#include "storm/modelchecker/prctl/helper/SparseDtmcPrctlHelper.h"
#include "storm/modelchecker/csl/helper/SparseCtmcCslHelper.h"
#include "storm/utility/macros.h"
#include "storm/utility/vector.h"
#include "storm/utility/graph.h"
#include "storm/storage/StronglyConnectedComponentDecomposition.h"
#include "storm/storage/DynamicPriorityQueue.h"
#include "storm/storage/ConsecutiveUint64DynamicPriorityQueue.h"
#include "storm/solver/LinearEquationSolver.h"
#include "storm/solver/Multiplier.h"
#include "storm/modelchecker/results/ExplicitQuantitativeCheckResult.h"
#include "storm/modelchecker/hints/ExplicitModelCheckerHint.h"
#include "storm/modelchecker/prctl/helper/DsMpiUpperRewardBoundsComputer.h"
#include "storm/modelchecker/prctl/helper/rewardbounded/MultiDimensionalRewardUnfolding.h"
#include "storm/environment/solver/SolverEnvironment.h"
#include "storm/settings/SettingsManager.h"
#include "storm/settings/modules/GeneralSettings.h"
#include "storm/settings/modules/CoreSettings.h"
#include "storm/settings/modules/IOSettings.h"
#include "storm/settings/modules/ModelCheckerSettings.h"
#include "storm/utility/Stopwatch.h"
#include "storm/utility/ProgressMeasurement.h"
#include "storm/utility/SignalHandler.h"
#include "storm/utility/export.h"
#include "storm/utility/macros.h"
#include "storm/utility/ConstantsComparator.h"
#include "storm/exceptions/InvalidStateException.h"
#include "storm/exceptions/InvalidPropertyException.h"
#include "storm/exceptions/IllegalArgumentException.h"
#include "storm/exceptions/UncheckedRequirementException.h"
#include "storm/exceptions/NotSupportedException.h"
namespace storm {
namespace modelchecker {
namespace helper {
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeStepBoundedUntilProbabilities(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, uint_fast64_t stepBound, ModelCheckerHint const& hint) {
std::vector<ValueType> result(transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
// If we identify the states that have probability 0 of reaching the target states, we can exclude them in the further analysis.
storm::storage::BitVector maybeStates;
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().getComputeOnlyMaybeStates()) {
maybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getMaybeStates();
} else {
maybeStates = storm::utility::graph::performProbGreater0(backwardTransitions, phiStates, psiStates, true, stepBound);
maybeStates &= ~psiStates;
}
STORM_LOG_INFO("Preprocessing: " << maybeStates.getNumberOfSetBits() << " non-target states with probability greater 0.");
storm::utility::vector::setVectorValues<ValueType>(result, psiStates, storm::utility::one<ValueType>());
if (!maybeStates.empty()) {
// We can eliminate the rows and columns from the original transition probability matrix that have probability 0.
storm::storage::SparseMatrix<ValueType> submatrix = transitionMatrix.getSubmatrix(true, maybeStates, maybeStates, true);
// Create the vector of one-step probabilities to go to target states.
std::vector<ValueType> b = transitionMatrix.getConstrainedRowSumVector(maybeStates, psiStates);
// Create the vector with which to multiply.
std::vector<ValueType> subresult(maybeStates.getNumberOfSetBits());
// Perform the matrix vector multiplication
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, submatrix);
multiplier->repeatedMultiply(env, subresult, &b, stepBound);
// Set the values of the resulting vector accordingly.
storm::utility::vector::setVectorValues(result, maybeStates, subresult);
}
return result;
}
template<>
std::map<storm::storage::sparse::state_type, storm::RationalFunction> SparseDtmcPrctlHelper<storm::RationalFunction>::computeRewardBoundedValues(Environment const& env, storm::models::sparse::Dtmc<storm::RationalFunction> const& model, std::shared_ptr<storm::logic::OperatorFormula const> rewardBoundedFormula) {
STORM_LOG_THROW(false, storm::exceptions::NotSupportedException, "The specified property is not supported by this value type.");
return std::map<storm::storage::sparse::state_type, storm::RationalFunction>();
}
template<typename ValueType, typename RewardModelType>
std::map<storm::storage::sparse::state_type, ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeRewardBoundedValues(Environment const& env, storm::models::sparse::Dtmc<ValueType> const& model, std::shared_ptr<storm::logic::OperatorFormula const> rewardBoundedFormula) {
storm::utility::Stopwatch swAll(true), swBuild, swCheck;
storm::modelchecker::helper::rewardbounded::MultiDimensionalRewardUnfolding<ValueType, true> rewardUnfolding(model, rewardBoundedFormula);
// Get lower and upper bounds for the solution.
auto lowerBound = rewardUnfolding.getLowerObjectiveBound();
auto upperBound = rewardUnfolding.getUpperObjectiveBound();
// Initialize epoch models
auto initEpoch = rewardUnfolding.getStartEpoch();
auto epochOrder = rewardUnfolding.getEpochComputationOrder(initEpoch);
// initialize data that will be needed for each epoch
std::vector<ValueType> x, b;
std::unique_ptr<storm::solver::LinearEquationSolver<ValueType>> linEqSolver;
Environment preciseEnv = env;
ValueType precision = rewardUnfolding.getRequiredEpochModelPrecision(initEpoch, storm::utility::convertNumber<ValueType>(storm::settings::getModule<storm::settings::modules::GeneralSettings>().getPrecision()));
preciseEnv.solver().setLinearEquationSolverPrecision(storm::utility::convertNumber<storm::RationalNumber>(precision));
// In case of cdf export we store the necessary data.
std::vector<std::vector<ValueType>> cdfData;
// Set the correct equation problem format.
storm::solver::GeneralLinearEquationSolverFactory<ValueType> linearEquationSolverFactory;
rewardUnfolding.setEquationSystemFormatForEpochModel(linearEquationSolverFactory.getEquationProblemFormat(preciseEnv));
storm::utility::ProgressMeasurement progress("epochs");
progress.setMaxCount(epochOrder.size());
progress.startNewMeasurement(0);
uint64_t numCheckedEpochs = 0;
for (auto const& epoch : epochOrder) {
swBuild.start();
auto& epochModel = rewardUnfolding.setCurrentEpoch(epoch);
swBuild.stop(); swCheck.start();
rewardUnfolding.setSolutionForCurrentEpoch(epochModel.analyzeSingleObjective(preciseEnv, x, b, linEqSolver, lowerBound, upperBound));
swCheck.stop();
if (storm::settings::getModule<storm::settings::modules::IOSettings>().isExportCdfSet() && !rewardUnfolding.getEpochManager().hasBottomDimension(epoch)) {
std::vector<ValueType> cdfEntry;
for (uint64_t i = 0; i < rewardUnfolding.getEpochManager().getDimensionCount(); ++i) {
uint64_t offset = rewardUnfolding.getDimension(i).boundType == helper::rewardbounded::DimensionBoundType::LowerBound ? 1 : 0;
cdfEntry.push_back(storm::utility::convertNumber<ValueType>(rewardUnfolding.getEpochManager().getDimensionOfEpoch(epoch, i) + offset) * rewardUnfolding.getDimension(i).scalingFactor);
}
cdfEntry.push_back(rewardUnfolding.getInitialStateResult(epoch));
cdfData.push_back(std::move(cdfEntry));
}
++numCheckedEpochs;
progress.updateProgress(numCheckedEpochs);
if (storm::utility::resources::isTerminate()) {
break;
}
}
std::map<storm::storage::sparse::state_type, ValueType> result;
for (auto const& initState : model.getInitialStates()) {
result[initState] = rewardUnfolding.getInitialStateResult(initEpoch, initState);
}
swAll.stop();
if (storm::settings::getModule<storm::settings::modules::IOSettings>().isExportCdfSet()) {
std::vector<std::string> headers;
for (uint64_t i = 0; i < rewardUnfolding.getEpochManager().getDimensionCount(); ++i) {
headers.push_back(rewardUnfolding.getDimension(i).formula->toString());
}
headers.push_back("Result");
storm::utility::exportDataToCSVFile<ValueType, std::string, std::string>(storm::settings::getModule<storm::settings::modules::IOSettings>().getExportCdfDirectory() + "cdf.csv", cdfData, headers);
}
if (storm::settings::getModule<storm::settings::modules::CoreSettings>().isShowStatisticsSet()) {
STORM_PRINT_AND_LOG("---------------------------------" << std::endl);
STORM_PRINT_AND_LOG("Statistics:" << std::endl);
STORM_PRINT_AND_LOG("---------------------------------" << std::endl);
STORM_PRINT_AND_LOG(" #checked epochs: " << epochOrder.size() << "." << std::endl);
STORM_PRINT_AND_LOG(" overall Time: " << swAll << "." << std::endl);
STORM_PRINT_AND_LOG("Epoch Model building Time: " << swBuild << "." << std::endl);
STORM_PRINT_AND_LOG("Epoch Model checking Time: " << swCheck << "." << std::endl);
STORM_PRINT_AND_LOG("---------------------------------" << std::endl);
}
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeUntilProbabilities(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative, ModelCheckerHint const& hint) {
std::vector<ValueType> result(transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
// We need to identify the maybe states (states which have a probability for satisfying the until formula
// that is strictly between 0 and 1) and the states that satisfy the formula with probability 1.
storm::storage::BitVector maybeStates, statesWithProbability1;
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().getComputeOnlyMaybeStates()) {
maybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getMaybeStates();
// Treat the states with probability one
std::vector<ValueType> const& resultsForNonMaybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getResultHint();
statesWithProbability1 = storm::storage::BitVector(maybeStates.size(), false);
storm::storage::BitVector nonMaybeStates = ~maybeStates;
for (auto const& state : nonMaybeStates) {
if (storm::utility::isOne(resultsForNonMaybeStates[state])) {
statesWithProbability1.set(state, true);
result[state] = storm::utility::one<ValueType>();
} else {
STORM_LOG_THROW(storm::utility::isZero(resultsForNonMaybeStates[state]), storm::exceptions::IllegalArgumentException, "Expected that the result hint specifies probabilities in {0,1} for non-maybe states");
}
}
STORM_LOG_INFO("Preprocessing: " << statesWithProbability1.getNumberOfSetBits() << " states with probability 1 (" << maybeStates.getNumberOfSetBits() << " states remaining).");
} else {
// Get all states that have probability 0 and 1 of satisfying the until-formula.
std::pair<storm::storage::BitVector, storm::storage::BitVector> statesWithProbability01 = storm::utility::graph::performProb01(backwardTransitions, phiStates, psiStates);
storm::storage::BitVector statesWithProbability0 = std::move(statesWithProbability01.first);
statesWithProbability1 = std::move(statesWithProbability01.second);
maybeStates = ~(statesWithProbability0 | statesWithProbability1);
STORM_LOG_INFO("Preprocessing: " << statesWithProbability1.getNumberOfSetBits() << " states with probability 1, " << statesWithProbability0.getNumberOfSetBits() << " with probability 0 (" << maybeStates.getNumberOfSetBits() << " states remaining).");
// Set values of resulting vector that are known exactly.
storm::utility::vector::setVectorValues<ValueType>(result, statesWithProbability0, storm::utility::zero<ValueType>());
storm::utility::vector::setVectorValues<ValueType>(result, statesWithProbability1, storm::utility::one<ValueType>());
}
// Check whether we need to compute exact probabilities for some states.
if (qualitative) {
// Set the values for all maybe-states to 0.5 to indicate that their probability values are neither 0 nor 1.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, storm::utility::convertNumber<ValueType>(0.5));
} else {
if (!maybeStates.empty()) {
// In this case we have to compute the probabilities.
// Check whether we need to convert the input to equation system format.
storm::solver::GeneralLinearEquationSolverFactory<ValueType> linearEquationSolverFactory;
bool convertToEquationSystem = linearEquationSolverFactory.getEquationProblemFormat(env) == storm::solver::LinearEquationSolverProblemFormat::EquationSystem;
// We can eliminate the rows and columns from the original transition probability matrix.
storm::storage::SparseMatrix<ValueType> submatrix = transitionMatrix.getSubmatrix(true, maybeStates, maybeStates, convertToEquationSystem);
if (convertToEquationSystem) {
// Converting the matrix from the fixpoint notation to the form needed for the equation
// system. That is, we go from x = A*x + b to (I-A)x = b.
submatrix.convertToEquationSystem();
}
// Initialize the x vector with the hint (if available) or with 0.5 for each element.
// This is the initial guess for the iterative solvers. It should be safe as for all
// 'maybe' states we know that the probability is strictly larger than 0.
std::vector<ValueType> x;
if(hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().hasResultHint()) {
x = storm::utility::vector::filterVector(hint.template asExplicitModelCheckerHint<ValueType>().getResultHint(), maybeStates);
} else {
x = std::vector<ValueType>(maybeStates.getNumberOfSetBits(), storm::utility::convertNumber<ValueType>(0.5));
}
// Prepare the right-hand side of the equation system. For entry i this corresponds to
// the accumulated probability of going from state i to some 'yes' state.
std::vector<ValueType> b = transitionMatrix.getConstrainedRowSumVector(maybeStates, statesWithProbability1);
// Now solve the created system of linear equations.
goal.restrictRelevantValues(maybeStates);
std::unique_ptr<storm::solver::LinearEquationSolver<ValueType>> solver = storm::solver::configureLinearEquationSolver(env, std::move(goal), linearEquationSolverFactory, std::move(submatrix));
solver->setBounds(storm::utility::zero<ValueType>(), storm::utility::one<ValueType>());
solver->solveEquations(env, x, b);
// Set values of resulting vector according to result.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, x);
}
}
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeAllUntilProbabilities(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& initialStates, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
uint_fast64_t numberOfStates = transitionMatrix.getRowCount();
std::vector<ValueType> result(numberOfStates, storm::utility::zero<ValueType>());
// All states are relevant
storm::storage::BitVector relevantStates(numberOfStates, true);
// Compute exact probabilities for some states.
if (!relevantStates.empty()) {
// Check whether we need to convert the input to equation system format.
storm::solver::GeneralLinearEquationSolverFactory<ValueType> linearEquationSolverFactory;
bool convertToEquationSystem = linearEquationSolverFactory.getEquationProblemFormat(env) == storm::solver::LinearEquationSolverProblemFormat::EquationSystem;
storm::storage::SparseMatrix<ValueType> submatrix(transitionMatrix);
submatrix.makeRowsAbsorbing(phiStates);
submatrix.makeRowsAbsorbing(psiStates);
//submatrix.deleteDiagonalEntries(psiStates);
//storm::storage::BitVector failState(numberOfStates, false);
//failState.set(0, true);
submatrix.deleteDiagonalEntries();
submatrix = submatrix.transpose();
submatrix = submatrix.getSubmatrix(true, relevantStates, relevantStates, convertToEquationSystem);
if (convertToEquationSystem) {
// Converting the matrix from the fixpoint notation to the form needed for the equation
// system. That is, we go from x = A*x + b to (I-A)x = b.
submatrix.convertToEquationSystem();
}
// Initialize the x vector with 0.5 for each element.
// This is the initial guess for the iterative solvers. It should be safe as for all
// 'maybe' states we know that the probability is strictly larger than 0.
std::vector<ValueType> x = std::vector<ValueType>(relevantStates.getNumberOfSetBits(), storm::utility::convertNumber<ValueType>(0.5));
// Prepare the right-hand side of the equation system.
std::vector<ValueType> b(relevantStates.getNumberOfSetBits(), storm::utility::zero<ValueType>());
// Set initial states
size_t i = 0;
ValueType initDist = storm::utility::one<ValueType>() / storm::utility::convertNumber<ValueType>(initialStates.getNumberOfSetBits());
for (auto const& state : relevantStates) {
if (initialStates.get(state)) {
b[i] = initDist;
}
++i;
}
// Now solve the created system of linear equations.
goal.restrictRelevantValues(relevantStates);
std::unique_ptr<storm::solver::LinearEquationSolver<ValueType>> solver = storm::solver::configureLinearEquationSolver(env, std::move(goal), linearEquationSolverFactory, std::move(submatrix));
solver->setBounds(storm::utility::zero<ValueType>(), storm::utility::one<ValueType>());
solver->solveEquations(env, x, b);
// Set values of resulting vector according to result.
storm::utility::vector::setVectorValues<ValueType>(result, relevantStates, x);
}
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeGloballyProbabilities(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& psiStates, bool qualitative) {
goal.oneMinus();
std::vector<ValueType> result = computeUntilProbabilities(env, std::move(goal), transitionMatrix, backwardTransitions, storm::storage::BitVector(transitionMatrix.getRowCount(), true), ~psiStates, qualitative);
for (auto& entry : result) {
entry = storm::utility::one<ValueType>() - entry;
}
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeNextProbabilities(Environment const& env, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& nextStates) {
// Create the vector with which to multiply and initialize it correctly.
std::vector<ValueType> result(transitionMatrix.getRowCount());
storm::utility::vector::setVectorValues(result, nextStates, storm::utility::one<ValueType>());
// Perform one single matrix-vector multiplication.
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, transitionMatrix);
multiplier->multiply(env, result, nullptr, result);
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeCumulativeRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, uint_fast64_t stepBound) {
// Initialize result to the null vector.
std::vector<ValueType> result(transitionMatrix.getRowCount());
// Compute the reward vector to add in each step based on the available reward models.
std::vector<ValueType> totalRewardVector = rewardModel.getTotalRewardVector(transitionMatrix);
// Perform the matrix vector multiplication as often as required by the formula bound.
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, transitionMatrix);
multiplier->repeatedMultiply(env, result, &totalRewardVector, stepBound);
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeInstantaneousRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, uint_fast64_t stepCount) {
// Only compute the result if the model has a state-based reward this->getModel().
STORM_LOG_THROW(rewardModel.hasStateRewards(), storm::exceptions::InvalidPropertyException, "Missing reward model for formula. Skipping formula.");
// Initialize result to state rewards of the model.
std::vector<ValueType> result = rewardModel.getStateRewardVector();
// Perform the matrix vector multiplication as often as required by the formula bound.
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, transitionMatrix);
multiplier->repeatedMultiply(env, result, nullptr, stepCount);
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeTotalRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, RewardModelType const& rewardModel, bool qualitative, ModelCheckerHint const& hint) {
// Identify the states from which only states with zero reward are reachable.
// We can then compute reachability rewards assuming these states as target set.
storm::storage::BitVector statesWithoutReward = rewardModel.getStatesWithZeroReward(transitionMatrix);
storm::storage::BitVector rew0States = storm::utility::graph::performProbGreater0(backwardTransitions, statesWithoutReward, ~statesWithoutReward);
rew0States.complement();
return computeReachabilityRewards(env, std::move(goal), transitionMatrix, backwardTransitions, rewardModel, rew0States, qualitative, hint);
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, RewardModelType const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, ModelCheckerHint const& hint) {
return computeReachabilityRewards(env, std::move(goal), transitionMatrix, backwardTransitions,
[&] (uint_fast64_t numberOfRows, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& maybeStates) {
return rewardModel.getTotalRewardVector(numberOfRows, transitionMatrix, maybeStates);
},
targetStates, qualitative,
[&] () {
return rewardModel.getStatesWithZeroReward(transitionMatrix);
},
hint);
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& totalStateRewardVector, storm::storage::BitVector const& targetStates, bool qualitative, ModelCheckerHint const& hint) {
return computeReachabilityRewards(env, std::move(goal), transitionMatrix, backwardTransitions,
[&] (uint_fast64_t numberOfRows, storm::storage::SparseMatrix<ValueType> const&, storm::storage::BitVector const& maybeStates) {
std::vector<ValueType> result(numberOfRows);
storm::utility::vector::selectVectorValues(result, maybeStates, totalStateRewardVector);
return result;
},
targetStates, qualitative,
[&] () {
return storm::utility::vector::filterZero(totalStateRewardVector);
},
hint);
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeReachabilityTimes(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& targetStates, bool qualitative, ModelCheckerHint const& hint) {
return computeReachabilityRewards(env, std::move(goal), transitionMatrix, backwardTransitions,
[&] (uint_fast64_t numberOfRows, storm::storage::SparseMatrix<ValueType> const&, storm::storage::BitVector const&) {
return std::vector<ValueType>(numberOfRows, storm::utility::one<ValueType>());
},
targetStates, qualitative,
[&] () {
return storm::storage::BitVector(transitionMatrix.getRowGroupCount(), false);
},
hint);
}
// This function computes an upper bound on the reachability rewards (see Baier et al, CAV'17).
template<typename ValueType>
std::vector<ValueType> computeUpperRewardBounds(storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& rewards, std::vector<ValueType> const& oneStepTargetProbabilities) {
DsMpiDtmcUpperRewardBoundsComputer<ValueType> dsmpi(transitionMatrix, rewards, oneStepTargetProbabilities);
std::vector<ValueType> bounds = dsmpi.computeUpperBounds();
return bounds;
}
template<>
std::vector<storm::RationalFunction> computeUpperRewardBounds(storm::storage::SparseMatrix<storm::RationalFunction> const& transitionMatrix, std::vector<storm::RationalFunction> const& rewards, std::vector<storm::RationalFunction> const& oneStepTargetProbabilities) {
STORM_LOG_THROW(false, storm::exceptions::NotSupportedException, "Computing upper reward bounds is not supported for rational functions.");
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::function<std::vector<ValueType>(uint_fast64_t, storm::storage::SparseMatrix<ValueType> const&, storm::storage::BitVector const&)> const& totalStateRewardVectorGetter, storm::storage::BitVector const& targetStates, bool qualitative, std::function<storm::storage::BitVector()> const& zeroRewardStatesGetter, ModelCheckerHint const& hint) {
std::vector<ValueType> result(transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
// Determine which states have reward zero
storm::storage::BitVector rew0States;
if (storm::settings::getModule<storm::settings::modules::ModelCheckerSettings>().isFilterRewZeroSet()) {
rew0States = storm::utility::graph::performProb1(backwardTransitions, zeroRewardStatesGetter(), targetStates);
} else {
rew0States = targetStates;
}
// Determine which states have a reward that is less than infinity.
storm::storage::BitVector maybeStates;
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().getComputeOnlyMaybeStates()) {
maybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getMaybeStates();
storm::utility::vector::setVectorValues(result, ~(maybeStates | rew0States), storm::utility::infinity<ValueType>());
STORM_LOG_INFO("Preprocessing: " << rew0States.getNumberOfSetBits() << " States with reward zero (" << maybeStates.getNumberOfSetBits() << " states remaining).");
} else {
storm::storage::BitVector trueStates(transitionMatrix.getRowCount(), true);
storm::storage::BitVector infinityStates = storm::utility::graph::performProb1(backwardTransitions, trueStates, rew0States);
infinityStates.complement();
maybeStates = ~(rew0States | infinityStates);
STORM_LOG_INFO("Preprocessing: " << infinityStates.getNumberOfSetBits() << " states with reward infinity, " << rew0States.getNumberOfSetBits() << " states with reward zero (" << maybeStates.getNumberOfSetBits() << " states remaining).");
storm::utility::vector::setVectorValues(result, infinityStates, storm::utility::infinity<ValueType>());
}
// Check whether we need to compute exact rewards for some states.
if (qualitative) {
// Set the values for all maybe-states to 1 to indicate that their reward values
// are neither 0 nor infinity.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, storm::utility::one<ValueType>());
} else {
if (!maybeStates.empty()) {
// Check whether we need to convert the input to equation system format.
storm::solver::GeneralLinearEquationSolverFactory<ValueType> linearEquationSolverFactory;
bool convertToEquationSystem = linearEquationSolverFactory.getEquationProblemFormat(env) == storm::solver::LinearEquationSolverProblemFormat::EquationSystem;
// In this case we have to compute the reward values for the remaining states.
// We can eliminate the rows and columns from the original transition probability matrix.
storm::storage::SparseMatrix<ValueType> submatrix = transitionMatrix.getSubmatrix(true, maybeStates, maybeStates, convertToEquationSystem);
// Initialize the x vector with the hint (if available) or with 1 for each element.
// This is the initial guess for the iterative solvers.
std::vector<ValueType> x;
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().hasResultHint()) {
x = storm::utility::vector::filterVector(hint.template asExplicitModelCheckerHint<ValueType>().getResultHint(), maybeStates);
} else {
x = std::vector<ValueType>(submatrix.getColumnCount(), storm::utility::one<ValueType>());
}
// Prepare the right-hand side of the equation system.
std::vector<ValueType> b = totalStateRewardVectorGetter(submatrix.getRowCount(), transitionMatrix, maybeStates);
storm::solver::LinearEquationSolverRequirements requirements = linearEquationSolverFactory.getRequirements(env);
boost::optional<std::vector<ValueType>> upperRewardBounds;
requirements.clearLowerBounds();
if (requirements.upperBounds()) {
upperRewardBounds = computeUpperRewardBounds(submatrix, b, transitionMatrix.getConstrainedRowSumVector(maybeStates, rew0States));
requirements.clearUpperBounds();
}
STORM_LOG_THROW(!requirements.hasEnabledCriticalRequirement(), storm::exceptions::UncheckedRequirementException, "Solver requirements " + requirements.getEnabledRequirementsAsString() + " not checked.");
// If necessary, convert the matrix from the fixpoint notation to the form needed for the equation system.
if (convertToEquationSystem) {
// go from x = A*x + b to (I-A)x = b.
submatrix.convertToEquationSystem();
}
// Create the solver.
goal.restrictRelevantValues(maybeStates);
std::unique_ptr<storm::solver::LinearEquationSolver<ValueType>> solver = storm::solver::configureLinearEquationSolver(env, std::move(goal), linearEquationSolverFactory, std::move(submatrix));
solver->setLowerBound(storm::utility::zero<ValueType>());
if (upperRewardBounds) {
solver->setUpperBounds(std::move(upperRewardBounds.get()));
}
// Now solve the resulting equation system.
solver->solveEquations(env, x, b);
// Set values of resulting vector according to result.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, x);
}
}
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeLongRunAverageProbabilities(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& psiStates) {
return SparseCtmcCslHelper::computeLongRunAverageProbabilities<ValueType>(env, std::move(goal), transitionMatrix, psiStates, nullptr);
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeLongRunAverageRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel) {
return SparseCtmcCslHelper::computeLongRunAverageRewards<ValueType, RewardModelType>(env, std::move(goal), transitionMatrix, rewardModel, nullptr);
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeLongRunAverageRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& stateRewards) {
return SparseCtmcCslHelper::computeLongRunAverageRewards<ValueType>(env, std::move(goal), transitionMatrix, stateRewards, nullptr);
}
template<typename ValueType, typename RewardModelType>
typename SparseDtmcPrctlHelper<ValueType, RewardModelType>::BaierTransformedModel SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeBaierTransformation(Environment const& env, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& targetStates, storm::storage::BitVector const& conditionStates, boost::optional<std::vector<ValueType>> const& stateRewards) {
BaierTransformedModel result;
// Start by computing all 'before' states, i.e. the states for which the conditional probability is defined.
std::vector<ValueType> probabilitiesToReachConditionStates = computeUntilProbabilities(env, storm::solver::SolveGoal<ValueType>(), transitionMatrix, backwardTransitions, storm::storage::BitVector(transitionMatrix.getRowCount(), true), conditionStates, false);
result.beforeStates = storm::storage::BitVector(targetStates.size(), true);
uint_fast64_t state = 0;
uint_fast64_t beforeStateIndex = 0;
for (auto const& value : probabilitiesToReachConditionStates) {
if (value == storm::utility::zero<ValueType>()) {
result.beforeStates.set(state, false);
} else {
probabilitiesToReachConditionStates[beforeStateIndex] = value;
++beforeStateIndex;
}
++state;
}
probabilitiesToReachConditionStates.resize(beforeStateIndex);
if (targetStates.empty()) {
result.noTargetStates = true;
return result;
} else if (!result.beforeStates.empty()) {
// If there are some states for which the conditional probability is defined and there are some
// states that can reach the target states without visiting condition states first, we need to
// do more work.
// First, compute the relevant states and some offsets.
storm::storage::BitVector allStates(targetStates.size(), true);
std::vector<uint_fast64_t> numberOfBeforeStatesUpToState = result.beforeStates.getNumberOfSetBitsBeforeIndices();
storm::storage::BitVector statesWithProbabilityGreater0 = storm::utility::graph::performProbGreater0(backwardTransitions, allStates, targetStates);
statesWithProbabilityGreater0 &= storm::utility::graph::getReachableStates(transitionMatrix, conditionStates, allStates, targetStates);
uint_fast64_t normalStatesOffset = result.beforeStates.getNumberOfSetBits();
std::vector<uint_fast64_t> numberOfNormalStatesUpToState = statesWithProbabilityGreater0.getNumberOfSetBitsBeforeIndices();
// All transitions going to states with probability zero, need to be redirected to a deadlock state.
bool addDeadlockState = false;
uint_fast64_t deadlockState = normalStatesOffset + statesWithProbabilityGreater0.getNumberOfSetBits();
// Now, we create the matrix of 'before' and 'normal' states.
storm::storage::SparseMatrixBuilder<ValueType> builder;
// Start by creating the transitions of the 'before' states.
uint_fast64_t currentRow = 0;
for (auto beforeState : result.beforeStates) {
if (conditionStates.get(beforeState)) {
// For condition states, we move to the 'normal' states.
ValueType zeroProbability = storm::utility::zero<ValueType>();
for (auto const& successorEntry : transitionMatrix.getRow(beforeState)) {
if (statesWithProbabilityGreater0.get(successorEntry.getColumn())) {
builder.addNextValue(currentRow, normalStatesOffset + numberOfNormalStatesUpToState[successorEntry.getColumn()], successorEntry.getValue());
} else {
zeroProbability += successorEntry.getValue();
}
}
if (!storm::utility::isZero(zeroProbability)) {
builder.addNextValue(currentRow, deadlockState, zeroProbability);
}
} else {
// For non-condition states, we scale the probabilities going to other before states.
for (auto const& successorEntry : transitionMatrix.getRow(beforeState)) {
if (result.beforeStates.get(successorEntry.getColumn())) {
builder.addNextValue(currentRow, numberOfBeforeStatesUpToState[successorEntry.getColumn()], successorEntry.getValue() * probabilitiesToReachConditionStates[numberOfBeforeStatesUpToState[successorEntry.getColumn()]] / probabilitiesToReachConditionStates[currentRow]);
}
}
}
++currentRow;
}
// Then, create the transitions of the 'normal' states.
for (auto state : statesWithProbabilityGreater0) {
ValueType zeroProbability = storm::utility::zero<ValueType>();
for (auto const& successorEntry : transitionMatrix.getRow(state)) {
if (statesWithProbabilityGreater0.get(successorEntry.getColumn())) {
builder.addNextValue(currentRow, normalStatesOffset + numberOfNormalStatesUpToState[successorEntry.getColumn()], successorEntry.getValue());
} else {
zeroProbability += successorEntry.getValue();
}
}
if (!storm::utility::isZero(zeroProbability)) {
addDeadlockState = true;
builder.addNextValue(currentRow, deadlockState, zeroProbability);
}
++currentRow;
}
if (addDeadlockState) {
builder.addNextValue(deadlockState, deadlockState, storm::utility::one<ValueType>());
}
// Build the new transition matrix and the new targets.
result.transitionMatrix = builder.build(addDeadlockState ? (deadlockState + 1) : deadlockState);
storm::storage::BitVector newTargetStates = targetStates % result.beforeStates;
newTargetStates.resize(result.transitionMatrix.get().getRowCount());
for (auto state : targetStates % statesWithProbabilityGreater0) {
newTargetStates.set(normalStatesOffset + state, true);
}
result.targetStates = std::move(newTargetStates);
// If a reward model was given, we need to compute the rewards for the transformed model.
if (stateRewards) {
std::vector<ValueType> newStateRewards(result.beforeStates.getNumberOfSetBits());
storm::utility::vector::selectVectorValues(newStateRewards, result.beforeStates, stateRewards.get());
newStateRewards.reserve(result.transitionMatrix.get().getRowCount());
for (auto state : statesWithProbabilityGreater0) {
newStateRewards.push_back(stateRewards.get()[state]);
}
// Add a zero reward to the deadlock state.
if (addDeadlockState) {
newStateRewards.push_back(storm::utility::zero<ValueType>());
}
result.stateRewards = std::move(newStateRewards);
}
}
return result;
}
template<typename ValueType, typename RewardModelType>
storm::storage::BitVector SparseDtmcPrctlHelper<ValueType, RewardModelType>::BaierTransformedModel::getNewRelevantStates() const {
storm::storage::BitVector newRelevantStates(transitionMatrix.get().getRowCount());
for (uint64_t i = 0; i < this->beforeStates.getNumberOfSetBits(); ++i) {
newRelevantStates.set(i);
}
return newRelevantStates;
}
template<typename ValueType, typename RewardModelType>
storm::storage::BitVector SparseDtmcPrctlHelper<ValueType, RewardModelType>::BaierTransformedModel::getNewRelevantStates(storm::storage::BitVector const& oldRelevantStates) const {
storm::storage::BitVector result = oldRelevantStates % this->beforeStates;
result.resize(transitionMatrix.get().getRowCount());
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeConditionalProbabilities(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& targetStates, storm::storage::BitVector const& conditionStates, bool qualitative) {
// Prepare result vector.
std::vector<ValueType> result(transitionMatrix.getRowCount(), storm::utility::infinity<ValueType>());
if (!conditionStates.empty()) {
BaierTransformedModel transformedModel = computeBaierTransformation(env, transitionMatrix, backwardTransitions, targetStates, conditionStates, boost::none);
if (transformedModel.noTargetStates) {
storm::utility::vector::setVectorValues(result, transformedModel.beforeStates, storm::utility::zero<ValueType>());
} else {
// At this point, we do not need to check whether there are 'before' states, since the condition
// states were non-empty so there is at least one state with a positive probability of satisfying
// the condition.
// Now compute reachability probabilities in the transformed model.
storm::storage::SparseMatrix<ValueType> const& newTransitionMatrix = transformedModel.transitionMatrix.get();
storm::storage::BitVector newRelevantValues;
if (goal.hasRelevantValues()) {
newRelevantValues = transformedModel.getNewRelevantStates(goal.relevantValues());
} else {
newRelevantValues = transformedModel.getNewRelevantStates();
}
goal.setRelevantValues(std::move(newRelevantValues));
std::vector<ValueType> conditionalProbabilities = computeUntilProbabilities(env, std::move(goal), newTransitionMatrix, newTransitionMatrix.transpose(), storm::storage::BitVector(newTransitionMatrix.getRowCount(), true), transformedModel.targetStates.get(), qualitative);
storm::utility::vector::setVectorValues(result, transformedModel.beforeStates, conditionalProbabilities);
}
}
return result;
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseDtmcPrctlHelper<ValueType, RewardModelType>::computeConditionalRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, RewardModelType const& rewardModel, storm::storage::BitVector const& targetStates, storm::storage::BitVector const& conditionStates, bool qualitative) {
// Prepare result vector.
std::vector<ValueType> result(transitionMatrix.getRowCount(), storm::utility::infinity<ValueType>());
if (!conditionStates.empty()) {
BaierTransformedModel transformedModel = computeBaierTransformation(env, transitionMatrix, backwardTransitions, targetStates, conditionStates, rewardModel.getTotalRewardVector(transitionMatrix));
if (transformedModel.noTargetStates) {
storm::utility::vector::setVectorValues(result, transformedModel.beforeStates, storm::utility::zero<ValueType>());
} else {
// At this point, we do not need to check whether there are 'before' states, since the condition
// states were non-empty so there is at least one state with a positive probability of satisfying
// the condition.
// Now compute reachability probabilities in the transformed model.
storm::storage::SparseMatrix<ValueType> const& newTransitionMatrix = transformedModel.transitionMatrix.get();
storm::storage::BitVector newRelevantValues;
if (goal.hasRelevantValues()) {
newRelevantValues = transformedModel.getNewRelevantStates(goal.relevantValues());
} else {
newRelevantValues = transformedModel.getNewRelevantStates();
}
goal.setRelevantValues(std::move(newRelevantValues));
std::vector<ValueType> conditionalRewards = computeReachabilityRewards(env, std::move(goal), newTransitionMatrix, newTransitionMatrix.transpose(), transformedModel.stateRewards.get(), transformedModel.targetStates.get(), qualitative);
storm::utility::vector::setVectorValues(result, transformedModel.beforeStates, conditionalRewards);
}
}
return result;
}
template class SparseDtmcPrctlHelper<double>;
#ifdef STORM_HAVE_CARL
template class SparseDtmcPrctlHelper<storm::RationalNumber>;
template class SparseDtmcPrctlHelper<storm::RationalFunction>;
#endif
}
}
}