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tempest/src/storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.cpp

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#include "storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.h"
#include <boost/container/flat_map.hpp>
#include "storm/modelchecker/results/ExplicitQuantitativeCheckResult.h"
#include "storm/modelchecker/hints/ExplicitModelCheckerHint.h"
#include "storm/modelchecker/prctl/helper/DsMpiUpperRewardBoundsComputer.h"
#include "storm/modelchecker/prctl/helper/BaierUpperRewardBoundsComputer.h"
#include "storm/modelchecker/prctl/helper/SparseMdpEndComponentInformation.h"
#include "storm/models/sparse/StandardRewardModel.h"
#include "storm/storage/MaximalEndComponentDecomposition.h"
#include "storm/utility/macros.h"
#include "storm/utility/vector.h"
#include "storm/utility/graph.h"
#include "storm/storage/expressions/Variable.h"
#include "storm/storage/expressions/Expression.h"
#include "storm/storage/Scheduler.h"
#include "storm/solver/MinMaxLinearEquationSolver.h"
#include "storm/solver/Multiplier.h"
#include "storm/solver/LpSolver.h"
#include "storm/settings/SettingsManager.h"
#include "storm/settings/modules/ModelCheckerSettings.h"
#include "storm/settings/modules/GeneralSettings.h"
#include "storm/settings/modules/CoreSettings.h"
#include "storm/settings/modules/IOSettings.h"
#include "storm/utility/Stopwatch.h"
#include "storm/utility/ProgressMeasurement.h"
#include "storm/utility/SignalHandler.h"
#include "storm/utility/export.h"
#include "storm/utility/NumberTraits.h"
#include "storm/transformer/EndComponentEliminator.h"
#include "storm/environment/solver/MinMaxSolverEnvironment.h"
#include "storm/environment/solver/LongRunAverageSolverEnvironment.h"
#include "storm/exceptions/InvalidStateException.h"
#include "storm/exceptions/InvalidPropertyException.h"
#include "storm/exceptions/InvalidSettingsException.h"
#include "storm/exceptions/IllegalFunctionCallException.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>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::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.getRowGroupCount(), storm::utility::zero<ValueType>());
// Determine the states that have 0 probability of reaching the target states.
storm::storage::BitVector maybeStates;
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().getComputeOnlyMaybeStates()) {
maybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getMaybeStates();
} else {
if (goal.minimize()) {
maybeStates = storm::utility::graph::performProbGreater0A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, phiStates, psiStates, true, stepBound);
} else {
maybeStates = storm::utility::graph::performProbGreater0E(backwardTransitions, phiStates, psiStates, true, stepBound);
}
maybeStates &= ~psiStates;
}
STORM_LOG_INFO("Preprocessing: " << maybeStates.getNumberOfSetBits() << " non-target states with probability greater 0.");
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, false);
std::vector<ValueType> b = transitionMatrix.getConstrainedRowGroupSumVector(maybeStates, psiStates);
// Create the vector with which to multiply.
std::vector<ValueType> subresult(maybeStates.getNumberOfSetBits());
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, submatrix);
multiplier->repeatedMultiplyAndReduce(env, goal.direction(), subresult, &b, stepBound);
// Set the values of the resulting vector accordingly.
storm::utility::vector::setVectorValues(result, maybeStates, subresult);
}
storm::utility::vector::setVectorValues(result, psiStates, storm::utility::one<ValueType>());
return result;
}
template<typename ValueType>
std::map<storm::storage::sparse::state_type, ValueType> SparseMdpPrctlHelper<ValueType>::computeRewardBoundedValues(Environment const& env, OptimizationDirection dir, rewardbounded::MultiDimensionalRewardUnfolding<ValueType, true>& rewardUnfolding, storm::storage::BitVector const& initialStates) {
storm::utility::Stopwatch swAll(true), swBuild, swCheck;
// 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::MinMaxLinearEquationSolver<ValueType>> minMaxSolver;
ValueType precision = rewardUnfolding.getRequiredEpochModelPrecision(initEpoch, storm::utility::convertNumber<ValueType>(storm::settings::getModule<storm::settings::modules::GeneralSettings>().getPrecision()));
Environment preciseEnv = env;
preciseEnv.solver().minMax().setPrecision(storm::utility::convertNumber<storm::RationalNumber>(precision));
// In case of cdf export we store the necessary data.
std::vector<std::vector<ValueType>> cdfData;
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, dir, x, b, minMaxSolver, 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 : initialStates) {
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>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeNextProbabilities(Environment const& env, OptimizationDirection dir, 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.getRowGroupCount());
storm::utility::vector::setVectorValues(result, nextStates, storm::utility::one<ValueType>());
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, transitionMatrix);
multiplier->multiplyAndReduce(env, dir, result, nullptr, result);
return result;
}
template<typename ValueType>
std::vector<uint_fast64_t> computeValidSchedulerHint(Environment const& env, SolutionType const& type, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& maybeStates, storm::storage::BitVector const& filterStates, storm::storage::BitVector const& targetStates) {
storm::storage::Scheduler<ValueType> validScheduler(maybeStates.size());
if (type == SolutionType::UntilProbabilities) {
storm::utility::graph::computeSchedulerProbGreater0E(transitionMatrix, backwardTransitions, filterStates, targetStates, validScheduler, boost::none);
} else if (type == SolutionType::ExpectedRewards) {
storm::utility::graph::computeSchedulerProb1E(maybeStates | targetStates, transitionMatrix, backwardTransitions, filterStates, targetStates, validScheduler);
} else {
STORM_LOG_ASSERT(false, "Unexpected equation system type.");
}
// Extract the relevant parts of the scheduler for the solver.
std::vector<uint_fast64_t> schedulerHint(maybeStates.getNumberOfSetBits());
auto maybeIt = maybeStates.begin();
for (auto& choice : schedulerHint) {
choice = validScheduler.getChoice(*maybeIt).getDeterministicChoice();
++maybeIt;
}
return schedulerHint;
}
template<typename ValueType>
struct SparseMdpHintType {
SparseMdpHintType() : eliminateEndComponents(false), computeUpperBounds(false), uniqueSolution(false), noEndComponents(false) {
// Intentionally left empty.
}
bool hasSchedulerHint() const {
return static_cast<bool>(schedulerHint);
}
bool hasValueHint() const {
return static_cast<bool>(valueHint);
}
bool hasLowerResultBound() const {
return static_cast<bool>(lowerResultBound);
}
ValueType const& getLowerResultBound() const {
return lowerResultBound.get();
}
bool hasUpperResultBound() const {
return static_cast<bool>(upperResultBound);
}
bool hasUpperResultBounds() const {
return static_cast<bool>(upperResultBounds);
}
ValueType const& getUpperResultBound() const {
return upperResultBound.get();
}
std::vector<ValueType>& getUpperResultBounds() {
return upperResultBounds.get();
}
std::vector<ValueType> const& getUpperResultBounds() const {
return upperResultBounds.get();
}
std::vector<uint64_t>& getSchedulerHint() {
return schedulerHint.get();
}
std::vector<ValueType>& getValueHint() {
return valueHint.get();
}
bool getEliminateEndComponents() const {
return eliminateEndComponents;
}
bool getComputeUpperBounds() {
return computeUpperBounds;
}
bool hasUniqueSolution() const {
return uniqueSolution;
}
bool hasNoEndComponents() const {
return noEndComponents;
}
boost::optional<std::vector<uint64_t>> schedulerHint;
boost::optional<std::vector<ValueType>> valueHint;
boost::optional<ValueType> lowerResultBound;
boost::optional<ValueType> upperResultBound;
boost::optional<std::vector<ValueType>> upperResultBounds;
bool eliminateEndComponents;
bool computeUpperBounds;
bool uniqueSolution;
bool noEndComponents;
};
template<typename ValueType>
void extractValueAndSchedulerHint(SparseMdpHintType<ValueType>& hintStorage, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& maybeStates, boost::optional<storm::storage::BitVector> const& selectedChoices, ModelCheckerHint const& hint, bool skipECWithinMaybeStatesCheck) {
// Deal with scheduler hint.
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().hasSchedulerHint()) {
if (hintStorage.hasSchedulerHint()) {
STORM_LOG_WARN("A scheduler hint was provided, but the solver requires a specific one. The provided scheduler hint will be ignored.");
} else {
auto const& schedulerHint = hint.template asExplicitModelCheckerHint<ValueType>().getSchedulerHint();
std::vector<uint64_t> hintChoices;
// The scheduler hint is only applicable if it induces no BSCC consisting of maybe states.
bool hintApplicable;
if (!skipECWithinMaybeStatesCheck) {
hintChoices.reserve(maybeStates.size());
for (uint_fast64_t state = 0; state < maybeStates.size(); ++state) {
hintChoices.push_back(schedulerHint.getChoice(state).getDeterministicChoice());
}
hintApplicable = storm::utility::graph::performProb1(transitionMatrix.transposeSelectedRowsFromRowGroups(hintChoices), maybeStates, ~maybeStates).full();
} else {
hintApplicable = true;
}
if (hintApplicable) {
// Compute the hint w.r.t. the given subsystem.
hintChoices.clear();
hintChoices.reserve(maybeStates.getNumberOfSetBits());
for (auto const& state : maybeStates) {
uint_fast64_t hintChoice = schedulerHint.getChoice(state).getDeterministicChoice();
if (selectedChoices) {
uint_fast64_t firstChoice = transitionMatrix.getRowGroupIndices()[state];
uint_fast64_t lastChoice = firstChoice + hintChoice;
hintChoice = 0;
for (uint_fast64_t choice = selectedChoices->getNextSetIndex(firstChoice); choice < lastChoice; choice = selectedChoices->getNextSetIndex(choice + 1)) {
++hintChoice;
}
}
hintChoices.push_back(hintChoice);
}
hintStorage.schedulerHint = std::move(hintChoices);
}
}
}
// Deal with solution value hint. Only applicable if there are no End Components consisting of maybe states.
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().hasResultHint() && (skipECWithinMaybeStatesCheck || hintStorage.hasSchedulerHint() || storm::utility::graph::performProb1A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, maybeStates, ~maybeStates).full())) {
hintStorage.valueHint = storm::utility::vector::filterVector(hint.template asExplicitModelCheckerHint<ValueType>().getResultHint(), maybeStates);
}
}
template<typename ValueType>
SparseMdpHintType<ValueType> computeHints(Environment const& env, SolutionType const& type, ModelCheckerHint const& hint, storm::OptimizationDirection const& dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& maybeStates, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& targetStates, bool produceScheduler, boost::optional<storm::storage::BitVector> const& selectedChoices = boost::none) {
SparseMdpHintType<ValueType> result;
// There are no end components if we minimize until probabilities or
// maximize reachability rewards or if the hint tells us so.
result.noEndComponents = (dir == storm::solver::OptimizationDirection::Minimize && type == SolutionType::UntilProbabilities)
|| (dir == storm::solver::OptimizationDirection::Maximize && type == SolutionType::ExpectedRewards)
|| (hint.isExplicitModelCheckerHint() && hint.asExplicitModelCheckerHint<ValueType>().getNoEndComponentsInMaybeStates());
// If there are no end components, the solution is unique. (Note that the other direction does not hold,
// e.g., end components in which infinite reward is collected.
result.uniqueSolution = result.hasNoEndComponents();
// Check for requirements of the solver.
bool hasSchedulerHint = hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().hasSchedulerHint();
storm::solver::GeneralMinMaxLinearEquationSolverFactory<ValueType> minMaxLinearEquationSolverFactory;
storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(env, result.uniqueSolution, result.noEndComponents, dir, hasSchedulerHint, produceScheduler);
if (requirements.hasEnabledRequirement()) {
// If the solver still requires no end-components, we have to eliminate them later.
if (requirements.uniqueSolution()) {
STORM_LOG_ASSERT(!result.hasUniqueSolution(), "The solver requires to eliminate the end components although the solution is already assumed to be unique.");
STORM_LOG_DEBUG("Scheduling EC elimination, because the solver requires a unique solution.");
result.eliminateEndComponents = true;
// If end components have been eliminated we can assume a unique solution.
result.uniqueSolution = true;
requirements.clearUniqueSolution();
// If we compute until probabilities, we can even assume the absence of end components.
// Note that in the case of minimizing expected rewards there might still be end components in which reward is collected.
result.noEndComponents = (type == SolutionType::UntilProbabilities);
}
// If the solver requires an initial scheduler, compute one now. Note that any scheduler is valid if there are no end components.
if (requirements.validInitialScheduler() && !result.noEndComponents) {
STORM_LOG_DEBUG("Computing valid scheduler, because the solver requires it.");
result.schedulerHint = computeValidSchedulerHint(env, type, transitionMatrix, backwardTransitions, maybeStates, phiStates, targetStates);
requirements.clearValidInitialScheduler();
}
// Finally, we have information on the bounds depending on the problem type.
if (type == SolutionType::UntilProbabilities) {
requirements.clearBounds();
} else if (type == SolutionType::ExpectedRewards) {
requirements.clearLowerBounds();
}
if (requirements.upperBounds()) {
result.computeUpperBounds = true;
requirements.clearUpperBounds();
}
STORM_LOG_THROW(!requirements.hasEnabledCriticalRequirement(), storm::exceptions::UncheckedRequirementException, "Solver requirements " + requirements.getEnabledRequirementsAsString() + " not checked.");
} else {
STORM_LOG_DEBUG("Solver has no requirements.");
}
// Only if there is no end component decomposition that we will need to do later, we use value and scheduler
// hints from the provided hint.
if (!result.eliminateEndComponents) {
extractValueAndSchedulerHint(result, transitionMatrix, backwardTransitions, maybeStates, selectedChoices, hint, result.uniqueSolution);
} else {
STORM_LOG_WARN_COND(hint.isEmpty(), "A non-empty hint was provided, but its information will be disregarded.");
}
// Only set bounds if we did not obtain them from the hint.
if (!result.hasLowerResultBound()) {
result.lowerResultBound = storm::utility::zero<ValueType>();
}
if (!result.hasUpperResultBound() && type == SolutionType::UntilProbabilities) {
result.upperResultBound = storm::utility::one<ValueType>();
}
// If we received an upper bound, we can drop the requirement to compute one.
if (result.hasUpperResultBound()) {
result.computeUpperBounds = false;
}
return result;
}
template<typename ValueType>
struct MaybeStateResult {
MaybeStateResult(std::vector<ValueType>&& values) : values(std::move(values)) {
// Intentionally left empty.
}
bool hasScheduler() const {
return static_cast<bool>(scheduler);
}
std::vector<uint64_t> const& getScheduler() const {
return scheduler.get();
}
std::vector<ValueType> const& getValues() const {
return values;
}
std::vector<ValueType> values;
boost::optional<std::vector<uint64_t>> scheduler;
};
template<typename ValueType>
MaybeStateResult<ValueType> computeValuesForMaybeStates(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType>&& submatrix, std::vector<ValueType> const& b, bool produceScheduler, SparseMdpHintType<ValueType>& hint) {
// Initialize the solution vector.
std::vector<ValueType> x = hint.hasValueHint() ? std::move(hint.getValueHint()) : std::vector<ValueType>(submatrix.getRowGroupCount(), hint.hasLowerResultBound() ? hint.getLowerResultBound() : storm::utility::zero<ValueType>());
// Set up the solver.
storm::solver::GeneralMinMaxLinearEquationSolverFactory<ValueType> minMaxLinearEquationSolverFactory;
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = storm::solver::configureMinMaxLinearEquationSolver(env, std::move(goal), minMaxLinearEquationSolverFactory, std::move(submatrix));
solver->setRequirementsChecked();
solver->setHasUniqueSolution(hint.hasUniqueSolution());
solver->setHasNoEndComponents(hint.hasNoEndComponents());
if (hint.hasLowerResultBound()) {
solver->setLowerBound(hint.getLowerResultBound());
}
if (hint.hasUpperResultBound()) {
solver->setUpperBound(hint.getUpperResultBound());
}
if (hint.hasUpperResultBounds()) {
solver->setUpperBounds(std::move(hint.getUpperResultBounds()));
}
if (hint.hasSchedulerHint()) {
solver->setInitialScheduler(std::move(hint.getSchedulerHint()));
}
solver->setTrackScheduler(produceScheduler);
// Solve the corresponding system of equations.
solver->solveEquations(env, x, b);
#ifndef NDEBUG
// As a sanity check, make sure our local upper bounds were in fact correct.
if (solver->hasUpperBound(storm::solver::AbstractEquationSolver<ValueType>::BoundType::Local)) {
auto resultIt = x.begin();
for (auto const& entry : solver->getUpperBounds()) {
STORM_LOG_ASSERT(*resultIt <= entry + env.solver().minMax().getPrecision(), "Expecting result value for state " << std::distance(x.begin(), resultIt) << " to be <= " << entry << ", but got " << *resultIt << ".");
++resultIt;
}
}
#endif
// Create result.
MaybeStateResult<ValueType> result(std::move(x));
// If requested, return the requested scheduler.
if (produceScheduler) {
result.scheduler = std::move(solver->getSchedulerChoices());
}
return result;
}
struct QualitativeStateSetsUntilProbabilities {
storm::storage::BitVector maybeStates;
storm::storage::BitVector statesWithProbability0;
storm::storage::BitVector statesWithProbability1;
};
template<typename ValueType>
QualitativeStateSetsUntilProbabilities getQualitativeStateSetsUntilProbabilitiesFromHint(ModelCheckerHint const& hint) {
QualitativeStateSetsUntilProbabilities result;
result.maybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getMaybeStates();
// Treat the states with probability zero/one.
std::vector<ValueType> const& resultsForNonMaybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getResultHint();
result.statesWithProbability1 = storm::storage::BitVector(result.maybeStates.size());
result.statesWithProbability0 = storm::storage::BitVector(result.maybeStates.size());
storm::storage::BitVector nonMaybeStates = ~result.maybeStates;
for (auto const& state : nonMaybeStates) {
if (storm::utility::isOne(resultsForNonMaybeStates[state])) {
result.statesWithProbability1.set(state, true);
} 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");
result.statesWithProbability0.set(state, true);
}
}
return result;
}
template<typename ValueType>
QualitativeStateSetsUntilProbabilities computeQualitativeStateSetsUntilProbabilities(storm::solver::SolveGoal<ValueType> const& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
QualitativeStateSetsUntilProbabilities result;
// Get all states that have probability 0 and 1 of satisfying the until-formula.
std::pair<storm::storage::BitVector, storm::storage::BitVector> statesWithProbability01;
if (goal.minimize()) {
statesWithProbability01 = storm::utility::graph::performProb01Min(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, phiStates, psiStates);
} else {
statesWithProbability01 = storm::utility::graph::performProb01Max(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, phiStates, psiStates);
}
result.statesWithProbability0 = std::move(statesWithProbability01.first);
result.statesWithProbability1 = std::move(statesWithProbability01.second);
result.maybeStates = ~(result.statesWithProbability0 | result.statesWithProbability1);
return result;
}
template<typename ValueType>
QualitativeStateSetsUntilProbabilities getQualitativeStateSetsUntilProbabilities(storm::solver::SolveGoal<ValueType> const& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, ModelCheckerHint const& hint) {
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().getComputeOnlyMaybeStates()) {
return getQualitativeStateSetsUntilProbabilitiesFromHint<ValueType>(hint);
} else {
return computeQualitativeStateSetsUntilProbabilities(goal, transitionMatrix, backwardTransitions, phiStates, psiStates);
}
}
template<typename ValueType>
void extractSchedulerChoices(storm::storage::Scheduler<ValueType>& scheduler, std::vector<uint_fast64_t> const& subChoices, storm::storage::BitVector const& maybeStates) {
auto subChoiceIt = subChoices.begin();
for (auto maybeState : maybeStates) {
scheduler.setChoice(*subChoiceIt, maybeState);
++subChoiceIt;
}
assert(subChoiceIt == subChoices.end());
}
template<typename ValueType>
void extendScheduler(storm::storage::Scheduler<ValueType>& scheduler, storm::solver::SolveGoal<ValueType> const& goal, QualitativeStateSetsUntilProbabilities const& qualitativeStateSets, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
// Finally, if we need to produce a scheduler, we also need to figure out the parts of the scheduler for
// the states with probability 1 or 0 (depending on whether we maximize or minimize).
// We also need to define some arbitrary choice for the remaining states to obtain a fully defined scheduler.
if (goal.minimize()) {
storm::utility::graph::computeSchedulerProb0E(qualitativeStateSets.statesWithProbability0, transitionMatrix, scheduler);
for (auto const& prob1State : qualitativeStateSets.statesWithProbability1) {
scheduler.setChoice(0, prob1State);
}
} else {
storm::utility::graph::computeSchedulerProb1E(qualitativeStateSets.statesWithProbability1, transitionMatrix, backwardTransitions, phiStates, psiStates, scheduler);
for (auto const& prob0State : qualitativeStateSets.statesWithProbability0) {
scheduler.setChoice(0, prob0State);
}
}
}
template<typename ValueType>
void computeFixedPointSystemUntilProbabilities(storm::solver::SolveGoal<ValueType>& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, QualitativeStateSetsUntilProbabilities const& qualitativeStateSets, storm::storage::SparseMatrix<ValueType>& submatrix, std::vector<ValueType>& b) {
// First, we can eliminate the rows and columns from the original transition probability matrix for states
// whose probabilities are already known.
submatrix = transitionMatrix.getSubmatrix(true, qualitativeStateSets.maybeStates, qualitativeStateSets.maybeStates, false);
// 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 state that has probability 1.
b = transitionMatrix.getConstrainedRowGroupSumVector(qualitativeStateSets.maybeStates, qualitativeStateSets.statesWithProbability1);
// If the solve goal has relevant values, we need to adjust them.
goal.restrictRelevantValues(qualitativeStateSets.maybeStates);
}
template<typename ValueType>
boost::optional<SparseMdpEndComponentInformation<ValueType>> computeFixedPointSystemUntilProbabilitiesEliminateEndComponents(storm::solver::SolveGoal<ValueType>& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, QualitativeStateSetsUntilProbabilities const& qualitativeStateSets, storm::storage::SparseMatrix<ValueType>& submatrix, std::vector<ValueType>& b) {
// Get the set of states that (under some scheduler) can stay in the set of maybestates forever
storm::storage::BitVector candidateStates = storm::utility::graph::performProb0E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, qualitativeStateSets.maybeStates, ~qualitativeStateSets.maybeStates);
bool doDecomposition = !candidateStates.empty();
storm::storage::MaximalEndComponentDecomposition<ValueType> endComponentDecomposition;
if (doDecomposition) {
// Compute the states that are in MECs.
endComponentDecomposition = storm::storage::MaximalEndComponentDecomposition<ValueType>(transitionMatrix, backwardTransitions, candidateStates);
}
// Only do more work if there are actually end-components.
if (doDecomposition && !endComponentDecomposition.empty()) {
STORM_LOG_DEBUG("Eliminating " << endComponentDecomposition.size() << " EC(s).");
SparseMdpEndComponentInformation<ValueType> result = SparseMdpEndComponentInformation<ValueType>::eliminateEndComponents(endComponentDecomposition, transitionMatrix, qualitativeStateSets.maybeStates, &qualitativeStateSets.statesWithProbability1, nullptr, nullptr, submatrix, &b, nullptr);
// If the solve goal has relevant values, we need to adjust them.
if (goal.hasRelevantValues()) {
storm::storage::BitVector newRelevantValues(submatrix.getRowGroupCount());
for (auto state : goal.relevantValues()) {
if (qualitativeStateSets.maybeStates.get(state)) {
newRelevantValues.set(result.getRowGroupAfterElimination(state));
}
}
if (!newRelevantValues.empty()) {
goal.setRelevantValues(std::move(newRelevantValues));
}
}
return result;
} else {
STORM_LOG_DEBUG("Not eliminating ECs as there are none.");
computeFixedPointSystemUntilProbabilities(goal, transitionMatrix, qualitativeStateSets, submatrix, b);
return boost::none;
}
}
template<typename ValueType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::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, bool produceScheduler, ModelCheckerHint const& hint) {
STORM_LOG_THROW(!qualitative || !produceScheduler, storm::exceptions::InvalidSettingsException, "Cannot produce scheduler when performing qualitative model checking only.");
// Prepare resulting vector.
std::vector<ValueType> result(transitionMatrix.getRowGroupCount(), 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 probablity 1 and 0, respectively.
QualitativeStateSetsUntilProbabilities qualitativeStateSets = getQualitativeStateSetsUntilProbabilities(goal, transitionMatrix, backwardTransitions, phiStates, psiStates, hint);
STORM_LOG_INFO("Preprocessing: " << qualitativeStateSets.statesWithProbability1.getNumberOfSetBits() << " states with probability 1, " << qualitativeStateSets.statesWithProbability0.getNumberOfSetBits() << " with probability 0 (" << qualitativeStateSets.maybeStates.getNumberOfSetBits() << " states remaining).");
// Set values of resulting vector that are known exactly.
storm::utility::vector::setVectorValues<ValueType>(result, qualitativeStateSets.statesWithProbability1, storm::utility::one<ValueType>());
// If requested, we will produce a scheduler.
std::unique_ptr<storm::storage::Scheduler<ValueType>> scheduler;
if (produceScheduler) {
scheduler = std::make_unique<storm::storage::Scheduler<ValueType>>(transitionMatrix.getRowGroupCount());
}
// 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, qualitativeStateSets.maybeStates, storm::utility::convertNumber<ValueType>(0.5));
} else {
if (!qualitativeStateSets.maybeStates.empty()) {
// In this case we have have to compute the remaining probabilities.
// Obtain proper hint information either from the provided hint or from requirements of the solver.
SparseMdpHintType<ValueType> hintInformation = computeHints(env, SolutionType::UntilProbabilities, hint, goal.direction(), transitionMatrix, backwardTransitions, qualitativeStateSets.maybeStates, phiStates, qualitativeStateSets.statesWithProbability1, produceScheduler);
// Declare the components of the equation system we will solve.
storm::storage::SparseMatrix<ValueType> submatrix;
std::vector<ValueType> b;
// If the hint information tells us that we have to eliminate MECs, we do so now.
boost::optional<SparseMdpEndComponentInformation<ValueType>> ecInformation;
if (hintInformation.getEliminateEndComponents()) {
ecInformation = computeFixedPointSystemUntilProbabilitiesEliminateEndComponents(goal, transitionMatrix, backwardTransitions, qualitativeStateSets, submatrix, b);
// Make sure we are not supposed to produce a scheduler if we actually eliminate end components.
STORM_LOG_THROW(!ecInformation || !ecInformation.get().getEliminatedEndComponents() || !produceScheduler, storm::exceptions::NotSupportedException, "Producing schedulers is not supported if end-components need to be eliminated for the solver.");
} else {
// Otherwise, we compute the standard equations.
computeFixedPointSystemUntilProbabilities(goal, transitionMatrix, qualitativeStateSets, submatrix, b);
}
// Now compute the results for the maybe states.
MaybeStateResult<ValueType> resultForMaybeStates = computeValuesForMaybeStates(env, std::move(goal), std::move(submatrix), b, produceScheduler, hintInformation);
// If we eliminated end components, we need to extract the result differently.
if (ecInformation && ecInformation.get().getEliminatedEndComponents()) {
ecInformation.get().setValues(result, qualitativeStateSets.maybeStates, resultForMaybeStates.getValues());
} else {
// Set values of resulting vector according to result.
storm::utility::vector::setVectorValues<ValueType>(result, qualitativeStateSets.maybeStates, resultForMaybeStates.getValues());
}
if (produceScheduler) {
extractSchedulerChoices(*scheduler, resultForMaybeStates.getScheduler(), qualitativeStateSets.maybeStates);
}
}
}
// Extend scheduler with choices for the states in the qualitative state sets.
if (produceScheduler) {
extendScheduler(*scheduler, goal, qualitativeStateSets, transitionMatrix, backwardTransitions, phiStates, psiStates);
}
// Sanity check for created scheduler.
STORM_LOG_ASSERT(!produceScheduler || scheduler, "Expected that a scheduler was obtained.");
STORM_LOG_ASSERT((!produceScheduler && !scheduler) || !scheduler->isPartialScheduler(), "Expected a fully defined scheduler");
STORM_LOG_ASSERT((!produceScheduler && !scheduler) || scheduler->isDeterministicScheduler(), "Expected a deterministic scheduler");
STORM_LOG_ASSERT((!produceScheduler && !scheduler) || scheduler->isMemorylessScheduler(), "Expected a memoryless scheduler");
// Return result.
return MDPSparseModelCheckingHelperReturnType<ValueType>(std::move(result), std::move(scheduler));
}
template<typename ValueType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::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, bool useMecBasedTechnique) {
if (useMecBasedTechnique) {
storm::storage::MaximalEndComponentDecomposition<ValueType> mecDecomposition(transitionMatrix, backwardTransitions, psiStates);
storm::storage::BitVector statesInPsiMecs(transitionMatrix.getRowGroupCount());
for (auto const& mec : mecDecomposition) {
for (auto const& stateActionsPair : mec) {
statesInPsiMecs.set(stateActionsPair.first, true);
}
}
return std::move(computeUntilProbabilities(env, std::move(goal), transitionMatrix, backwardTransitions, psiStates, statesInPsiMecs, qualitative, false).values);
} else {
goal.oneMinus();
std::vector<ValueType> result = computeUntilProbabilities(env, std::move(goal), transitionMatrix, backwardTransitions, storm::storage::BitVector(transitionMatrix.getRowGroupCount(), true), ~psiStates, qualitative, false).values;
for (auto& element : result) {
element = storm::utility::one<ValueType>() - element;
}
return std::move(result);
}
}
template<typename ValueType>
template<typename RewardModelType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::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 this->getModel().
std::vector<ValueType> result(rewardModel.getStateRewardVector());
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, transitionMatrix);
multiplier->repeatedMultiplyAndReduce(env, goal.direction(), result, nullptr, stepCount);
return result;
}
template<typename ValueType>
template<typename RewardModelType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeCumulativeRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, uint_fast64_t stepBound) {
// Only compute the result if the model has at least one reward this->getModel().
STORM_LOG_THROW(!rewardModel.empty(), storm::exceptions::InvalidPropertyException, "Missing reward model for formula. Skipping formula.");
// Compute the reward vector to add in each step based on the available reward models.
std::vector<ValueType> totalRewardVector = rewardModel.getTotalRewardVector(transitionMatrix);
// Initialize result to the zero vector.
std::vector<ValueType> result(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, transitionMatrix);
multiplier->repeatedMultiplyAndReduce(env, goal.direction(), result, &totalRewardVector, stepBound);
return result;
}
template<typename ValueType>
template<typename RewardModelType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::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, bool produceScheduler, ModelCheckerHint const& hint) {
// Reduce to reachability rewards
if (goal.minimize()) {
STORM_LOG_ERROR_COND(!produceScheduler, "Can not produce scheduler for this property (functionality not implemented");
// Identify the states from which no reward can be collected under some scheduler
storm::storage::BitVector choicesWithoutReward = rewardModel.getChoicesWithZeroReward(transitionMatrix);
storm::storage::BitVector statesWithZeroRewardChoice(transitionMatrix.getRowGroupCount(), false);
for (uint64_t state = 0; state < transitionMatrix.getRowGroupCount(); ++state) {
if (choicesWithoutReward.getNextSetIndex(transitionMatrix.getRowGroupIndices()[state])< transitionMatrix.getRowGroupIndices()[state + 1]) {
statesWithZeroRewardChoice.set(state);
}
}
storm::storage::BitVector rew0EStates = storm::utility::graph::performProbGreater0A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, statesWithZeroRewardChoice, ~statesWithZeroRewardChoice, false, 0, choicesWithoutReward);
rew0EStates.complement();
return computeReachabilityRewards(env, std::move(goal), transitionMatrix, backwardTransitions, rewardModel, rew0EStates, qualitative, false, hint);
} else {
// Identify the states from which only states with zero reward are reachable.
storm::storage::BitVector statesWithoutReward = rewardModel.getStatesWithZeroReward(transitionMatrix);
storm::storage::BitVector rew0AStates = storm::utility::graph::performProbGreater0E(backwardTransitions, statesWithoutReward, ~statesWithoutReward);
rew0AStates.complement();
// There might be end components that consists only of states/choices with zero rewards. The reachability reward semantics would assign such
// end components reward infinity. To avoid this, we potentially need to eliminate such end components
storm::storage::BitVector trueStates(transitionMatrix.getRowGroupCount(), true);
if (storm::utility::graph::performProb1A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, trueStates, rew0AStates).full()) {
return computeReachabilityRewards(env, std::move(goal), transitionMatrix, backwardTransitions, rewardModel, rew0AStates, qualitative, produceScheduler, hint);
} else {
// The transformation of schedulers for the ec-eliminated system back to the original one is not implemented.
STORM_LOG_ERROR_COND(!produceScheduler, "Can not produce scheduler for this property (functionality not implemented");
storm::storage::BitVector choicesWithoutReward = rewardModel.getChoicesWithZeroReward(transitionMatrix);
auto ecElimResult = storm::transformer::EndComponentEliminator<ValueType>::transform(transitionMatrix, storm::storage::BitVector(transitionMatrix.getRowGroupCount(), true), choicesWithoutReward, rew0AStates, true);
storm::storage::BitVector newRew0AStates(ecElimResult.matrix.getRowGroupCount(), false);
for (auto const& oldRew0AState : rew0AStates) {
newRew0AStates.set(ecElimResult.oldToNewStateMapping[oldRew0AState]);
}
MDPSparseModelCheckingHelperReturnType<ValueType> result = computeReachabilityRewardsHelper(env, std::move(goal), ecElimResult.matrix, ecElimResult.matrix.transpose(true),
[&] (uint_fast64_t rowCount, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& maybeStates) {
std::vector<ValueType> result;
std::vector<ValueType> oldChoiceRewards = rewardModel.getTotalRewardVector(transitionMatrix);
result.reserve(rowCount);
for (uint64_t newState : maybeStates) {
for (uint64_t newChoice = transitionMatrix.getRowGroupIndices()[newState]; newChoice < transitionMatrix.getRowGroupIndices()[newState + 1]; ++newChoice) {
uint64_t oldChoice = ecElimResult.newToOldRowMapping[newChoice];
result.push_back(oldChoiceRewards[oldChoice]);
}
}
STORM_LOG_ASSERT(result.size() == rowCount, "Unexpected size of reward vector.");
return result;
}, newRew0AStates, qualitative, false,
[&] () {
storm::storage::BitVector newStatesWithoutReward(ecElimResult.matrix.getRowGroupCount(), false);
for (auto const& oldStateWithoutRew : statesWithoutReward) {
newStatesWithoutReward.set(ecElimResult.oldToNewStateMapping[oldStateWithoutRew]);
}
return newStatesWithoutReward;
},
[&] () {
storm::storage::BitVector newChoicesWithoutReward(ecElimResult.matrix.getRowGroupCount(), false);
for (uint64_t newChoice = 0; newChoice < ecElimResult.matrix.getRowCount(); ++newChoice) {
if (choicesWithoutReward.get(ecElimResult.newToOldRowMapping[newChoice])) {
newChoicesWithoutReward.set(newChoice);
}
}
return newChoicesWithoutReward;
});
std::vector<ValueType> resultInEcQuotient = std::move(result.values);
result.values.resize(ecElimResult.oldToNewStateMapping.size());
storm::utility::vector::selectVectorValues(result.values, ecElimResult.oldToNewStateMapping, resultInEcQuotient);
return result;
}
}
}
template<typename ValueType>
template<typename RewardModelType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::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, bool produceScheduler, ModelCheckerHint const& hint) {
// Only compute the result if the model has at least one reward this->getModel().
STORM_LOG_THROW(!rewardModel.empty(), storm::exceptions::InvalidPropertyException, "Reward model for formula is empty. Skipping formula.");
return computeReachabilityRewardsHelper(env, std::move(goal), transitionMatrix, backwardTransitions,
[&rewardModel] (uint_fast64_t rowCount, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& maybeStates) {
return rewardModel.getTotalRewardVector(rowCount, transitionMatrix, maybeStates);
},
targetStates, qualitative, produceScheduler,
[&] () {
return rewardModel.getStatesWithZeroReward(transitionMatrix);
},
[&] () {
return rewardModel.getChoicesWithZeroReward(transitionMatrix);
},
hint);
}
template<typename ValueType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::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, bool produceScheduler, ModelCheckerHint const& hint) {
return computeReachabilityRewardsHelper(env, std::move(goal), transitionMatrix, backwardTransitions,
[] (uint_fast64_t rowCount, storm::storage::SparseMatrix<ValueType> const&, storm::storage::BitVector const&) {
return std::vector<ValueType>(rowCount, storm::utility::one<ValueType>());
},
targetStates, qualitative, produceScheduler,
[&] () {
return storm::storage::BitVector(transitionMatrix.getRowGroupCount(), false);
},
[&] () {
return storm::storage::BitVector(transitionMatrix.getRowCount(), false);
},
hint);
}
#ifdef STORM_HAVE_CARL
template<typename ValueType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::models::sparse::StandardRewardModel<storm::Interval> const& intervalRewardModel, bool lowerBoundOfIntervals, storm::storage::BitVector const& targetStates, bool qualitative) {
// Only compute the result if the reward model is not empty.
STORM_LOG_THROW(!intervalRewardModel.empty(), storm::exceptions::InvalidPropertyException, "Missing reward model for formula. Skipping formula.");
return computeReachabilityRewardsHelper(env, std::move(goal), transitionMatrix, backwardTransitions, \
[&] (uint_fast64_t rowCount, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& maybeStates) {
std::vector<ValueType> result;
result.reserve(rowCount);
std::vector<storm::Interval> subIntervalVector = intervalRewardModel.getTotalRewardVector(rowCount, transitionMatrix, maybeStates);
for (auto const& interval : subIntervalVector) {
result.push_back(lowerBoundOfIntervals ? interval.lower() : interval.upper());
}
return result;
},
targetStates, qualitative, false,
[&] () {
return intervalRewardModel.getStatesWithFilter(transitionMatrix, [&](storm::Interval const& i) {return storm::utility::isZero(lowerBoundOfIntervals ? i.lower() : i.upper());});
},
[&] () {
return intervalRewardModel.getChoicesWithFilter(transitionMatrix, [&](storm::Interval const& i) {return storm::utility::isZero(lowerBoundOfIntervals ? i.lower() : i.upper());});
}).values;
}
template<>
std::vector<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&&, storm::storage::SparseMatrix<storm::RationalNumber> const&, storm::storage::SparseMatrix<storm::RationalNumber> const&, storm::models::sparse::StandardRewardModel<storm::Interval> const&, bool, storm::storage::BitVector const&, bool) {
STORM_LOG_THROW(false, storm::exceptions::IllegalFunctionCallException, "Computing reachability rewards is unsupported for this data type.");
}
#endif
struct QualitativeStateSetsReachabilityRewards {
storm::storage::BitVector maybeStates;
storm::storage::BitVector infinityStates;
storm::storage::BitVector rewardZeroStates;
};
template<typename ValueType>
QualitativeStateSetsReachabilityRewards getQualitativeStateSetsReachabilityRewardsFromHint(ModelCheckerHint const& hint, storm::storage::BitVector const& targetStates) {
QualitativeStateSetsReachabilityRewards result;
result.maybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getMaybeStates();
// Treat the states with reward zero/infinity.
std::vector<ValueType> const& resultsForNonMaybeStates = hint.template asExplicitModelCheckerHint<ValueType>().getResultHint();
result.infinityStates = storm::storage::BitVector(result.maybeStates.size());
result.rewardZeroStates = storm::storage::BitVector(result.maybeStates.size());
storm::storage::BitVector nonMaybeStates = ~result.maybeStates;
for (auto const& state : nonMaybeStates) {
if (storm::utility::isZero(resultsForNonMaybeStates[state])) {
result.rewardZeroStates.set(state, true);
} else {
STORM_LOG_THROW(storm::utility::isInfinity(resultsForNonMaybeStates[state]), storm::exceptions::IllegalArgumentException, "Expected that the result hint specifies probabilities in {0,infinity} for non-maybe states");
result.infinityStates.set(state, true);
}
}
return result;
}
template<typename ValueType>
QualitativeStateSetsReachabilityRewards computeQualitativeStateSetsReachabilityRewards(storm::solver::SolveGoal<ValueType> const& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& targetStates, std::function<storm::storage::BitVector()> const& zeroRewardStatesGetter, std::function<storm::storage::BitVector()> const& zeroRewardChoicesGetter) {
QualitativeStateSetsReachabilityRewards result;
storm::storage::BitVector trueStates(transitionMatrix.getRowGroupCount(), true);
if (goal.minimize()) {
result.infinityStates = storm::utility::graph::performProb1E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, trueStates, targetStates);
} else {
result.infinityStates = storm::utility::graph::performProb1A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, trueStates, targetStates);
}
result.infinityStates.complement();
if (storm::settings::getModule<storm::settings::modules::ModelCheckerSettings>().isFilterRewZeroSet()) {
if (goal.minimize()) {
result.rewardZeroStates = storm::utility::graph::performProb1E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, trueStates, targetStates, zeroRewardChoicesGetter());
} else {
result.rewardZeroStates = storm::utility::graph::performProb1A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, zeroRewardStatesGetter(), targetStates);
}
} else {
result.rewardZeroStates = targetStates;
}
result.maybeStates = ~(result.rewardZeroStates | result.infinityStates);
return result;
}
template<typename ValueType>
QualitativeStateSetsReachabilityRewards getQualitativeStateSetsReachabilityRewards(storm::solver::SolveGoal<ValueType> const& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& targetStates, ModelCheckerHint const& hint, std::function<storm::storage::BitVector()> const& zeroRewardStatesGetter, std::function<storm::storage::BitVector()> const& zeroRewardChoicesGetter) {
if (hint.isExplicitModelCheckerHint() && hint.template asExplicitModelCheckerHint<ValueType>().getComputeOnlyMaybeStates()) {
return getQualitativeStateSetsReachabilityRewardsFromHint<ValueType>(hint, targetStates);
} else {
return computeQualitativeStateSetsReachabilityRewards(goal, transitionMatrix, backwardTransitions, targetStates, zeroRewardStatesGetter, zeroRewardChoicesGetter);
}
}
template<typename ValueType>
void extendScheduler(storm::storage::Scheduler<ValueType>& scheduler, storm::solver::SolveGoal<ValueType> const& goal, QualitativeStateSetsReachabilityRewards const& qualitativeStateSets, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& targetStates, std::function<storm::storage::BitVector()> const& zeroRewardChoicesGetter) {
// Finally, if we need to produce a scheduler, we also need to figure out the parts of the scheduler for
// the states with reward zero/infinity.
if (goal.minimize()) {
storm::utility::graph::computeSchedulerProb1E(qualitativeStateSets.rewardZeroStates, transitionMatrix, backwardTransitions, qualitativeStateSets.rewardZeroStates, targetStates, scheduler, zeroRewardChoicesGetter());
for (auto const& state : qualitativeStateSets.infinityStates) {
scheduler.setChoice(0, state);
}
} else {
storm::utility::graph::computeSchedulerRewInf(qualitativeStateSets.infinityStates, transitionMatrix, scheduler);
for (auto const& state : qualitativeStateSets.rewardZeroStates) {
scheduler.setChoice(0, state);
}
}
}
template<typename ValueType>
void extractSchedulerChoices(storm::storage::Scheduler<ValueType>& scheduler, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<uint_fast64_t> const& subChoices, storm::storage::BitVector const& maybeStates, boost::optional<storm::storage::BitVector> const& selectedChoices) {
auto subChoiceIt = subChoices.begin();
if (selectedChoices) {
for (auto maybeState : maybeStates) {
// find the rowindex that corresponds to the selected row of the submodel
uint_fast64_t firstRowIndex = transitionMatrix.getRowGroupIndices()[maybeState];
uint_fast64_t selectedRowIndex = selectedChoices->getNextSetIndex(firstRowIndex);
for (uint_fast64_t choice = 0; choice < *subChoiceIt; ++choice) {
selectedRowIndex = selectedChoices->getNextSetIndex(selectedRowIndex + 1);
}
scheduler.setChoice(selectedRowIndex - firstRowIndex, maybeState);
++subChoiceIt;
}
} else {
for (auto maybeState : maybeStates) {
scheduler.setChoice(*subChoiceIt, maybeState);
++subChoiceIt;
}
}
assert(subChoiceIt == subChoices.end());
}
template<typename ValueType>
void computeFixedPointSystemReachabilityRewards(storm::solver::SolveGoal<ValueType>& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, QualitativeStateSetsReachabilityRewards const& qualitativeStateSets, boost::optional<storm::storage::BitVector> const& selectedChoices, std::function<std::vector<ValueType>(uint_fast64_t, storm::storage::SparseMatrix<ValueType> const&, storm::storage::BitVector const&)> const& totalStateRewardVectorGetter, storm::storage::SparseMatrix<ValueType>& submatrix, std::vector<ValueType>& b, std::vector<ValueType>* oneStepTargetProbabilities = nullptr) {
// Remove rows and columns from the original transition probability matrix for states whose reward values are already known.
// If there are infinity states, we additionally have to remove choices of maybeState that lead to infinity.
if (qualitativeStateSets.infinityStates.empty()) {
submatrix = transitionMatrix.getSubmatrix(true, qualitativeStateSets.maybeStates, qualitativeStateSets.maybeStates, false);
b = totalStateRewardVectorGetter(submatrix.getRowCount(), transitionMatrix, qualitativeStateSets.maybeStates);
if (oneStepTargetProbabilities) {
(*oneStepTargetProbabilities) = transitionMatrix.getConstrainedRowGroupSumVector(qualitativeStateSets.maybeStates, qualitativeStateSets.rewardZeroStates);
}
} else {
submatrix = transitionMatrix.getSubmatrix(false, *selectedChoices, qualitativeStateSets.maybeStates, false);
b = totalStateRewardVectorGetter(transitionMatrix.getRowCount(), transitionMatrix, storm::storage::BitVector(transitionMatrix.getRowGroupCount(), true));
storm::utility::vector::filterVectorInPlace(b, *selectedChoices);
if (oneStepTargetProbabilities) {
(*oneStepTargetProbabilities) = transitionMatrix.getConstrainedRowSumVector(*selectedChoices, qualitativeStateSets.rewardZeroStates);
}
}
// If the solve goal has relevant values, we need to adjust them.
goal.restrictRelevantValues(qualitativeStateSets.maybeStates);
}
template<typename ValueType>
boost::optional<SparseMdpEndComponentInformation<ValueType>> computeFixedPointSystemReachabilityRewardsEliminateEndComponents(storm::solver::SolveGoal<ValueType>& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, QualitativeStateSetsReachabilityRewards const& qualitativeStateSets, boost::optional<storm::storage::BitVector> const& selectedChoices, std::function<std::vector<ValueType>(uint_fast64_t, storm::storage::SparseMatrix<ValueType> const&, storm::storage::BitVector const&)> const& totalStateRewardVectorGetter, storm::storage::SparseMatrix<ValueType>& submatrix, std::vector<ValueType>& b, boost::optional<std::vector<ValueType>>& oneStepTargetProbabilities) {
// Start by computing the choices with reward 0, as we only want ECs within this fragment.
storm::storage::BitVector zeroRewardChoices(transitionMatrix.getRowCount());
// Get the rewards of all choices.
std::vector<ValueType> rewardVector = totalStateRewardVectorGetter(transitionMatrix.getRowCount(), transitionMatrix, storm::storage::BitVector(transitionMatrix.getRowGroupCount(), true));
uint64_t index = 0;
for (auto const& e : rewardVector) {
if (storm::utility::isZero(e)) {
zeroRewardChoices.set(index);
}
++index;
}
// Compute the states that have some zero reward choice.
storm::storage::BitVector candidateStates(qualitativeStateSets.maybeStates);
for (auto state : qualitativeStateSets.maybeStates) {
bool keepState = false;
for (auto row = transitionMatrix.getRowGroupIndices()[state], rowEnd = transitionMatrix.getRowGroupIndices()[state + 1]; row < rowEnd; ++row) {
if (zeroRewardChoices.get(row)) {
keepState = true;
break;
}
}
if (!keepState) {
candidateStates.set(state, false);
}
}
// Only keep the candidate states that (under some scheduler) can stay in the set of candidates forever
candidateStates = storm::utility::graph::performProb0E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, candidateStates, ~candidateStates);
bool doDecomposition = !candidateStates.empty();
storm::storage::MaximalEndComponentDecomposition<ValueType> endComponentDecomposition;
if (doDecomposition) {
// Then compute the states that are in MECs with zero reward.
endComponentDecomposition = storm::storage::MaximalEndComponentDecomposition<ValueType>(transitionMatrix, backwardTransitions, candidateStates, zeroRewardChoices);
}
// Only do more work if there are actually end-components.
if (doDecomposition && !endComponentDecomposition.empty()) {
STORM_LOG_DEBUG("Eliminating " << endComponentDecomposition.size() << " ECs.");
SparseMdpEndComponentInformation<ValueType> result = SparseMdpEndComponentInformation<ValueType>::eliminateEndComponents(endComponentDecomposition, transitionMatrix, qualitativeStateSets.maybeStates, oneStepTargetProbabilities ? &qualitativeStateSets.rewardZeroStates : nullptr, selectedChoices ? &selectedChoices.get() : nullptr, &rewardVector, submatrix, oneStepTargetProbabilities ? &oneStepTargetProbabilities.get() : nullptr, &b);
// If the solve goal has relevant values, we need to adjust them.
if (goal.hasRelevantValues()) {
storm::storage::BitVector newRelevantValues(submatrix.getRowGroupCount());
for (auto state : goal.relevantValues()) {
if (qualitativeStateSets.maybeStates.get(state)) {
newRelevantValues.set(result.getRowGroupAfterElimination(state));
}
}
if (!newRelevantValues.empty()) {
goal.setRelevantValues(std::move(newRelevantValues));
}
}
return result;
} else {
STORM_LOG_DEBUG("Not eliminating ECs as there are none.");
computeFixedPointSystemReachabilityRewards(goal, transitionMatrix, qualitativeStateSets, selectedChoices, totalStateRewardVectorGetter, submatrix, b, oneStepTargetProbabilities ? &oneStepTargetProbabilities.get() : nullptr);
return boost::none;
}
}
template<typename ValueType>
void computeUpperRewardBounds(SparseMdpHintType<ValueType>& hintInformation, storm::OptimizationDirection const& direction, storm::storage::SparseMatrix<ValueType> const& submatrix, std::vector<ValueType> const& choiceRewards, std::vector<ValueType> const& oneStepTargetProbabilities) {
// For the min-case, we use DS-MPI, for the max-case variant 2 of the Baier et al. paper (CAV'17).
if (direction == storm::OptimizationDirection::Minimize) {
DsMpiMdpUpperRewardBoundsComputer<ValueType> dsmpi(submatrix, choiceRewards, oneStepTargetProbabilities);
hintInformation.upperResultBounds = dsmpi.computeUpperBounds();
} else {
BaierUpperRewardBoundsComputer<ValueType> baier(submatrix, choiceRewards, oneStepTargetProbabilities);
hintInformation.upperResultBound = baier.computeUpperBound();
}
}
template<typename ValueType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::computeReachabilityRewardsHelper(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, bool produceScheduler, std::function<storm::storage::BitVector()> const& zeroRewardStatesGetter, std::function<storm::storage::BitVector()> const& zeroRewardChoicesGetter, ModelCheckerHint const& hint) {
// Prepare resulting vector.
std::vector<ValueType> result(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
// Determine which states have a reward that is infinity or less than infinity.
QualitativeStateSetsReachabilityRewards qualitativeStateSets = getQualitativeStateSetsReachabilityRewards(goal, transitionMatrix, backwardTransitions, targetStates, hint, zeroRewardStatesGetter, zeroRewardChoicesGetter);
STORM_LOG_INFO("Preprocessing: " << qualitativeStateSets.infinityStates.getNumberOfSetBits() << " states with reward infinity, " << qualitativeStateSets.rewardZeroStates.getNumberOfSetBits() << " states with reward zero (" << qualitativeStateSets.maybeStates.getNumberOfSetBits() << " states remaining).");
storm::utility::vector::setVectorValues(result, qualitativeStateSets.infinityStates, storm::utility::infinity<ValueType>());
// If requested, we will produce a scheduler.
std::unique_ptr<storm::storage::Scheduler<ValueType>> scheduler;
if (produceScheduler) {
scheduler = std::make_unique<storm::storage::Scheduler<ValueType>>(transitionMatrix.getRowGroupCount());
}
// Check whether we need to compute exact rewards for some states.
if (qualitative) {
STORM_LOG_INFO("The rewards for the initial states were determined in a preprocessing step. No exact rewards were computed.");
// 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, qualitativeStateSets.maybeStates, storm::utility::one<ValueType>());
} else {
if (!qualitativeStateSets.maybeStates.empty()) {
// In this case we have to compute the reward values for the remaining states.
// Store the choices that lead to non-infinity values. If none, all choices im maybe states can be selected.
boost::optional<storm::storage::BitVector> selectedChoices;
if (!qualitativeStateSets.infinityStates.empty()) {
selectedChoices = transitionMatrix.getRowFilter(qualitativeStateSets.maybeStates, ~qualitativeStateSets.infinityStates);
}
// Obtain proper hint information either from the provided hint or from requirements of the solver.
SparseMdpHintType<ValueType> hintInformation = computeHints(env, SolutionType::ExpectedRewards, hint, goal.direction(), transitionMatrix, backwardTransitions, qualitativeStateSets.maybeStates, ~qualitativeStateSets.rewardZeroStates, qualitativeStateSets.rewardZeroStates, produceScheduler, selectedChoices);
// Declare the components of the equation system we will solve.
storm::storage::SparseMatrix<ValueType> submatrix;
std::vector<ValueType> b;
// If we need to compute upper bounds on the reward values, we need the one step probabilities
// to a target state.
boost::optional<std::vector<ValueType>> oneStepTargetProbabilities;
if (hintInformation.getComputeUpperBounds()) {
oneStepTargetProbabilities = std::vector<ValueType>();
}
// If the hint information tells us that we have to eliminate MECs, we do so now.
boost::optional<SparseMdpEndComponentInformation<ValueType>> ecInformation;
if (hintInformation.getEliminateEndComponents()) {
ecInformation = computeFixedPointSystemReachabilityRewardsEliminateEndComponents(goal, transitionMatrix, backwardTransitions, qualitativeStateSets, selectedChoices, totalStateRewardVectorGetter, submatrix, b, oneStepTargetProbabilities);
// Make sure we are not supposed to produce a scheduler if we actually eliminate end components.
STORM_LOG_THROW(!ecInformation || !ecInformation.get().getEliminatedEndComponents() || !produceScheduler, storm::exceptions::NotSupportedException, "Producing schedulers is not supported if end-components need to be eliminated for the solver.");
} else {
// Otherwise, we compute the standard equations.
computeFixedPointSystemReachabilityRewards(goal, transitionMatrix, qualitativeStateSets, selectedChoices, totalStateRewardVectorGetter, submatrix, b, oneStepTargetProbabilities ? &oneStepTargetProbabilities.get() : nullptr);
}
// If we need to compute upper bounds, do so now.
if (hintInformation.getComputeUpperBounds()) {
STORM_LOG_ASSERT(oneStepTargetProbabilities, "Expecting one step target probability vector to be available.");
computeUpperRewardBounds(hintInformation, goal.direction(), submatrix, b, oneStepTargetProbabilities.get());
}
// Now compute the results for the maybe states.
MaybeStateResult<ValueType> resultForMaybeStates = computeValuesForMaybeStates(env, std::move(goal), std::move(submatrix), b, produceScheduler, hintInformation);
// If we eliminated end components, we need to extract the result differently.
if (ecInformation && ecInformation.get().getEliminatedEndComponents()) {
ecInformation.get().setValues(result, qualitativeStateSets.maybeStates, resultForMaybeStates.getValues());
} else {
// Set values of resulting vector according to result.
storm::utility::vector::setVectorValues<ValueType>(result, qualitativeStateSets.maybeStates, resultForMaybeStates.getValues());
}
if (produceScheduler) {
extractSchedulerChoices(*scheduler, transitionMatrix, resultForMaybeStates.getScheduler(), qualitativeStateSets.maybeStates, selectedChoices);
}
}
}
// Extend scheduler with choices for the states in the qualitative state sets.
if (produceScheduler) {
extendScheduler(*scheduler, goal, qualitativeStateSets, transitionMatrix, backwardTransitions, targetStates, zeroRewardChoicesGetter);
}
// Sanity check for created scheduler.
STORM_LOG_ASSERT(!produceScheduler || scheduler, "Expected that a scheduler was obtained.");
STORM_LOG_ASSERT((!produceScheduler && !scheduler) || !scheduler->isPartialScheduler(), "Expected a fully defined scheduler");
STORM_LOG_ASSERT((!produceScheduler && !scheduler) || scheduler->isDeterministicScheduler(), "Expected a deterministic scheduler");
STORM_LOG_ASSERT((!produceScheduler && !scheduler) || scheduler->isMemorylessScheduler(), "Expected a memoryless scheduler");
return MDPSparseModelCheckingHelperReturnType<ValueType>(std::move(result), std::move(scheduler));
}
template<typename ValueType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::computeLongRunAverageProbabilities(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 produceScheduler) {
// If there are no goal states, we avoid the computation and directly return zero.
if (psiStates.empty()) {
return std::vector<ValueType>(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
}
// Likewise, if all bits are set, we can avoid the computation and set.
if (psiStates.full()) {
return std::vector<ValueType>(transitionMatrix.getRowGroupCount(), storm::utility::one<ValueType>());
}
// Reduce long run average probabilities to long run average rewards by
// building a reward model assigning one reward to every psi state
std::vector<ValueType> stateRewards(psiStates.size(), storm::utility::zero<ValueType>());
storm::utility::vector::setVectorValues(stateRewards, psiStates, storm::utility::one<ValueType>());
storm::models::sparse::StandardRewardModel<ValueType> rewardModel(std::move(stateRewards));
return computeLongRunAverageRewards(env, std::move(goal), transitionMatrix, backwardTransitions, rewardModel, produceScheduler);
}
template<typename ValueType>
template<typename RewardModelType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::computeLongRunAverageRewards(Environment const& env, storm::solver::SolveGoal<ValueType>&& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, RewardModelType const& rewardModel, bool produceScheduler) {
uint64_t numberOfStates = transitionMatrix.getRowGroupCount();
std::unique_ptr<storm::storage::Scheduler<ValueType>> scheduler;
if (produceScheduler) {
scheduler = std::make_unique<storm::storage::Scheduler<ValueType>>(numberOfStates);
}
// Start by decomposing the MDP into its MECs.
storm::storage::MaximalEndComponentDecomposition<ValueType> mecDecomposition(transitionMatrix, backwardTransitions);
// Get some data members for convenience.
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
ValueType zero = storm::utility::zero<ValueType>();
//first calculate LRA for the Maximal End Components.
storm::storage::BitVector statesInMecs(numberOfStates);
std::vector<uint_fast64_t> stateToMecIndexMap(transitionMatrix.getColumnCount());
std::vector<ValueType> lraValuesForEndComponents(mecDecomposition.size(), zero);
auto underlyingSolverEnvironment = env;
if (env.solver().isForceSoundness()) {
// For sound computations, the error in the MECS plus the error in the remaining system should be less than the user defined precsion.
underlyingSolverEnvironment.solver().lra().setPrecision(env.solver().lra().getPrecision() / storm::utility::convertNumber<storm::RationalNumber>(2));
underlyingSolverEnvironment.solver().minMax().setPrecision(env.solver().lra().getPrecision() / storm::utility::convertNumber<storm::RationalNumber>(2));
underlyingSolverEnvironment.solver().minMax().setRelativeTerminationCriterion(env.solver().lra().getRelativeTerminationCriterion());
}
for (uint_fast64_t currentMecIndex = 0; currentMecIndex < mecDecomposition.size(); ++currentMecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[currentMecIndex];
lraValuesForEndComponents[currentMecIndex] = computeLraForMaximalEndComponent(underlyingSolverEnvironment, goal.direction(), transitionMatrix, rewardModel, mec, scheduler);
// Gather information for later use.
for (auto const& stateChoicesPair : mec) {
statesInMecs.set(stateChoicesPair.first);
stateToMecIndexMap[stateChoicesPair.first] = currentMecIndex;
}
}
// For fast transition rewriting, we build some auxiliary data structures.
storm::storage::BitVector statesNotContainedInAnyMec = ~statesInMecs;
uint_fast64_t firstAuxiliaryStateIndex = statesNotContainedInAnyMec.getNumberOfSetBits();
uint_fast64_t lastStateNotInMecs = 0;
uint_fast64_t numberOfStatesNotInMecs = 0;
std::vector<uint_fast64_t> statesNotInMecsBeforeIndex;
statesNotInMecsBeforeIndex.reserve(numberOfStates);
for (auto state : statesNotContainedInAnyMec) {
while (lastStateNotInMecs <= state) {
statesNotInMecsBeforeIndex.push_back(numberOfStatesNotInMecs);
++lastStateNotInMecs;
}
++numberOfStatesNotInMecs;
}
// Finally, we are ready to create the SSP matrix and right-hand side of the SSP.
std::vector<ValueType> b;
uint64_t numberOfSspStates = numberOfStatesNotInMecs + mecDecomposition.size();
typename storm::storage::SparseMatrixBuilder<ValueType> sspMatrixBuilder(0, numberOfSspStates, 0, false, true, numberOfSspStates);
// If the source state is not contained in any MEC, we copy its choices (and perform the necessary modifications).
uint_fast64_t currentChoice = 0;
for (auto state : statesNotContainedInAnyMec) {
sspMatrixBuilder.newRowGroup(currentChoice);
for (uint_fast64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice, ++currentChoice) {
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
b.push_back(storm::utility::zero<ValueType>());
for (auto element : transitionMatrix.getRow(choice)) {
if (statesNotContainedInAnyMec.get(element.getColumn())) {
// If the target state is not contained in an MEC, we can copy over the entry.
sspMatrixBuilder.addNextValue(currentChoice, statesNotInMecsBeforeIndex[element.getColumn()], element.getValue());
} else {
// If the target state is contained in MEC i, we need to add the probability to the corresponding field in the vector
// so that we are able to write the cumulative probability to the MEC into the matrix.
auxiliaryStateToProbabilityMap[stateToMecIndexMap[element.getColumn()]] += element.getValue();
}
}
// Now insert all (cumulative) probability values that target an MEC.
for (uint_fast64_t mecIndex = 0; mecIndex < auxiliaryStateToProbabilityMap.size(); ++mecIndex) {
if (!storm::utility::isZero(auxiliaryStateToProbabilityMap[mecIndex])) {
sspMatrixBuilder.addNextValue(currentChoice, firstAuxiliaryStateIndex + mecIndex, auxiliaryStateToProbabilityMap[mecIndex]);
}
}
}
}
std::vector<std::pair<uint_fast64_t, uint_fast64_t>> sspMecChoicesToOriginalMap; // for scheduler extraction
// Now we are ready to construct the choices for the auxiliary states.
for (uint_fast64_t mecIndex = 0; mecIndex < mecDecomposition.size(); ++mecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[mecIndex];
sspMatrixBuilder.newRowGroup(currentChoice);
for (auto const& stateChoicesPair : mec) {
uint_fast64_t state = stateChoicesPair.first;
storm::storage::FlatSet<uint_fast64_t> const& choicesInMec = stateChoicesPair.second;
for (uint_fast64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice) {
// If the choice is not contained in the MEC itself, we have to add a similar distribution to the auxiliary state.
if (choicesInMec.find(choice) == choicesInMec.end()) {
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
b.push_back(storm::utility::zero<ValueType>());
for (auto element : transitionMatrix.getRow(choice)) {
if (statesNotContainedInAnyMec.get(element.getColumn())) {
// If the target state is not contained in an MEC, we can copy over the entry.
sspMatrixBuilder.addNextValue(currentChoice, statesNotInMecsBeforeIndex[element.getColumn()], element.getValue());
} else {
// If the target state is contained in MEC i, we need to add the probability to the corresponding field in the vector
// so that we are able to write the cumulative probability to the MEC into the matrix.
auxiliaryStateToProbabilityMap[stateToMecIndexMap[element.getColumn()]] += element.getValue();
}
}
// Now insert all (cumulative) probability values that target an MEC.
for (uint_fast64_t targetMecIndex = 0; targetMecIndex < auxiliaryStateToProbabilityMap.size(); ++targetMecIndex) {
if (!storm::utility::isZero(auxiliaryStateToProbabilityMap[targetMecIndex])) {
sspMatrixBuilder.addNextValue(currentChoice, firstAuxiliaryStateIndex + targetMecIndex, auxiliaryStateToProbabilityMap[targetMecIndex]);
}
}
if (produceScheduler) {
sspMecChoicesToOriginalMap.emplace_back(state, choice - nondeterministicChoiceIndices[state]);
}
++currentChoice;
}
}
}
// For each auxiliary state, there is the option to achieve the reward value of the LRA associated with the MEC.
++currentChoice;
b.push_back(lraValuesForEndComponents[mecIndex]);
if (produceScheduler) {
// Insert some invalid values
sspMecChoicesToOriginalMap.emplace_back(std::numeric_limits<uint_fast64_t>::max(), std::numeric_limits<uint_fast64_t>::max());
}
}
// Finalize the matrix and solve the corresponding system of equations.
storm::storage::SparseMatrix<ValueType> sspMatrix = sspMatrixBuilder.build(currentChoice, numberOfSspStates, numberOfSspStates);
// Check for requirements of the solver.
storm::solver::GeneralMinMaxLinearEquationSolverFactory<ValueType> minMaxLinearEquationSolverFactory;
storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(underlyingSolverEnvironment, true, true, goal.direction(), false, produceScheduler);
requirements.clearBounds();
STORM_LOG_THROW(!requirements.hasEnabledCriticalRequirement(), storm::exceptions::UncheckedRequirementException, "Solver requirements " + requirements.getEnabledRequirementsAsString() + " not checked.");
std::vector<ValueType> sspResult(numberOfSspStates);
goal.restrictRelevantValues(statesNotContainedInAnyMec);
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = storm::solver::configureMinMaxLinearEquationSolver(underlyingSolverEnvironment, std::move(goal), minMaxLinearEquationSolverFactory, sspMatrix);
solver->setLowerBound(storm::utility::zero<ValueType>());
solver->setUpperBound(*std::max_element(lraValuesForEndComponents.begin(), lraValuesForEndComponents.end()));
solver->setHasUniqueSolution();
solver->setHasNoEndComponents();
solver->setTrackScheduler(produceScheduler);
solver->setRequirementsChecked();
solver->solveEquations(underlyingSolverEnvironment, sspResult, b);
// Prepare result vector.
std::vector<ValueType> result(numberOfStates, zero);
// Set the values for states not contained in MECs.
storm::utility::vector::setVectorValues(result, statesNotContainedInAnyMec, sspResult);
// Set the values for all states in MECs.
for (auto state : statesInMecs) {
result[state] = sspResult[firstAuxiliaryStateIndex + stateToMecIndexMap[state]];
}
if (produceScheduler && solver->hasScheduler()) {
// Translate result for ssp matrix to original model
auto const& sspChoices = solver->getSchedulerChoices();
uint64_t sspState = 0;
for (auto state : statesNotContainedInAnyMec) {
scheduler->setChoice(sspChoices[sspState], state);
++sspState;
}
// The other sspStates correspond to MECS in the original system.
uint_fast64_t rowOffset = sspMatrix.getRowGroupIndices()[sspState];
for (uint_fast64_t mecIndex = 0; mecIndex < mecDecomposition.size(); ++mecIndex) {
// Obtain the state and choice of the original model to which the selected choice corresponds.
auto const& originalStateChoice = sspMecChoicesToOriginalMap[sspMatrix.getRowGroupIndices()[sspState] + sspChoices[sspState] - rowOffset];
// Check if the best choice is to stay in this MEC
if (originalStateChoice.first == std::numeric_limits<uint_fast64_t>::max()) {
STORM_LOG_ASSERT(sspMatrix.getRow(sspState, sspChoices[sspState]).getNumberOfEntries() == 0, "Expected empty row at choice that stays in MEC.");
// In this case, no further operations are necessary. The scheduler has already been set to the optimal choices during the call of computeLraForMaximalEndComponent.
} else {
// The best choice is to leave this MEC via the selected state and choice.
scheduler->setChoice(originalStateChoice.second, originalStateChoice.first);
// The remaining states in this MEC need to reach this state with probability 1.
storm::storage::BitVector exitStateAsBitVector(transitionMatrix.getRowGroupCount(), false);
exitStateAsBitVector.set(originalStateChoice.first, true);
storm::storage::BitVector otherStatesAsBitVector(transitionMatrix.getRowGroupCount(), false);
for (auto const& stateChoices : mecDecomposition[mecIndex]) {
if (stateChoices.first != originalStateChoice.first) {
otherStatesAsBitVector.set(stateChoices.first, true);
}
}
storm::utility::graph::computeSchedulerProb1E(otherStatesAsBitVector, transitionMatrix, backwardTransitions, otherStatesAsBitVector, exitStateAsBitVector, *scheduler);
}
++sspState;
}
assert(sspState == sspMatrix.getRowGroupCount());
} else {
STORM_LOG_ERROR_COND(!produceScheduler, "Requested to produce a scheduler, but no scheduler was generated.");
}
return MDPSparseModelCheckingHelperReturnType<ValueType>(std::move(result), std::move(scheduler));
}
template<typename ValueType>
template<typename RewardModelType>
ValueType SparseMdpPrctlHelper<ValueType>::computeLraForMaximalEndComponent(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec, std::unique_ptr<storm::storage::Scheduler<ValueType>>& scheduler) {
// If the mec only consists of a single state, we compute the LRA value directly
if (++mec.begin() == mec.end()) {
uint64_t state = mec.begin()->first;
auto choiceIt = mec.begin()->second.begin();
ValueType result = rewardModel.getTotalStateActionReward(state, *choiceIt, transitionMatrix);
uint_fast64_t bestChoice = *choiceIt;
for (++choiceIt; choiceIt != mec.begin()->second.end(); ++choiceIt) {
ValueType choiceValue = rewardModel.getTotalStateActionReward(state, *choiceIt, transitionMatrix);
if (storm::solver::minimize(dir)) {
if (result > choiceValue) {
result = std::move(choiceValue);
bestChoice = *choiceIt;
}
} else {
if (result < choiceValue) {
result = std::move(choiceValue);
bestChoice = *choiceIt;
}
}
}
if (scheduler) {
scheduler->setChoice(bestChoice - transitionMatrix.getRowGroupIndices()[state], state);
}
return result;
}
// Solve MEC with the method specified in the settings
storm::solver::LraMethod method = env.solver().lra().getNondetLraMethod();
if ((storm::NumberTraits<ValueType>::IsExact || env.solver().isForceExact()) && env.solver().lra().isNondetLraMethodSetFromDefault() && method != storm::solver::LraMethod::LinearProgramming) {
STORM_LOG_INFO("Selecting 'LP' as the solution technique for long-run properties to guarantee exact results. If you want to override this, please explicitly specify a different LRA method.");
method = storm::solver::LraMethod::LinearProgramming;
} else if (env.solver().isForceSoundness() && env.solver().lra().isNondetLraMethodSetFromDefault() && method != storm::solver::LraMethod::ValueIteration) {
STORM_LOG_INFO("Selecting 'VI' as the solution technique for long-run properties to guarantee sound results. If you want to override this, please explicitly specify a different LRA method.");
method = storm::solver::LraMethod::ValueIteration;
}
STORM_LOG_ERROR_COND(scheduler == nullptr || method == storm::solver::LraMethod::ValueIteration, "Scheduler generation not supported for the chosen LRA method. Try value-iteration.");
if (method == storm::solver::LraMethod::LinearProgramming) {
return computeLraForMaximalEndComponentLP(env, dir, transitionMatrix, rewardModel, mec);
} else if (method == storm::solver::LraMethod::ValueIteration) {
return computeLraForMaximalEndComponentVI(env, dir, transitionMatrix, rewardModel, mec, scheduler);
} else {
STORM_LOG_THROW(false, storm::exceptions::InvalidSettingsException, "Unsupported technique.");
}
}
template<typename ValueType>
template<typename RewardModelType>
ValueType SparseMdpPrctlHelper<ValueType>::computeLraForMaximalEndComponentVI(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec, std::unique_ptr<storm::storage::Scheduler<ValueType>>& scheduler) {
// Initialize data about the mec
storm::storage::BitVector mecStates(transitionMatrix.getRowGroupCount(), false);
storm::storage::BitVector mecChoices(transitionMatrix.getRowCount(), false);
for (auto const& stateChoicesPair : mec) {
mecStates.set(stateChoicesPair.first);
for (auto const& choice : stateChoicesPair.second) {
mecChoices.set(choice);
}
}
boost::container::flat_map<uint64_t, uint64_t> toSubModelStateMapping;
uint64_t currState = 0;
toSubModelStateMapping.reserve(mecStates.getNumberOfSetBits());
for (auto const& mecState : mecStates) {
toSubModelStateMapping.insert(std::pair<uint64_t, uint64_t>(mecState, currState));
++currState;
}
// Get a transition matrix that only considers the states and choices within the MEC
storm::storage::SparseMatrixBuilder<ValueType> mecTransitionBuilder(mecChoices.getNumberOfSetBits(), mecStates.getNumberOfSetBits(), 0, true, true, mecStates.getNumberOfSetBits());
std::vector<ValueType> choiceRewards;
choiceRewards.reserve(mecChoices.getNumberOfSetBits());
uint64_t currRow = 0;
ValueType selfLoopProb = storm::utility::convertNumber<ValueType>(env.solver().lra().getAperiodicFactor());
ValueType scalingFactor = storm::utility::one<ValueType>() - selfLoopProb;
for (auto const& mecState : mecStates) {
mecTransitionBuilder.newRowGroup(currRow);
uint64_t groupStart = transitionMatrix.getRowGroupIndices()[mecState];
uint64_t groupEnd = transitionMatrix.getRowGroupIndices()[mecState + 1];
for (uint64_t choice = mecChoices.getNextSetIndex(groupStart); choice < groupEnd; choice = mecChoices.getNextSetIndex(choice + 1)) {
bool insertedDiagElement = false;
for (auto const& entry : transitionMatrix.getRow(choice)) {
uint64_t column = toSubModelStateMapping[entry.getColumn()];
if (!insertedDiagElement && entry.getColumn() > mecState) {
mecTransitionBuilder.addNextValue(currRow, toSubModelStateMapping[mecState], selfLoopProb);
insertedDiagElement = true;
}
if (!insertedDiagElement && entry.getColumn() == mecState) {
mecTransitionBuilder.addNextValue(currRow, column, selfLoopProb + scalingFactor * entry.getValue());
insertedDiagElement = true;
} else {
mecTransitionBuilder.addNextValue(currRow, column, scalingFactor * entry.getValue());
}
}
if (!insertedDiagElement) {
mecTransitionBuilder.addNextValue(currRow, toSubModelStateMapping[mecState], selfLoopProb);
}
// Compute the rewards obtained for this choice
choiceRewards.push_back(scalingFactor * rewardModel.getTotalStateActionReward(mecState, choice, transitionMatrix));
++currRow;
}
}
auto mecTransitions = mecTransitionBuilder.build();
STORM_LOG_ASSERT(mecTransitions.isProbabilistic(), "The MEC-Matrix is not probabilistic.");
// start the iterations
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().lra().getPrecision()) / scalingFactor;
bool relative = env.solver().lra().getRelativeTerminationCriterion();
std::vector<ValueType> x(mecTransitions.getRowGroupCount(), storm::utility::zero<ValueType>());
std::vector<ValueType> xPrime = x;
auto multiplier = storm::solver::MultiplierFactory<ValueType>().create(env, mecTransitions);
ValueType maxDiff, minDiff;
uint64_t iter = 0;
boost::optional<uint64_t> maxIter;
if (env.solver().lra().isMaximalIterationCountSet()) {
maxIter = env.solver().lra().getMaximalIterationCount();
}
while (!maxIter.is_initialized() || iter < maxIter.get()) {
++iter;
// Compute the obtained rewards for the next step
multiplier->multiplyAndReduce(env, dir, x, &choiceRewards, x);
// update xPrime and check for convergence
// to avoid large (and numerically unstable) x-values, we substract a reference value.
auto xIt = x.begin();
auto xPrimeIt = xPrime.begin();
ValueType refVal = *xIt;
maxDiff = *xIt - *xPrimeIt;
minDiff = maxDiff;
*xIt -= refVal;
*xPrimeIt = *xIt;
for (++xIt, ++xPrimeIt; xIt != x.end(); ++xIt, ++xPrimeIt) {
ValueType diff = *xIt - *xPrimeIt;
maxDiff = std::max(maxDiff, diff);
minDiff = std::min(minDiff, diff);
*xIt -= refVal;
*xPrimeIt = *xIt;
}
if ((maxDiff - minDiff) <= (relative ? (precision * minDiff) : precision)) {
break;
}
}
if (maxIter.is_initialized() && iter == maxIter.get()) {
STORM_LOG_WARN("LRA computation did not converge within " << iter << " iterations.");
} else {
STORM_LOG_TRACE("LRA computation converged after " << iter << " iterations.");
}
if (scheduler) {
std::vector<uint_fast64_t> localMecChoices(mecTransitions.getRowGroupCount(), 0);
multiplier->multiplyAndReduce(env, dir, x, &choiceRewards, x, &localMecChoices);
auto localMecChoiceIt = localMecChoices.begin();
for (auto const& mecState : mecStates) {
// Get the choice index of the selected mec choice with respect to the global transition matrix.
uint_fast64_t globalChoice = mecChoices.getNextSetIndex(transitionMatrix.getRowGroupIndices()[mecState]);
for (uint_fast64_t i = 0; i < *localMecChoiceIt; ++i) {
globalChoice = mecChoices.getNextSetIndex(globalChoice + 1);
}
STORM_LOG_ASSERT(globalChoice < transitionMatrix.getRowGroupIndices()[mecState + 1], "Invalid global choice for mec state.");
scheduler->setChoice(globalChoice - transitionMatrix.getRowGroupIndices()[mecState], mecState);
++localMecChoiceIt;
}
}
return (maxDiff + minDiff) / (storm::utility::convertNumber<ValueType>(2.0) * scalingFactor);
}
template<typename ValueType>
template<typename RewardModelType>
ValueType SparseMdpPrctlHelper<ValueType>::computeLraForMaximalEndComponentLP(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec) {
std::shared_ptr<storm::solver::LpSolver<ValueType>> solver = storm::utility::solver::getLpSolver<ValueType>("LRA for MEC");
solver->setOptimizationDirection(invert(dir));
// First, we need to create the variables for the problem.
std::map<uint_fast64_t, storm::expressions::Variable> stateToVariableMap;
for (auto const& stateChoicesPair : mec) {
std::string variableName = "h" + std::to_string(stateChoicesPair.first);
stateToVariableMap[stateChoicesPair.first] = solver->addUnboundedContinuousVariable(variableName);
}
storm::expressions::Variable lambda = solver->addUnboundedContinuousVariable("L", 1);
solver->update();
// Now we encode the problem as constraints.
for (auto const& stateChoicesPair : mec) {
uint_fast64_t state = stateChoicesPair.first;
// Now, based on the type of the state, create a suitable constraint.
for (auto choice : stateChoicesPair.second) {
storm::expressions::Expression constraint = -lambda;
for (auto element : transitionMatrix.getRow(choice)) {
constraint = constraint + stateToVariableMap.at(element.getColumn()) * solver->getConstant(element.getValue());
}
typename RewardModelType::ValueType r = rewardModel.getTotalStateActionReward(state, choice, transitionMatrix);
constraint = solver->getConstant(r) + constraint;
if (dir == OptimizationDirection::Minimize) {
constraint = stateToVariableMap.at(state) <= constraint;
} else {
constraint = stateToVariableMap.at(state) >= constraint;
}
solver->addConstraint("state" + std::to_string(state) + "," + std::to_string(choice), constraint);
}
}
solver->optimize();
return solver->getContinuousValue(lambda);
}
template<typename ValueType>
std::unique_ptr<CheckResult> SparseMdpPrctlHelper<ValueType>::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) {
std::chrono::high_resolution_clock::time_point start = std::chrono::high_resolution_clock::now();
// For the max-case, we can simply take the given target states. For the min-case, however, we need to
// find the MECs of non-target states and make them the new target states.
storm::storage::BitVector fixedTargetStates;
if (!goal.minimize()) {
fixedTargetStates = targetStates;
} else {
fixedTargetStates = storm::storage::BitVector(targetStates.size());
storm::storage::MaximalEndComponentDecomposition<ValueType> mecDecomposition(transitionMatrix, backwardTransitions, ~targetStates);
for (auto const& mec : mecDecomposition) {
for (auto const& stateActionsPair : mec) {
fixedTargetStates.set(stateActionsPair.first);
}
}
}
storm::storage::BitVector allStates(fixedTargetStates.size(), true);
// Extend the target states by computing all states that have probability 1 to go to a target state
// under *all* schedulers.
fixedTargetStates = storm::utility::graph::performProb1A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, allStates, fixedTargetStates);
// We solve the max-case and later adjust the result if the optimization direction was to minimize.
storm::storage::BitVector initialStatesBitVector = goal.relevantValues();
STORM_LOG_THROW(initialStatesBitVector.getNumberOfSetBits() == 1, storm::exceptions::NotSupportedException, "Computing conditional probabilities in MDPs is only supported for models with exactly one initial state.");
storm::storage::sparse::state_type initialState = *initialStatesBitVector.begin();
// Extend the condition states by computing all states that have probability 1 to go to a condition state
// under *all* schedulers.
storm::storage::BitVector extendedConditionStates = storm::utility::graph::performProb1A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, allStates, conditionStates);
STORM_LOG_DEBUG("Computing probabilities to satisfy condition.");
std::chrono::high_resolution_clock::time_point conditionStart = std::chrono::high_resolution_clock::now();
std::vector<ValueType> conditionProbabilities = std::move(computeUntilProbabilities(env, OptimizationDirection::Maximize, transitionMatrix, backwardTransitions, allStates, extendedConditionStates, false, false).values);
std::chrono::high_resolution_clock::time_point conditionEnd = std::chrono::high_resolution_clock::now();
STORM_LOG_DEBUG("Computed probabilities to satisfy for condition in " << std::chrono::duration_cast<std::chrono::milliseconds>(conditionEnd - conditionStart).count() << "ms.");
// If the conditional probability is undefined for the initial state, we return directly.
if (storm::utility::isZero(conditionProbabilities[initialState])) {
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(initialState, storm::utility::infinity<ValueType>()));
}
STORM_LOG_DEBUG("Computing probabilities to reach target.");
std::chrono::high_resolution_clock::time_point targetStart = std::chrono::high_resolution_clock::now();
std::vector<ValueType> targetProbabilities = std::move(computeUntilProbabilities(env, OptimizationDirection::Maximize, transitionMatrix, backwardTransitions, allStates, fixedTargetStates, false, false).values);
std::chrono::high_resolution_clock::time_point targetEnd = std::chrono::high_resolution_clock::now();
STORM_LOG_DEBUG("Computed probabilities to reach target in " << std::chrono::duration_cast<std::chrono::milliseconds>(targetEnd - targetStart).count() << "ms.");
storm::storage::BitVector statesWithProbabilityGreater0E(transitionMatrix.getRowGroupCount(), true);
storm::storage::sparse::state_type state = 0;
for (auto const& element : conditionProbabilities) {
if (storm::utility::isZero(element)) {
statesWithProbabilityGreater0E.set(state, false);
}
++state;
}
// Determine those states that need to be equipped with a restart mechanism.
STORM_LOG_DEBUG("Computing problematic states.");
storm::storage::BitVector pureResetStates = storm::utility::graph::performProb0A(backwardTransitions, allStates, extendedConditionStates);
storm::storage::BitVector problematicStates = storm::utility::graph::performProb0E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, allStates, extendedConditionStates | fixedTargetStates);
// Otherwise, we build the transformed MDP.
storm::storage::BitVector relevantStates = storm::utility::graph::getReachableStates(transitionMatrix, initialStatesBitVector, allStates, extendedConditionStates | fixedTargetStates | pureResetStates);
STORM_LOG_TRACE("Found " << relevantStates.getNumberOfSetBits() << " relevant states for conditional probability computation.");
std::vector<uint_fast64_t> numberOfStatesBeforeRelevantStates = relevantStates.getNumberOfSetBitsBeforeIndices();
storm::storage::sparse::state_type newGoalState = relevantStates.getNumberOfSetBits();
storm::storage::sparse::state_type newStopState = newGoalState + 1;
storm::storage::sparse::state_type newFailState = newStopState + 1;
// Build the transitions of the (relevant) states of the original model.
storm::storage::SparseMatrixBuilder<ValueType> builder(0, newFailState + 1, 0, true, true);
uint_fast64_t currentRow = 0;
for (auto state : relevantStates) {
builder.newRowGroup(currentRow);
if (fixedTargetStates.get(state)) {
if (!storm::utility::isZero(conditionProbabilities[state])) {
builder.addNextValue(currentRow, newGoalState, conditionProbabilities[state]);
}
if (!storm::utility::isOne(conditionProbabilities[state])) {
builder.addNextValue(currentRow, newFailState, storm::utility::one<ValueType>() - conditionProbabilities[state]);
}
++currentRow;
} else if (extendedConditionStates.get(state)) {
if (!storm::utility::isZero(targetProbabilities[state])) {
builder.addNextValue(currentRow, newGoalState, targetProbabilities[state]);
}
if (!storm::utility::isOne(targetProbabilities[state])) {
builder.addNextValue(currentRow, newStopState, storm::utility::one<ValueType>() - targetProbabilities[state]);
}
++currentRow;
} else if (pureResetStates.get(state)) {
builder.addNextValue(currentRow, numberOfStatesBeforeRelevantStates[initialState], storm::utility::one<ValueType>());
++currentRow;
} else {
for (uint_fast64_t row = transitionMatrix.getRowGroupIndices()[state]; row < transitionMatrix.getRowGroupIndices()[state + 1]; ++row) {
for (auto const& successorEntry : transitionMatrix.getRow(row)) {
builder.addNextValue(currentRow, numberOfStatesBeforeRelevantStates[successorEntry.getColumn()], successorEntry.getValue());
}
++currentRow;
}
if (problematicStates.get(state)) {
builder.addNextValue(currentRow, numberOfStatesBeforeRelevantStates[initialState], storm::utility::one<ValueType>());
++currentRow;
}
}
}
// Now build the transitions of the newly introduced states.
builder.newRowGroup(currentRow);
builder.addNextValue(currentRow, newGoalState, storm::utility::one<ValueType>());
++currentRow;
builder.newRowGroup(currentRow);
builder.addNextValue(currentRow, newStopState, storm::utility::one<ValueType>());
++currentRow;
builder.newRowGroup(currentRow);
builder.addNextValue(currentRow, numberOfStatesBeforeRelevantStates[initialState], storm::utility::one<ValueType>());
++currentRow;
std::chrono::high_resolution_clock::time_point end = std::chrono::high_resolution_clock::now();
STORM_LOG_DEBUG("Computed transformed model in " << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count() << "ms.");
// Finally, build the matrix and dispatch the query as a reachability query.
STORM_LOG_DEBUG("Computing conditional probabilties.");
storm::storage::BitVector newGoalStates(newFailState + 1);
newGoalStates.set(newGoalState);
storm::storage::SparseMatrix<ValueType> newTransitionMatrix = builder.build();
STORM_LOG_DEBUG("Transformed model has " << newTransitionMatrix.getRowGroupCount() << " states and " << newTransitionMatrix.getNonzeroEntryCount() << " transitions.");
storm::storage::SparseMatrix<ValueType> newBackwardTransitions = newTransitionMatrix.transpose(true);
storm::solver::OptimizationDirection dir = goal.direction();
if (goal.minimize()) {
goal.oneMinus();
}
std::chrono::high_resolution_clock::time_point conditionalStart = std::chrono::high_resolution_clock::now();
std::vector<ValueType> goalProbabilities = std::move(computeUntilProbabilities(env, std::move(goal), newTransitionMatrix, newBackwardTransitions, storm::storage::BitVector(newFailState + 1, true), newGoalStates, false, false).values);
std::chrono::high_resolution_clock::time_point conditionalEnd = std::chrono::high_resolution_clock::now();
STORM_LOG_DEBUG("Computed conditional probabilities in transformed model in " << std::chrono::duration_cast<std::chrono::milliseconds>(conditionalEnd - conditionalStart).count() << "ms.");
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(initialState, dir == OptimizationDirection::Maximize ? goalProbabilities[numberOfStatesBeforeRelevantStates[initialState]] : storm::utility::one<ValueType>() - goalProbabilities[numberOfStatesBeforeRelevantStates[initialState]]));
}
template class SparseMdpPrctlHelper<double>;
template std::vector<double> SparseMdpPrctlHelper<double>::computeInstantaneousRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, uint_fast64_t stepCount);
template std::vector<double> SparseMdpPrctlHelper<double>::computeCumulativeRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, uint_fast64_t stepBound);
template MDPSparseModelCheckingHelperReturnType<double> SparseMdpPrctlHelper<double>::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, bool produceScheduler, ModelCheckerHint const& hint);
template MDPSparseModelCheckingHelperReturnType<double> SparseMdpPrctlHelper<double>::computeTotalRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::models::sparse::StandardRewardModel<double> const& rewardModel, bool qualitative, bool produceScheduler, ModelCheckerHint const& hint);
template MDPSparseModelCheckingHelperReturnType<double> SparseMdpPrctlHelper<double>::computeLongRunAverageRewards(Environment const& env, storm::solver::SolveGoal<double>&& goal, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::models::sparse::StandardRewardModel<double> const& rewardModel, bool produceScheduler);
template double SparseMdpPrctlHelper<double>::computeLraForMaximalEndComponent(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec, std::unique_ptr<storm::storage::Scheduler<double>>& scheduler);
template double SparseMdpPrctlHelper<double>::computeLraForMaximalEndComponentVI(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec, std::unique_ptr<storm::storage::Scheduler<double>>& scheduler);
template double SparseMdpPrctlHelper<double>::computeLraForMaximalEndComponentLP(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec);
#ifdef STORM_HAVE_CARL
template class SparseMdpPrctlHelper<storm::RationalNumber>;
template std::vector<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeInstantaneousRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, uint_fast64_t stepCount);
template std::vector<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeCumulativeRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, uint_fast64_t stepBound);
template MDPSparseModelCheckingHelperReturnType<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeReachabilityRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, bool produceScheduler, ModelCheckerHint const& hint);
template MDPSparseModelCheckingHelperReturnType<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeTotalRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, bool qualitative, bool produceScheduler, ModelCheckerHint const& hint);
template MDPSparseModelCheckingHelperReturnType<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeLongRunAverageRewards(Environment const& env, storm::solver::SolveGoal<storm::RationalNumber>&& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, bool produceScheduler);
template storm::RationalNumber SparseMdpPrctlHelper<storm::RationalNumber>::computeLraForMaximalEndComponent(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec, std::unique_ptr<storm::storage::Scheduler<storm::RationalNumber>>& scheduler);
template storm::RationalNumber SparseMdpPrctlHelper<storm::RationalNumber>::computeLraForMaximalEndComponentVI(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec, std::unique_ptr<storm::storage::Scheduler<storm::RationalNumber>>& scheduler);
template storm::RationalNumber SparseMdpPrctlHelper<storm::RationalNumber>::computeLraForMaximalEndComponentLP(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec);
#endif
}
}
}