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total reward formulas for ctmcs and markov automata

tempestpy_adaptions
TimQu 7 years ago
parent
b5566fa861
commit
8df9b461cb
8 changed files with 81 additions and 3 deletions
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  1. 10
      src/storm/modelchecker/csl/SparseCtmcCslModelChecker.cpp
  2. 1
      src/storm/modelchecker/csl/SparseCtmcCslModelChecker.h
  3. 11
      src/storm/modelchecker/csl/SparseMarkovAutomatonCslModelChecker.cpp
  4. 1
      src/storm/modelchecker/csl/SparseMarkovAutomatonCslModelChecker.h
  5. 37
      src/storm/modelchecker/csl/helper/SparseCtmcCslHelper.cpp
  6. 3
      src/storm/modelchecker/csl/helper/SparseCtmcCslHelper.h
  7. 18
      src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.cpp
  8. 3
      src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.h

10
src/storm/modelchecker/csl/SparseCtmcCslModelChecker.cpp
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@ -37,14 +37,14 @@ namespace storm {
template<typename CValueType, typename std::enable_if<storm::NumberTraits<CValueType>::SupportsExponential, int>::type>
bool SparseCtmcCslModelChecker<SparseCtmcModelType>::canHandleImplementation(CheckTask<storm::logic::Formula, CValueType> const& checkTask) const {
storm::logic::Formula const& formula = checkTask.getFormula();
return formula.isInFragment(storm::logic::csrl().setGloballyFormulasAllowed(false).setLongRunAverageRewardFormulasAllowed(true).setLongRunAverageProbabilitiesAllowed(true).setTimeAllowed(true));
return formula.isInFragment(storm::logic::csrl().setGloballyFormulasAllowed(false).setLongRunAverageRewardFormulasAllowed(true).setLongRunAverageProbabilitiesAllowed(true).setTimeAllowed(true).setTotalRewardFormulasAllowed(true));
}
template <typename SparseCtmcModelType>
template<typename CValueType, typename std::enable_if<!storm::NumberTraits<CValueType>::SupportsExponential, int>::type>
bool SparseCtmcCslModelChecker<SparseCtmcModelType>::canHandleImplementation(CheckTask<storm::logic::Formula, CValueType> const& checkTask) const {
storm::logic::Formula const& formula = checkTask.getFormula();
return formula.isInFragment(storm::logic::prctl().setGloballyFormulasAllowed(false).setLongRunAverageRewardFormulasAllowed(true).setLongRunAverageProbabilitiesAllowed(true).setTimeAllowed(true));
return formula.isInFragment(storm::logic::prctl().setGloballyFormulasAllowed(false).setLongRunAverageRewardFormulasAllowed(true).setLongRunAverageProbabilitiesAllowed(true).setTimeAllowed(true).setTotalRewardFormulasAllowed(true));
}
template <typename SparseCtmcModelType>
@ -117,6 +117,12 @@ namespace storm {
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(std::move(numericResult)));
}
template<typename SparseCtmcModelType>
std::unique_ptr<CheckResult> SparseCtmcCslModelChecker<SparseCtmcModelType>::computeTotalRewards(Environment const& env, storm::logic::RewardMeasureType, CheckTask<storm::logic::TotalRewardFormula, ValueType> const& checkTask) {
std::vector<ValueType> numericResult = storm::modelchecker::helper::SparseCtmcCslHelper::computeTotalRewards(env, storm::solver::SolveGoal<ValueType>(this->getModel(), checkTask), this->getModel().getTransitionMatrix(), this->getModel().getBackwardTransitions(), this->getModel().getExitRateVector(), checkTask.isRewardModelSet() ? this->getModel().getRewardModel(checkTask.getRewardModel()) : this->getModel().getRewardModel(""), checkTask.isQualitativeSet());
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(std::move(numericResult)));
}
template <typename SparseCtmcModelType>
std::unique_ptr<CheckResult> SparseCtmcCslModelChecker<SparseCtmcModelType>::computeLongRunAverageProbabilities(Environment const& env, CheckTask<storm::logic::StateFormula, ValueType> const& checkTask) {
storm::logic::StateFormula const& stateFormula = checkTask.getFormula();

1
src/storm/modelchecker/csl/SparseCtmcCslModelChecker.h
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@ -33,6 +33,7 @@ namespace storm {
virtual std::unique_ptr<CheckResult> computeCumulativeRewards(Environment const& env, storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::CumulativeRewardFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeInstantaneousRewards(Environment const& env, storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::InstantaneousRewardFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeReachabilityRewards(Environment const& env, storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::EventuallyFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeTotalRewards(Environment const& env, storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::TotalRewardFormula, ValueType> const& checkTask) override;
private:
template<typename CValueType = ValueType, typename std::enable_if<storm::NumberTraits<CValueType>::SupportsExponential, int>::type = 0>

11
src/storm/modelchecker/csl/SparseMarkovAutomatonCslModelChecker.cpp
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@ -89,7 +89,16 @@ namespace storm {
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(std::move(result)));
}
template<typename SparseMarkovAutomatonModelType>
std::unique_ptr<CheckResult> SparseMarkovAutomatonCslModelChecker<SparseMarkovAutomatonModelType>::computeTotalRewards(Environment const& env, storm::logic::RewardMeasureType, CheckTask<storm::logic::TotalRewardFormula, ValueType> const& checkTask) {
STORM_LOG_THROW(checkTask.isOptimizationDirectionSet(), storm::exceptions::InvalidPropertyException, "Formula needs to specify whether minimal or maximal values are to be computed on nondeterministic model.");
STORM_LOG_THROW(this->getModel().isClosed(), storm::exceptions::InvalidPropertyException, "Unable to compute reachability rewards in non-closed Markov automaton.");
std::vector<ValueType> result = storm::modelchecker::helper::SparseMarkovAutomatonCslHelper::computeTotalRewards(env, checkTask.getOptimizationDirection(), this->getModel().getTransitionMatrix(), this->getModel().getBackwardTransitions(), this->getModel().getExitRates(), this->getModel().getMarkovianStates(), checkTask.isRewardModelSet() ? this->getModel().getRewardModel(checkTask.getRewardModel()) : this->getModel().getRewardModel(""));
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(std::move(result)));
}
template<typename SparseMarkovAutomatonModelType>
std::unique_ptr<CheckResult> SparseMarkovAutomatonCslModelChecker<SparseMarkovAutomatonModelType>::computeLongRunAverageProbabilities(Environment const& env, CheckTask<storm::logic::StateFormula, ValueType> const& checkTask) {
storm::logic::StateFormula const& stateFormula = checkTask.getFormula();

1
src/storm/modelchecker/csl/SparseMarkovAutomatonCslModelChecker.h
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@ -24,6 +24,7 @@ namespace storm {
virtual std::unique_ptr<CheckResult> computeBoundedUntilProbabilities(Environment const& env, CheckTask<storm::logic::BoundedUntilFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeUntilProbabilities(Environment const& env, CheckTask<storm::logic::UntilFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeReachabilityRewards(Environment const& env, storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::EventuallyFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeTotalRewards(Environment const& env, storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::TotalRewardFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeLongRunAverageProbabilities(Environment const& env, CheckTask<storm::logic::StateFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeLongRunAverageRewards(Environment const& env, storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::LongRunAverageRewardFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeReachabilityTimes(Environment const& env, storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::EventuallyFormula, ValueType> const& checkTask) override;

37
src/storm/modelchecker/csl/helper/SparseCtmcCslHelper.cpp
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@ -329,6 +329,38 @@ namespace storm {
return storm::modelchecker::helper::SparseDtmcPrctlHelper<ValueType>::computeReachabilityRewards(env, std::move(goal), probabilityMatrix, backwardTransitions, totalRewardVector, targetStates, qualitative);
}
template <typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseCtmcCslHelper::computeTotalRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& rateMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, RewardModelType const& rewardModel, bool qualitative) {
STORM_LOG_THROW(!rewardModel.empty(), storm::exceptions::InvalidPropertyException, "Missing reward model for formula. Skipping formula.");
storm::storage::SparseMatrix<ValueType> probabilityMatrix = computeProbabilityMatrix(rateMatrix, exitRateVector);
std::vector<ValueType> totalRewardVector;
if (rewardModel.hasStateRewards()) {
totalRewardVector = rewardModel.getStateRewardVector();
typename std::vector<ValueType>::const_iterator it2 = exitRateVector.begin();
for (typename std::vector<ValueType>::iterator it1 = totalRewardVector.begin(), ite1 = totalRewardVector.end(); it1 != ite1; ++it1, ++it2) {
*it1 /= *it2;
}
if (rewardModel.hasStateActionRewards()) {
storm::utility::vector::addVectors(totalRewardVector, rewardModel.getStateActionRewardVector(), totalRewardVector);
}
if (rewardModel.hasTransitionRewards()) {
storm::utility::vector::addVectors(totalRewardVector, probabilityMatrix.getPointwiseProductRowSumVector(rewardModel.getTransitionRewardMatrix()), totalRewardVector);
}
} else if (rewardModel.hasTransitionRewards()) {
totalRewardVector = probabilityMatrix.getPointwiseProductRowSumVector(rewardModel.getTransitionRewardMatrix());
if (rewardModel.hasStateActionRewards()) {
storm::utility::vector::addVectors(totalRewardVector, rewardModel.getStateActionRewardVector(), totalRewardVector);
}
} else {
totalRewardVector = rewardModel.getStateActionRewardVector();
}
RewardModelType dtmcRewardModel(std::move(totalRewardVector));
return storm::modelchecker::helper::SparseDtmcPrctlHelper<ValueType>::computeTotalRewards(env, std::move(goal), probabilityMatrix, backwardTransitions, dtmcRewardModel, qualitative);
}
template <typename ValueType>
std::vector<ValueType> SparseCtmcCslHelper::computeLongRunAverageProbabilities(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& probabilityMatrix, storm::storage::BitVector const& psiStates, std::vector<ValueType> const* exitRateVector) {
@ -743,6 +775,8 @@ namespace storm {
template std::vector<double> SparseCtmcCslHelper::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& rateMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative);
template std::vector<double> SparseCtmcCslHelper::computeTotalRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& rateMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::models::sparse::StandardRewardModel<double> const& rewardModel, bool qualitative);
template std::vector<double> SparseCtmcCslHelper::computeLongRunAverageProbabilities(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& probabilityMatrix, storm::storage::BitVector const& psiStates, std::vector<double> const* exitRateVector);
template std::vector<double> SparseCtmcCslHelper::computeLongRunAverageRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& probabilityMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, std::vector<double> const* exitRateVector);
template std::vector<double> SparseCtmcCslHelper::computeLongRunAverageRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& probabilityMatrix, std::vector<double> const& stateRewardVector, std::vector<double> const* exitRateVector);
@ -772,6 +806,9 @@ namespace storm {
template std::vector<storm::RationalNumber> SparseCtmcCslHelper::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& rateMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative);
template std::vector<storm::RationalFunction> SparseCtmcCslHelper::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalFunction>&& goal, storm::storage::SparseMatrix<storm::RationalFunction> const& rateMatrix, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, std::vector<storm::RationalFunction> const& exitRateVector, storm::models::sparse::StandardRewardModel<storm::RationalFunction> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative);
template std::vector<storm::RationalNumber> SparseCtmcCslHelper::computeTotalRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& rateMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, bool qualitative);
template std::vector<storm::RationalFunction> SparseCtmcCslHelper::computeTotalRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalFunction>&& goal, storm::storage::SparseMatrix<storm::RationalFunction> const& rateMatrix, storm::storage::SparseMatrix<storm::RationalFunction> const& backwardTransitions, std::vector<storm::RationalFunction> const& exitRateVector, storm::models::sparse::StandardRewardModel<storm::RationalFunction> const& rewardModel, bool qualitative);
template std::vector<storm::RationalNumber> SparseCtmcCslHelper::computeLongRunAverageProbabilities(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& probabilityMatrix, storm::storage::BitVector const& psiStates, std::vector<storm::RationalNumber> const* exitRateVector);
template std::vector<storm::RationalFunction> SparseCtmcCslHelper::computeLongRunAverageProbabilities(Environment const& env, storm::solver::SolveGoal<storm::RationalFunction>&& goal, storm::storage::SparseMatrix<storm::RationalFunction> const& probabilityMatrix, storm::storage::BitVector const& psiStates, std::vector<storm::RationalFunction> const* exitRateVector);

3
src/storm/modelchecker/csl/helper/SparseCtmcCslHelper.h
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@ -44,6 +44,9 @@ namespace storm {
template <typename ValueType, typename RewardModelType>
static std::vector<ValueType> computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& rateMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, RewardModelType const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative);
template <typename ValueType, typename RewardModelType>
static std::vector<ValueType> computeTotalRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& rateMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, RewardModelType const& rewardModel, bool qualitative);
template <typename ValueType>
static std::vector<ValueType> computeLongRunAverageProbabilities(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& probabilityMatrix, storm::storage::BitVector const& psiStates, std::vector<ValueType> const* exitRateVector);

18
src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.cpp
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@ -583,6 +583,20 @@ namespace storm {
return std::move(storm::modelchecker::helper::SparseMdpPrctlHelper<ValueType>::computeUntilProbabilities(env, dir, transitionMatrix, backwardTransitions, phiStates, psiStates, qualitative, false).values);
}
template <typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeTotalRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel) {
// Get a reward model where the state rewards are scaled accordingly
std::vector<ValueType> stateRewardWeights(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
for (auto const markovianState : markovianStates) {
stateRewardWeights[markovianState] = storm::utility::one<ValueType>() / exitRateVector[markovianState];
}
std::vector<ValueType> totalRewardVector = rewardModel.getTotalActionRewardVector(transitionMatrix, stateRewardWeights);
RewardModelType scaledRewardModel(boost::none, std::move(totalRewardVector));
return SparseMdpPrctlHelper<ValueType>::computeTotalRewards(env, dir, transitionMatrix, backwardTransitions, scaledRewardModel, false, false).values;
}
template <typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::BitVector const& psiStates) {
@ -1020,6 +1034,8 @@ namespace storm {
template std::vector<double> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::BitVector const& psiStates);
template std::vector<double> SparseMarkovAutomatonCslHelper::computeTotalRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel);
template std::vector<double> SparseMarkovAutomatonCslHelper::computeLongRunAverageProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates);
template std::vector<double> SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel);
@ -1038,6 +1054,8 @@ namespace storm {
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::BitVector const& psiStates);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeTotalRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeLongRunAverageProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel);

3
src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.h
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@ -26,6 +26,9 @@ namespace storm {
template <typename ValueType>
static std::vector<ValueType> computeUntilProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative);
template <typename ValueType, typename RewardModelType>
static std::vector<ValueType> computeTotalRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel);
template <typename ValueType, typename RewardModelType>
static std::vector<ValueType> computeReachabilityRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::BitVector const& psiStates);

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