, storm::storage::BitVector const& initialStates, boost::optional<storm::storage::BitVector> const& subsystem);
template storm::storage::BitVector performProbGreater0(storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0);
template storm::storage::BitVector performProb1(storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::BitVector const& statesWithProbabilityGreater0);
template storm::storage::BitVector performProb1(storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::models::sparse::DeterministicModel<storm::RationalFunction> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProbGreater0E(storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0) ;
template storm::storage::BitVector performProb0A(storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb1E(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb1E(storm::models::sparse::NondeterministicModel<storm::RationalFunction> const& model, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::models::sparse::NondeterministicModel<storm::RationalFunction> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template storm::storage::BitVector performProbGreater0A(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0, boost::optional<storm::storage::BitVector> const& choiceConstraint = boost::none);
template storm::storage::BitVector performProb0E(storm::models::sparse::NondeterministicModel<storm::RationalFunction> const& model, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb0E(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template storm::storage::BitVector performProb1A(storm::models::sparse::NondeterministicModel<storm::RationalFunction> const& model, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template storm::storage::BitVector performProb1A( storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
template std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::models::sparse::NondeterministicModel<storm::RationalFunction> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template std::vector<uint_fast64_t> getTopologicalSort(storm::storage::SparseMatrix<storm::RationalFunction> const& matrix);
#endif
// Instantiations for CUDD.
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProbGreater0(storm::models::symbolic::Model<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates, boost::optional<uint_fast64_t> const& stepBound = boost::optional<uint_fast64_t>());
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProb1(storm::models::symbolic::Model<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& statesWithProbabilityGreater0);
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProb1(storm::models::symbolic::Model<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::CUDD>, storm::dd::Bdd<storm::dd::DdType::CUDD>> performProb01(storm::models::symbolic::DeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::CUDD>, storm::dd::Bdd<storm::dd::DdType::CUDD>> performProb01(storm::models::symbolic::Model<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::CUDD> computeSchedulerProbGreater0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProbGreater0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProb0A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProbGreater0A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProb0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProb1A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& statesWithProbabilityGreater0A);
template storm::dd::Bdd<storm::dd::DdType::CUDD> performProb1E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& statesWithProbabilityGreater0E);
template storm::dd::Bdd<storm::dd::DdType::CUDD> computeSchedulerProb1E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& statesWithProbability1E);
template std::pair<storm::dd::Bdd<storm::dd::DdType::CUDD>, storm::dd::Bdd<storm::dd::DdType::CUDD>> performProb01Max(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::CUDD>, storm::dd::Bdd<storm::dd::DdType::CUDD>> performProb01Max(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::CUDD>, storm::dd::Bdd<storm::dd::DdType::CUDD>> performProb01Min(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::CUDD>, storm::dd::Bdd<storm::dd::DdType::CUDD>> performProb01Min(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates);
template GameProb01Result<storm::dd::DdType::CUDD> performProb0(storm::models::symbolic::StochasticTwoPlayerGame<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates, storm::OptimizationDirection const& player1Strategy, storm::OptimizationDirection const& player2Strategy, bool producePlayer1Strategy, bool producePlayer2Strategy);
template GameProb01Result<storm::dd::DdType::CUDD> performProb1(storm::models::symbolic::StochasticTwoPlayerGame<storm::dd::DdType::CUDD, double> const& model, storm::dd::Bdd<storm::dd::DdType::CUDD> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::CUDD> const& phiStates, storm::dd::Bdd<storm::dd::DdType::CUDD> const& psiStates, storm::OptimizationDirection const& player1Strategy, storm::OptimizationDirection const& player2Strategy, bool producePlayer1Strategy, bool producePlayer2Strategy, boost::optional<storm::dd::Bdd<storm::dd::DdType::CUDD>> const& player1Candidates);
// Instantiations for Sylvan (double).
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, boost::optional<uint_fast64_t> const& stepBound = boost::optional<uint_fast64_t>());
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01(storm::models::symbolic::DeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> computeSchedulerProbGreater0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb0A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0A);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0E);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> computeSchedulerProb1E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbability1E);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Max(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Max(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Min(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Min(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, double> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template GameProb01Result<storm::dd::DdType::Sylvan> performProb0(storm::models::symbolic::StochasticTwoPlayerGame<storm::dd::DdType::Sylvan> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::OptimizationDirection const& player1Strategy, storm::OptimizationDirection const& player2Strategy, bool producePlayer1Strategy, bool producePlayer2Strategy);
template GameProb01Result<storm::dd::DdType::Sylvan> performProb1(storm::models::symbolic::StochasticTwoPlayerGame<storm::dd::DdType::Sylvan> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::OptimizationDirection const& player1Strategy, storm::OptimizationDirection const& player2Strategy, bool producePlayer1Strategy, bool producePlayer2Strategy, boost::optional<storm::dd::Bdd<storm::dd::DdType::Sylvan>> const& player1Candidates);
// Instantiations for Sylvan (rational number).
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, boost::optional<uint_fast64_t> const& stepBound = boost::optional<uint_fast64_t>());
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01(storm::models::symbolic::DeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> computeSchedulerProbGreater0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb0A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0A);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0E);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> computeSchedulerProb1E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbability1E);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Max(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Max(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Min(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Min(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalNumber> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
// Instantiations for Sylvan (rational function).
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, boost::optional<uint_fast64_t> const& stepBound = boost::optional<uint_fast64_t>());
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01(storm::models::symbolic::DeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01(storm::models::symbolic::Model<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> computeSchedulerProbGreater0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb0A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProbGreater0A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb0E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1A(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0A);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> performProb1E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbabilityGreater0E);
template storm::dd::Bdd<storm::dd::DdType::Sylvan> computeSchedulerProb1E(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& statesWithProbability1E);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Max(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Max(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Min(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
template std::pair<storm::dd::Bdd<storm::dd::DdType::Sylvan>, storm::dd::Bdd<storm::dd::DdType::Sylvan>> performProb01Min(storm::models::symbolic::NondeterministicModel<storm::dd::DdType::Sylvan, storm::RationalFunction> const& model, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& transitionMatrix, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& phiStates, storm::dd::Bdd<storm::dd::DdType::Sylvan> const& psiStates);
} // namespace graph
} // namespace utility
} // namespace storm