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662 lines
51 KiB
662 lines
51 KiB
#include "storm/modelchecker/abstraction/GameBasedMdpModelChecker.h"
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#include "storm/modelchecker/results/ExplicitQuantitativeCheckResult.h"
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#include "storm/modelchecker/results/ExplicitQualitativeCheckResult.h"
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#include "storm/models/symbolic/StandardRewardModel.h"
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#include "storm/models/symbolic/Dtmc.h"
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#include "storm/models/symbolic/Mdp.h"
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#include "storm/storage/expressions/ExpressionManager.h"
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#include "storm/storage/dd/DdManager.h"
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#include "storm/abstraction/prism/PrismMenuGameAbstractor.h"
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#include "storm/logic/FragmentSpecification.h"
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#include "storm/solver/SymbolicGameSolver.h"
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#include "storm/utility/solver.h"
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#include "storm/utility/dd.h"
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#include "storm/utility/prism.h"
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#include "storm/utility/macros.h"
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#include "storm/exceptions/NotSupportedException.h"
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#include "storm/exceptions/InvalidPropertyException.h"
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#include "storm/exceptions/InvalidModelException.h"
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#include "storm/modelchecker/results/CheckResult.h"
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//#define LOCAL_DEBUG
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namespace storm {
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namespace modelchecker {
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template<storm::dd::DdType Type, typename ModelType>
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GameBasedMdpModelChecker<Type, ModelType>::GameBasedMdpModelChecker(storm::storage::SymbolicModelDescription const& model, std::shared_ptr<storm::utility::solver::SmtSolverFactory> const& smtSolverFactory) : smtSolverFactory(smtSolverFactory) {
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STORM_LOG_THROW(model.isPrismProgram(), storm::exceptions::NotSupportedException, "Currently only PRISM models are supported by the game-based model checker.");
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storm::prism::Program const& originalProgram = model.asPrismProgram();
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STORM_LOG_THROW(originalProgram.getModelType() == storm::prism::Program::ModelType::DTMC || originalProgram.getModelType() == storm::prism::Program::ModelType::MDP, storm::exceptions::NotSupportedException, "Currently only DTMCs/MDPs are supported by the game-based model checker.");
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storm::utility::prism::requireNoUndefinedConstants(originalProgram);
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// Start by preparing the program. That is, we flatten the modules if there is more than one.
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if (originalProgram.getNumberOfModules() > 1) {
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preprocessedModel = originalProgram.flattenModules(this->smtSolverFactory);
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} else {
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preprocessedModel = originalProgram;
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}
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}
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template<storm::dd::DdType Type, typename ModelType>
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bool GameBasedMdpModelChecker<Type, ModelType>::canHandle(CheckTask<storm::logic::Formula> const& checkTask) const {
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storm::logic::Formula const& formula = checkTask.getFormula();
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storm::logic::FragmentSpecification fragment = storm::logic::reachability();
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return formula.isInFragment(fragment) && checkTask.isOnlyInitialStatesRelevantSet();
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}
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template<storm::dd::DdType Type, typename ModelType>
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std::unique_ptr<CheckResult> GameBasedMdpModelChecker<Type, ModelType>::computeUntilProbabilities(CheckTask<storm::logic::UntilFormula> const& checkTask) {
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storm::logic::UntilFormula const& pathFormula = checkTask.getFormula();
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std::map<std::string, storm::expressions::Expression> labelToExpressionMapping = preprocessedModel.asPrismProgram().getLabelToExpressionMapping();
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return performGameBasedAbstractionRefinement(checkTask.substituteFormula<storm::logic::Formula>(pathFormula), pathFormula.getLeftSubformula().toExpression(preprocessedModel.getManager(), labelToExpressionMapping), pathFormula.getRightSubformula().toExpression(preprocessedModel.getManager(), labelToExpressionMapping));
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}
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template<storm::dd::DdType Type, typename ModelType>
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std::unique_ptr<CheckResult> GameBasedMdpModelChecker<Type, ModelType>::computeReachabilityProbabilities(CheckTask<storm::logic::EventuallyFormula> const& checkTask) {
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storm::logic::EventuallyFormula const& pathFormula = checkTask.getFormula();
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std::map<std::string, storm::expressions::Expression> labelToExpressionMapping = preprocessedModel.asPrismProgram().getLabelToExpressionMapping();
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return performGameBasedAbstractionRefinement(checkTask.substituteFormula<storm::logic::Formula>(pathFormula), preprocessedModel.getManager().boolean(true), pathFormula.getSubformula().toExpression(preprocessedModel.getManager(), labelToExpressionMapping));
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}
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template<storm::dd::DdType Type, typename ValueType>
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std::unique_ptr<CheckResult> checkForResultAfterQualitativeCheck(CheckTask<storm::logic::Formula> const& checkTask, storm::dd::Bdd<Type> const& initialStates, storm::dd::Bdd<Type> const& statesMin, storm::dd::Bdd<Type> const& statesMax, bool prob0) {
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std::unique_ptr<CheckResult> result;
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if ((initialStates && statesMin && statesMax) == initialStates) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), prob0 ? storm::utility::zero<ValueType>() : storm::utility::one<ValueType>());
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}
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return result;
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}
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template<storm::dd::DdType Type, typename ValueType>
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std::unique_ptr<CheckResult> checkForResultAfterQualitativeCheck(CheckTask<storm::logic::Formula> const& checkTask, storm::OptimizationDirection player2Direction, storm::dd::Bdd<Type> const& initialStates, storm::dd::Bdd<Type> const& prob0, storm::dd::Bdd<Type> const& prob1) {
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std::unique_ptr<CheckResult> result;
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boost::optional<storm::logic::Bound<ValueType>> const& bound = checkTask.getOptionalBound();
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if (bound) {
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if (player2Direction == storm::OptimizationDirection::Minimize && storm::logic::isLowerBound(bound.get().comparisonType)) {
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if ((prob1 && initialStates) == initialStates) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), storm::utility::one<ValueType>());
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} else if (checkTask.isQualitativeSet()) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), ValueType(0.5));
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}
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} else if (player2Direction == storm::OptimizationDirection::Maximize && !storm::logic::isLowerBound(bound.get().comparisonType)) {
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if ((prob0 && initialStates) == initialStates) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), storm::utility::zero<ValueType>());
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} else if (checkTask.isQualitativeSet()) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), ValueType(0.5));
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}
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}
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}
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return result;
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}
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template<storm::dd::DdType Type, typename ValueType>
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std::unique_ptr<CheckResult> checkForResultAfterQualitativeCheck(CheckTask<storm::logic::Formula> const& checkTask, storm::dd::Bdd<Type> const& initialStates, detail::GameProb01ResultMinMax<Type> const& qualitativeResult) {
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// Check whether we can already give the answer based on the current information.
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std::unique_ptr<CheckResult> result = checkForResultAfterQualitativeCheck<Type, ValueType>(checkTask, initialStates, qualitativeResult.prob0Min.getPlayer1States(), qualitativeResult.prob0Max.getPlayer1States(), true);
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if (result) {
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return result;
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}
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result = checkForResultAfterQualitativeCheck<Type, ValueType>(checkTask, initialStates, qualitativeResult.prob1Min.getPlayer1States(), qualitativeResult.prob1Max.getPlayer1States(), false);
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if (result) {
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return result;
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}
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return result;
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}
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template<typename ValueType>
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std::unique_ptr<CheckResult> checkForResultAfterQuantitativeCheck(CheckTask<storm::logic::Formula> const& checkTask, storm::OptimizationDirection const& player2Direction, ValueType const& value) {
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std::unique_ptr<CheckResult> result;
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// If the minimum value exceeds an upper threshold or the maximum value is below a lower threshold, we can
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// return the value because the property will definitely hold. Vice versa, if the minimum value exceeds an
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// upper bound or the maximum value is below a lower bound, the property will definitely not hold and we can
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// return the value.
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boost::optional<storm::logic::Bound<ValueType>> const& bound = checkTask.getOptionalBound();
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if (!bound) {
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return result;
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}
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storm::logic::ComparisonType comparisonType = bound.get().comparisonType;
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ValueType threshold = bound.get().threshold;
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if (storm::logic::isLowerBound(comparisonType)) {
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if (player2Direction == storm::OptimizationDirection::Minimize) {
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if ((storm::logic::isStrict(comparisonType) && value > threshold)
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|| (!storm::logic::isStrict(comparisonType) && value >= threshold)) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), value);
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}
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} else {
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if ((storm::logic::isStrict(comparisonType) && value <= threshold)
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|| (!storm::logic::isStrict(comparisonType) && value < threshold)) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), value);
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}
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}
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} else if (!storm::logic::isLowerBound(comparisonType)) {
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if (player2Direction == storm::OptimizationDirection::Maximize) {
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if ((storm::logic::isStrict(comparisonType) && value < threshold) ||
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(!storm::logic::isStrict(comparisonType) && value <= threshold)) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), value);
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}
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} else {
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if ((storm::logic::isStrict(comparisonType) && value >= threshold) ||
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(!storm::logic::isStrict(comparisonType) && value > threshold)) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), value);
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}
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}
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}
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return result;
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}
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template<typename ValueType>
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std::unique_ptr<CheckResult> checkForResultAfterQuantitativeCheck(CheckTask<storm::logic::Formula> const& checkTask, ValueType const& minValue, ValueType const& maxValue) {
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std::unique_ptr<CheckResult> result;
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// If the lower and upper bounds are close enough, we can return the result.
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if (maxValue - minValue < storm::utility::convertNumber<ValueType>(1e-3)) {
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result = std::make_unique<storm::modelchecker::ExplicitQuantitativeCheckResult<ValueType>>(storm::storage::sparse::state_type(0), (minValue + maxValue) / ValueType(2));
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}
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return result;
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}
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template<storm::dd::DdType Type>
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storm::dd::Bdd<Type> pickPivotState(storm::dd::Bdd<Type> const& initialStates, storm::dd::Bdd<Type> const& transitions, std::set<storm::expressions::Variable> const& rowVariables, std::set<storm::expressions::Variable> const& columnVariables, storm::dd::Bdd<Type> const& pivotStates) {
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// Perform a BFS and pick the first pivot state we encounter.
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storm::dd::Bdd<Type> pivotState;
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storm::dd::Bdd<Type> frontier = initialStates;
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storm::dd::Bdd<Type> frontierPivotStates = frontier && pivotStates;
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uint64_t level = 0;
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bool foundPivotState = !frontierPivotStates.isZero();
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if (foundPivotState) {
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pivotState = frontierPivotStates.existsAbstractRepresentative(rowVariables);
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STORM_LOG_TRACE("Picked pivot state from " << frontierPivotStates.getNonZeroCount() << " candidates on level " << level << ", " << pivotStates.getNonZeroCount() << " candidates in total.");
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} else {
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while (!foundPivotState) {
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frontier = frontier.relationalProduct(transitions, rowVariables, columnVariables);
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frontierPivotStates = frontier && pivotStates;
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if (!frontierPivotStates.isZero()) {
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STORM_LOG_TRACE("Picked pivot state from " << frontierPivotStates.getNonZeroCount() << " candidates on level " << level << ", " << pivotStates.getNonZeroCount() << " candidates in total.");
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pivotState = frontierPivotStates.existsAbstractRepresentative(rowVariables);
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foundPivotState = true;
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}
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++level;
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}
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}
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return pivotState;
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}
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template<storm::dd::DdType Type, typename ValueType>
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bool refineAfterQualitativeCheck(storm::abstraction::prism::PrismMenuGameAbstractor<Type, ValueType>& abstractor, storm::abstraction::MenuGame<Type, ValueType> const& game, detail::GameProb01ResultMinMax<Type> const& qualitativeResult, storm::dd::Bdd<Type> const& transitionMatrixBdd) {
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STORM_LOG_TRACE("Trying refinement after qualitative check.");
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// Get all relevant strategies.
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storm::dd::Bdd<Type> minPlayer1Strategy = qualitativeResult.prob0Min.getPlayer1Strategy();
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storm::dd::Bdd<Type> minPlayer2Strategy = qualitativeResult.prob0Min.getPlayer2Strategy();
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storm::dd::Bdd<Type> maxPlayer1Strategy = qualitativeResult.prob1Max.getPlayer1Strategy();
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storm::dd::Bdd<Type> maxPlayer2Strategy = qualitativeResult.prob1Max.getPlayer2Strategy();
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// Redirect all player 1 choices of the min strategy to that of the max strategy if this leads to a player 2
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// state that is also a prob 0 state.
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minPlayer1Strategy = (maxPlayer1Strategy && qualitativeResult.prob0Min.getPlayer2States()).existsAbstract(game.getPlayer1Variables()).ite(maxPlayer1Strategy, minPlayer1Strategy);
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// Build the fragment of transitions that is reachable by both the min and the max strategies.
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storm::dd::Bdd<Type> reachableTransitions = transitionMatrixBdd && (minPlayer1Strategy || minPlayer2Strategy) && maxPlayer1Strategy && maxPlayer2Strategy;
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reachableTransitions = reachableTransitions.existsAbstract(game.getNondeterminismVariables());
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storm::dd::Bdd<Type> pivotStates = storm::utility::dd::computeReachableStates(game.getInitialStates(), reachableTransitions, game.getRowVariables(), game.getColumnVariables());
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// Require the pivot state to be a [0, 1] state.
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// TODO: is this restriction necessary or is it already implied?
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// pivotStates &= prob01.min.first.getPlayer1States() && prob01.max.second.getPlayer1States();
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// Then constrain these states by the requirement that for either the lower or upper player 1 choice the player 2 choices must be different and
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// that the difference is not because of a missing strategy in either case.
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// Start with constructing the player 2 states that have a prob 0 (min) and prob 1 (max) strategy.
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storm::dd::Bdd<Type> constraint = minPlayer2Strategy.existsAbstract(game.getPlayer2Variables()) && maxPlayer2Strategy.existsAbstract(game.getPlayer2Variables());
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// Now construct all player 2 choices that actually exist and differ in the min and max case.
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constraint &= minPlayer2Strategy.exclusiveOr(maxPlayer2Strategy);
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// Then restrict the pivot states by requiring existing and different player 2 choices.
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pivotStates &= ((minPlayer1Strategy || maxPlayer1Strategy) && constraint).existsAbstract(game.getNondeterminismVariables());
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// We can only refine in case we have a reachable player 1 state with a player 2 successor (under either
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// player 1's min or max strategy) such that from this player 2 state, both prob0 min and prob0 max define
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// strategies and they differ. Hence, it is possible that we arrive at a point where no suitable pivot state
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// is found. In this case, we abort the qualitative refinement here.
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if (pivotStates.isZero()) {
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return false;
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}
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STORM_LOG_ASSERT(!pivotStates.isZero(), "Unable to proceed without pivot state candidates.");
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// Now that we have the pivot state candidates, we need to pick one.
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storm::dd::Bdd<Type> pivotState = pickPivotState<Type>(game.getInitialStates(), reachableTransitions, game.getRowVariables(), game.getColumnVariables(), pivotStates);
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// Compute the lower and the upper choice for the pivot state.
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std::set<storm::expressions::Variable> variablesToAbstract = game.getNondeterminismVariables();
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variablesToAbstract.insert(game.getRowVariables().begin(), game.getRowVariables().end());
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storm::dd::Bdd<Type> lowerChoice = pivotState && game.getExtendedTransitionMatrix().toBdd() && minPlayer1Strategy;
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storm::dd::Bdd<Type> lowerChoice1 = (lowerChoice && minPlayer2Strategy).existsAbstract(variablesToAbstract);
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storm::dd::Bdd<Type> lowerChoice2 = (lowerChoice && maxPlayer2Strategy).existsAbstract(variablesToAbstract);
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bool lowerChoicesDifferent = !lowerChoice1.exclusiveOr(lowerChoice2).isZero();
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if (lowerChoicesDifferent) {
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STORM_LOG_TRACE("Refining based on lower choice.");
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auto refinementStart = std::chrono::high_resolution_clock::now();
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abstractor.refine(pivotState, (pivotState && minPlayer1Strategy).existsAbstract(game.getRowVariables()), lowerChoice1, lowerChoice2);
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auto refinementEnd = std::chrono::high_resolution_clock::now();
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STORM_LOG_TRACE("Refinement completed in " << std::chrono::duration_cast<std::chrono::milliseconds>(refinementEnd - refinementStart).count() << "ms.");
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return true;
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} else {
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storm::dd::Bdd<Type> upperChoice = pivotState && game.getExtendedTransitionMatrix().toBdd() && maxPlayer1Strategy;
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storm::dd::Bdd<Type> upperChoice1 = (upperChoice && minPlayer2Strategy).existsAbstract(variablesToAbstract);
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storm::dd::Bdd<Type> upperChoice2 = (upperChoice && maxPlayer2Strategy).existsAbstract(variablesToAbstract);
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bool upperChoicesDifferent = !upperChoice1.exclusiveOr(upperChoice2).isZero();
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if (upperChoicesDifferent) {
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STORM_LOG_TRACE("Refining based on upper choice.");
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auto refinementStart = std::chrono::high_resolution_clock::now();
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abstractor.refine(pivotState, (pivotState && maxPlayer1Strategy).existsAbstract(game.getRowVariables()), upperChoice1, upperChoice2);
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auto refinementEnd = std::chrono::high_resolution_clock::now();
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STORM_LOG_TRACE("Refinement completed in " << std::chrono::duration_cast<std::chrono::milliseconds>(refinementEnd - refinementStart).count() << "ms.");
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return true;
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} else {
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STORM_LOG_ASSERT(false, "Did not find choices from which to derive predicates.");
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}
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}
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return false;
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}
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template<storm::dd::DdType Type, typename ValueType>
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struct QuantitativeResult {
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QuantitativeResult() = default;
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QuantitativeResult(ValueType initialStateValue, storm::dd::Add<Type, ValueType> const& values, storm::dd::Bdd<Type> const& player1Strategy, storm::dd::Bdd<Type> const& player2Strategy) : initialStateValue(initialStateValue), values(values), player1Strategy(player1Strategy), player2Strategy(player2Strategy) {
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// Intentionally left empty.
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}
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ValueType initialStateValue;
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storm::dd::Add<Type, ValueType> values;
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storm::dd::Bdd<Type> player1Strategy;
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storm::dd::Bdd<Type> player2Strategy;
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};
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template<storm::dd::DdType Type, typename ValueType>
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void refineAfterQuantitativeCheck(storm::abstraction::prism::PrismMenuGameAbstractor<Type, ValueType>& abstractor, storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& transitionMatrixBdd, QuantitativeResult<Type, ValueType> const& minResult, QuantitativeResult<Type, ValueType> const& maxResult) {
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STORM_LOG_TRACE("Refining after quantitative check.");
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// Get all relevant strategies.
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storm::dd::Bdd<Type> minPlayer1Strategy = minResult.player1Strategy;
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storm::dd::Bdd<Type> minPlayer2Strategy = minResult.player2Strategy;
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storm::dd::Bdd<Type> maxPlayer1Strategy = maxResult.player1Strategy;
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storm::dd::Bdd<Type> maxPlayer2Strategy = maxResult.player2Strategy;
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// TODO: fix min strategies to take the max strategies if possible.
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// Build the fragment of transitions that is reachable by both the min and the max strategies.
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storm::dd::Bdd<Type> reachableTransitions = transitionMatrixBdd && (minPlayer1Strategy || maxPlayer1Strategy) && minPlayer2Strategy && maxPlayer2Strategy;
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reachableTransitions = reachableTransitions.existsAbstract(game.getNondeterminismVariables());
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storm::dd::Bdd<Type> pivotStates = storm::utility::dd::computeReachableStates(game.getInitialStates(), reachableTransitions, game.getRowVariables(), game.getColumnVariables());
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// Require the pivot state to be a state with a lower bound strictly smaller than the upper bound.
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pivotStates &= minResult.values.less(maxResult.values);
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STORM_LOG_ASSERT(!pivotStates.isZero(), "Unable to refine without pivot state candidates.");
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// Then constrain these states by the requirement that for either the lower or upper player 1 choice the player 2 choices must be different and
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// that the difference is not because of a missing strategy in either case.
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// Start with constructing the player 2 states that have a (min) and a (max) strategy.
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// TODO: necessary?
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storm::dd::Bdd<Type> constraint = minPlayer2Strategy.existsAbstract(game.getPlayer2Variables()) && maxPlayer2Strategy.existsAbstract(game.getPlayer2Variables());
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// Now construct all player 2 choices that actually exist and differ in the min and max case.
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constraint &= minPlayer2Strategy.exclusiveOr(maxPlayer2Strategy);
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// Then restrict the pivot states by requiring existing and different player 2 choices.
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pivotStates &= ((minPlayer1Strategy || maxPlayer1Strategy) && constraint).existsAbstract(game.getNondeterminismVariables());
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STORM_LOG_ASSERT(!pivotStates.isZero(), "Unable to refine without pivot state candidates.");
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// Now that we have the pivot state candidates, we need to pick one.
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storm::dd::Bdd<Type> pivotState = pickPivotState<Type>(game.getInitialStates(), reachableTransitions, game.getRowVariables(), game.getColumnVariables(), pivotStates);
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// Compute the lower and the upper choice for the pivot state.
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std::set<storm::expressions::Variable> variablesToAbstract = game.getNondeterminismVariables();
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variablesToAbstract.insert(game.getRowVariables().begin(), game.getRowVariables().end());
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storm::dd::Bdd<Type> lowerChoice = pivotState && game.getExtendedTransitionMatrix().toBdd() && minPlayer1Strategy;
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storm::dd::Bdd<Type> lowerChoice1 = (lowerChoice && minPlayer2Strategy).existsAbstract(variablesToAbstract);
|
|
storm::dd::Bdd<Type> lowerChoice2 = (lowerChoice && maxPlayer2Strategy).existsAbstract(variablesToAbstract);
|
|
|
|
bool lowerChoicesDifferent = !lowerChoice1.exclusiveOr(lowerChoice2).isZero();
|
|
if (lowerChoicesDifferent) {
|
|
STORM_LOG_TRACE("Refining based on lower choice.");
|
|
auto refinementStart = std::chrono::high_resolution_clock::now();
|
|
abstractor.refine(pivotState, (pivotState && minPlayer1Strategy).existsAbstract(game.getRowVariables()), lowerChoice1, lowerChoice2);
|
|
auto refinementEnd = std::chrono::high_resolution_clock::now();
|
|
STORM_LOG_TRACE("Refinement completed in " << std::chrono::duration_cast<std::chrono::milliseconds>(refinementEnd - refinementStart).count() << "ms.");
|
|
} else {
|
|
storm::dd::Bdd<Type> upperChoice = pivotState && game.getExtendedTransitionMatrix().toBdd() && maxPlayer1Strategy;
|
|
storm::dd::Bdd<Type> upperChoice1 = (upperChoice && minPlayer2Strategy).existsAbstract(variablesToAbstract);
|
|
storm::dd::Bdd<Type> upperChoice2 = (upperChoice && maxPlayer2Strategy).existsAbstract(variablesToAbstract);
|
|
|
|
bool upperChoicesDifferent = !upperChoice1.exclusiveOr(upperChoice2).isZero();
|
|
if (upperChoicesDifferent) {
|
|
STORM_LOG_TRACE("Refining based on upper choice.");
|
|
auto refinementStart = std::chrono::high_resolution_clock::now();
|
|
abstractor.refine(pivotState, (pivotState && maxPlayer1Strategy).existsAbstract(game.getRowVariables()), upperChoice1, upperChoice2);
|
|
auto refinementEnd = std::chrono::high_resolution_clock::now();
|
|
STORM_LOG_TRACE("Refinement completed in " << std::chrono::duration_cast<std::chrono::milliseconds>(refinementEnd - refinementStart).count() << "ms.");
|
|
} else {
|
|
STORM_LOG_ASSERT(false, "Did not find choices from which to derive predicates.");
|
|
}
|
|
}
|
|
}
|
|
|
|
template<storm::dd::DdType Type, typename ValueType>
|
|
QuantitativeResult<Type, ValueType> solveMaybeStates(storm::OptimizationDirection const& player1Direction, storm::OptimizationDirection const& player2Direction, storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& maybeStates, storm::dd::Bdd<Type> const& prob1States, boost::optional<QuantitativeResult<Type, ValueType>> const& startInfo = boost::none) {
|
|
|
|
STORM_LOG_TRACE("Performing quantative solution step. Player 1: " << player1Direction << ", player 2: " << player2Direction << ".");
|
|
|
|
// Compute the ingredients of the equation system.
|
|
storm::dd::Add<Type, ValueType> maybeStatesAdd = maybeStates.template toAdd<ValueType>();
|
|
storm::dd::Add<Type, ValueType> submatrix = maybeStatesAdd * game.getTransitionMatrix();
|
|
storm::dd::Add<Type, ValueType> prob1StatesAsColumn = prob1States.template toAdd<ValueType>().swapVariables(game.getRowColumnMetaVariablePairs());
|
|
storm::dd::Add<Type, ValueType> subvector = submatrix * prob1StatesAsColumn;
|
|
subvector = subvector.sumAbstract(game.getColumnVariables());
|
|
|
|
// Cut away all columns targeting non-maybe states.
|
|
submatrix *= maybeStatesAdd.swapVariables(game.getRowColumnMetaVariablePairs());
|
|
|
|
// Cut the starting vector to the maybe states of this query.
|
|
storm::dd::Add<Type, ValueType> startVector;
|
|
if (startInfo) {
|
|
startVector = startInfo.get().values * maybeStatesAdd;
|
|
} else {
|
|
startVector = game.getManager().template getAddZero<ValueType>();
|
|
}
|
|
|
|
// Create the solver and solve the equation system.
|
|
storm::utility::solver::SymbolicGameSolverFactory<Type, ValueType> solverFactory;
|
|
std::unique_ptr<storm::solver::SymbolicGameSolver<Type, ValueType>> solver = solverFactory.create(submatrix, maybeStates, game.getIllegalPlayer1Mask(), game.getIllegalPlayer2Mask(), game.getRowVariables(), game.getColumnVariables(), game.getRowColumnMetaVariablePairs(), game.getPlayer1Variables(), game.getPlayer2Variables());
|
|
solver->setGeneratePlayersStrategies(true);
|
|
auto values = solver->solveGame(player1Direction, player2Direction, startVector, subvector, startInfo ? boost::make_optional(startInfo.get().player1Strategy) : boost::none, startInfo ? boost::make_optional(startInfo.get().player2Strategy) : boost::none);
|
|
return QuantitativeResult<Type, ValueType>(storm::utility::zero<ValueType>(), values, solver->getPlayer1Strategy(), solver->getPlayer2Strategy());
|
|
}
|
|
|
|
template<storm::dd::DdType Type, typename ValueType>
|
|
QuantitativeResult<Type, ValueType> computeQuantitativeResult(storm::OptimizationDirection player1Direction, storm::OptimizationDirection player2Direction, storm::abstraction::MenuGame<Type, ValueType> const& game, detail::GameProb01ResultMinMax<Type> const& qualitativeResult, storm::dd::Add<Type, ValueType> const& initialStatesAdd, storm::dd::Bdd<Type> const& maybeStates, boost::optional<QuantitativeResult<Type, ValueType>> const& startInfo = boost::none) {
|
|
|
|
bool min = player2Direction == storm::OptimizationDirection::Minimize;
|
|
|
|
// The minimal value after qualitative checking can only be zero. If it was 1, we could have given
|
|
// the result right away. Similarly, the maximal value can only be one at this point.
|
|
ValueType initialStateValue = min ? storm::utility::zero<ValueType>() : storm::utility::one<ValueType>();
|
|
|
|
QuantitativeResult<Type, ValueType> result;
|
|
auto start = std::chrono::high_resolution_clock::now();
|
|
if (!maybeStates.isZero()) {
|
|
// Solve the quantitative values of maybe states.
|
|
result = solveMaybeStates(player1Direction, player2Direction, game, maybeStates, min ? qualitativeResult.prob1Min.getPlayer1States() : qualitativeResult.prob1Max.getPlayer1States(), startInfo);
|
|
|
|
// Cut the obtained strategies to the reachable states of the game.
|
|
result.player1Strategy &= game.getReachableStates();
|
|
result.player2Strategy &= game.getReachableStates();
|
|
|
|
// Extend the values of the maybe states by the qualitative values.
|
|
result.values += min ? qualitativeResult.prob1Min.getPlayer1States().template toAdd<ValueType>() : qualitativeResult.prob1Max.getPlayer1States().template toAdd<ValueType>();
|
|
|
|
// Construct an ADD holding the initial values of initial states and check it for validity.
|
|
storm::dd::Add<Type, ValueType> initialStateValueAdd = initialStatesAdd * result.values;
|
|
// For min, we can only require a non-zero count of *at most* one, because the result may actually be 0.
|
|
STORM_LOG_ASSERT((!min || initialStateValueAdd.getNonZeroCount() == 1) && (min || initialStateValueAdd.getNonZeroCount() <= 1), "Wrong number of results for initial states. Expected " << (min ? "<= 1" : "1") << ", but got " << initialStateValueAdd.getNonZeroCount() << ".");
|
|
result.initialStateValue = initialStateValue = initialStateValueAdd.getMax();
|
|
|
|
// Finally, we fix the strategies. That is, we take the decisions of the strategies obtained in the
|
|
// qualitiative preprocessing if possible.
|
|
storm::dd::Bdd<Type> combinedPlayer1QualitativeStrategies;
|
|
storm::dd::Bdd<Type> combinedPlayer2QualitativeStrategies;
|
|
if (min) {
|
|
combinedPlayer1QualitativeStrategies = (qualitativeResult.prob0Min.getPlayer1Strategy() || qualitativeResult.prob1Min.getPlayer1Strategy());
|
|
combinedPlayer2QualitativeStrategies = (qualitativeResult.prob0Min.getPlayer2Strategy() || qualitativeResult.prob1Min.getPlayer2Strategy());
|
|
} else {
|
|
combinedPlayer1QualitativeStrategies = (qualitativeResult.prob0Max.getPlayer1Strategy() || qualitativeResult.prob1Max.getPlayer1Strategy());
|
|
combinedPlayer2QualitativeStrategies = (qualitativeResult.prob0Max.getPlayer2Strategy() || qualitativeResult.prob1Max.getPlayer2Strategy());
|
|
}
|
|
|
|
result.player1Strategy = combinedPlayer1QualitativeStrategies.existsAbstract(game.getPlayer1Variables()).ite(combinedPlayer1QualitativeStrategies, result.player1Strategy);
|
|
result.player2Strategy = combinedPlayer2QualitativeStrategies.existsAbstract(game.getPlayer2Variables()).ite(combinedPlayer2QualitativeStrategies, result.player2Strategy);
|
|
} else {
|
|
result = QuantitativeResult<Type, ValueType>(initialStateValue, game.getManager().template getAddZero<ValueType>(), game.getManager().getBddZero(), game.getManager().getBddZero());
|
|
}
|
|
|
|
auto end = std::chrono::high_resolution_clock::now();
|
|
STORM_LOG_TRACE("Obtained quantitative " << (player2Direction == storm::OptimizationDirection::Minimize ? "lower" : "upper") << " bound " << result.initialStateValue << " in " << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count() << "ms.");
|
|
|
|
return result;
|
|
}
|
|
|
|
template<storm::dd::DdType Type, typename ModelType>
|
|
std::unique_ptr<CheckResult> GameBasedMdpModelChecker<Type, ModelType>::performGameBasedAbstractionRefinement(CheckTask<storm::logic::Formula> const& checkTask, storm::expressions::Expression const& constraintExpression, storm::expressions::Expression const& targetStateExpression) {
|
|
STORM_LOG_THROW(checkTask.isOnlyInitialStatesRelevantSet(), storm::exceptions::InvalidPropertyException, "The game-based abstraction refinement model checker can only compute the result for the initial states.");
|
|
|
|
// Optimization: do not compute both bounds if not necessary (e.g. if bound given and exceeded, etc.)
|
|
|
|
// Set up initial predicates.
|
|
std::vector<storm::expressions::Expression> initialPredicates = getInitialPredicates(constraintExpression, targetStateExpression);
|
|
|
|
// Derive the optimization direction for player 1 (assuming menu-game abstraction).
|
|
storm::OptimizationDirection player1Direction = getPlayer1Direction(checkTask);
|
|
|
|
// Create the abstractor.
|
|
storm::abstraction::prism::PrismMenuGameAbstractor<Type, ValueType> abstractor(preprocessedModel.asPrismProgram(), initialPredicates, smtSolverFactory);
|
|
|
|
// TODO: create refiner and move initial predicates there.
|
|
|
|
// Enter the main-loop of abstraction refinement.
|
|
for (uint_fast64_t iterations = 0; iterations < 10000; ++iterations) {
|
|
auto iterationStart = std::chrono::high_resolution_clock::now();
|
|
STORM_LOG_TRACE("Starting iteration " << iterations << ".");
|
|
|
|
// (1) build initial abstraction based on the the constraint expression (if not 'true') and the target state expression.
|
|
storm::abstraction::MenuGame<Type, ValueType> game = abstractor.abstract();
|
|
STORM_LOG_DEBUG("Abstraction in iteration " << iterations << " has " << game.getNumberOfStates() << " (player 1) states and " << game.getNumberOfTransitions() << " transitions.");
|
|
STORM_LOG_THROW(game.getInitialStates().getNonZeroCount(), storm::exceptions::InvalidModelException, "Cannot treat models with more than one (abstract) initial state.");
|
|
|
|
// (2) Prepare transition matrix BDD and target state BDD for later use.
|
|
storm::dd::Bdd<Type> transitionMatrixBdd = game.getTransitionMatrix().toBdd();
|
|
storm::dd::Bdd<Type> initialStates = game.getInitialStates();
|
|
storm::dd::Bdd<Type> constraintStates = game.getStates(constraintExpression);
|
|
storm::dd::Bdd<Type> targetStates = game.getStates(targetStateExpression);
|
|
if (player1Direction == storm::OptimizationDirection::Minimize) {
|
|
targetStates |= game.getBottomStates();
|
|
}
|
|
|
|
// #ifdef LOCAL_DEBUG
|
|
// abstractor.exportToDot("game" + std::to_string(iterations) + ".dot", targetStates, game.getManager().getBddOne());
|
|
// #endif
|
|
|
|
// (3) compute all states with probability 0/1 wrt. to the two different player 2 goals (min/max).
|
|
auto qualitativeStart = std::chrono::high_resolution_clock::now();
|
|
detail::GameProb01ResultMinMax<Type> qualitativeResult;
|
|
std::unique_ptr<CheckResult> result = computeProb01States(checkTask, qualitativeResult, game, player1Direction, transitionMatrixBdd, initialStates, constraintStates, targetStates);
|
|
if (result) {
|
|
return result;
|
|
}
|
|
auto qualitativeEnd = std::chrono::high_resolution_clock::now();
|
|
STORM_LOG_DEBUG("Qualitative computation completed in " << std::chrono::duration_cast<std::chrono::milliseconds>(qualitativeEnd - qualitativeStart).count() << "ms.");
|
|
|
|
// (4) compute the states for which we have to determine quantitative information.
|
|
storm::dd::Bdd<Type> maybeMin = !(qualitativeResult.prob0Min.getPlayer1States() || qualitativeResult.prob1Min.getPlayer1States()) && game.getReachableStates();
|
|
storm::dd::Bdd<Type> maybeMax = !(qualitativeResult.prob0Max.getPlayer1States() || qualitativeResult.prob1Max.getPlayer1States()) && game.getReachableStates();
|
|
|
|
// (5) if the initial states are not maybe states, then we can refine at this point.
|
|
storm::dd::Bdd<Type> initialMaybeStates = (initialStates && maybeMin) || (initialStates && maybeMax);
|
|
bool qualitativeRefinement = false;
|
|
if (initialMaybeStates.isZero()) {
|
|
// In this case, we know the result for the initial states for both player 2 minimizing and maximizing.
|
|
STORM_LOG_TRACE("No initial state is a 'maybe' state. Refining abstraction based on qualitative check.");
|
|
|
|
result = checkForResultAfterQualitativeCheck<Type, ValueType>(checkTask, initialStates, qualitativeResult);
|
|
if (result) {
|
|
return result;
|
|
} else {
|
|
STORM_LOG_DEBUG("Obtained qualitative bounds [0, 1] on the actual value for the initial states.");
|
|
|
|
// If we get here, the initial states were all identified as prob0/1 states, but the value (0 or 1)
|
|
// depends on whether player 2 is minimizing or maximizing. Therefore, we need to find a place to refine.
|
|
qualitativeRefinement = refineAfterQualitativeCheck(abstractor, game, qualitativeResult, transitionMatrixBdd);
|
|
}
|
|
}
|
|
|
|
if (!qualitativeRefinement) {
|
|
// At this point, we know that we cannot answer the query without further numeric computation.
|
|
|
|
storm::dd::Add<Type, ValueType> initialStatesAdd = initialStates.template toAdd<ValueType>();
|
|
|
|
STORM_LOG_TRACE("Starting numerical solution step.");
|
|
auto quantitativeStart = std::chrono::high_resolution_clock::now();
|
|
|
|
// Solve the min values and check whether we can give the answer already.
|
|
QuantitativeResult<Type, ValueType> minResult = computeQuantitativeResult(player1Direction, storm::OptimizationDirection::Minimize, game, qualitativeResult, initialStatesAdd, maybeMin);
|
|
result = checkForResultAfterQuantitativeCheck<ValueType>(checkTask, storm::OptimizationDirection::Minimize, minResult.initialStateValue);
|
|
if (result) {
|
|
return result;
|
|
}
|
|
|
|
// Solve the max values and check whether we can give the answer already.
|
|
QuantitativeResult<Type, ValueType> maxResult = computeQuantitativeResult(player1Direction, storm::OptimizationDirection::Maximize, game, qualitativeResult, initialStatesAdd, maybeMax, boost::make_optional(minResult));
|
|
result = checkForResultAfterQuantitativeCheck<ValueType>(checkTask, storm::OptimizationDirection::Maximize, maxResult.initialStateValue);
|
|
if (result) {
|
|
return result;
|
|
}
|
|
|
|
auto quantitativeEnd = std::chrono::high_resolution_clock::now();
|
|
STORM_LOG_DEBUG("Obtained quantitative bounds [" << minResult.initialStateValue << ", " << maxResult.initialStateValue << "] on the actual value for the initial states in " << std::chrono::duration_cast<std::chrono::milliseconds>(quantitativeEnd - quantitativeStart).count() << "ms.");
|
|
|
|
result = checkForResultAfterQuantitativeCheck<ValueType>(checkTask, minResult.initialStateValue, maxResult.initialStateValue);
|
|
if (result) {
|
|
return result;
|
|
}
|
|
|
|
// If we arrived at this point, it means that we have all qualitative and quantitative information
|
|
// about the game, but we could not yet answer the query. In this case, we need to refine.
|
|
|
|
// Make sure that all strategies are still valid strategies.
|
|
STORM_LOG_ASSERT(minResult.player1Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer1Variables()).getMax() <= 1, "Player 1 strategy for min is illegal.");
|
|
STORM_LOG_ASSERT(maxResult.player1Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer1Variables()).getMax() <= 1, "Player 1 strategy for max is illegal.");
|
|
STORM_LOG_ASSERT(minResult.player2Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer2Variables()).getMax() <= 1, "Player 2 strategy for min is illegal.");
|
|
STORM_LOG_ASSERT(maxResult.player2Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer2Variables()).getMax() <= 1, "Player 2 strategy for max is illegal.");
|
|
|
|
#ifdef LOCAL_DEBUG
|
|
// Check whether the strategies coincide over the reachable parts.
|
|
// storm::dd::Bdd<Type> tmp = game.getTransitionMatrix().toBdd() && (minMaybeStateResult.player1Strategy || maxMaybeStateResult.player1Strategy) && (minMaybeStateResult.player2Strategy || maxMaybeStateResult.player2Strategy);
|
|
// storm::dd::Bdd<Type> commonReach = storm::utility::dd::computeReachableStates(initialStates, tmp.existsAbstract(game.getNondeterminismVariables()), game.getRowVariables(), game.getColumnVariables());
|
|
// STORM_LOG_ASSERT((commonReach && minMaybeStateResult.player1Strategy) != (commonReach && maxMaybeStateResult.player1Strategy) || (commonReach && minMaybeStateResult.player2Strategy) != (commonReach && maxMaybeStateResult.player2Strategy), "The strategies fully coincide.");
|
|
#endif
|
|
|
|
refineAfterQuantitativeCheck(abstractor, game, transitionMatrixBdd, minResult, maxResult);
|
|
}
|
|
auto iterationEnd = std::chrono::high_resolution_clock::now();
|
|
STORM_LOG_DEBUG("Iteration " << iterations << " took " << std::chrono::duration_cast<std::chrono::milliseconds>(iterationEnd - iterationStart).count() << "ms.");
|
|
}
|
|
|
|
STORM_LOG_ASSERT(false, "This point must not be reached.");
|
|
return nullptr;
|
|
}
|
|
|
|
template<storm::dd::DdType Type, typename ModelType>
|
|
std::vector<storm::expressions::Expression> GameBasedMdpModelChecker<Type, ModelType>::getInitialPredicates(storm::expressions::Expression const& constraintExpression, storm::expressions::Expression const& targetStateExpression) {
|
|
std::vector<storm::expressions::Expression> initialPredicates;
|
|
initialPredicates.push_back(targetStateExpression);
|
|
if (!constraintExpression.isTrue() && !constraintExpression.isFalse()) {
|
|
initialPredicates.push_back(constraintExpression);
|
|
}
|
|
return initialPredicates;
|
|
}
|
|
|
|
template<storm::dd::DdType Type, typename ModelType>
|
|
storm::OptimizationDirection GameBasedMdpModelChecker<Type, ModelType>::getPlayer1Direction(CheckTask<storm::logic::Formula> const& checkTask) {
|
|
if (preprocessedModel.getModelType() == storm::storage::SymbolicModelDescription::ModelType::DTMC) {
|
|
return storm::OptimizationDirection::Maximize;
|
|
} else if (checkTask.isOptimizationDirectionSet()) {
|
|
return checkTask.getOptimizationDirection();
|
|
} else if (checkTask.isBoundSet() && preprocessedModel.getModelType() != storm::storage::SymbolicModelDescription::ModelType::DTMC) {
|
|
return storm::logic::isLowerBound(checkTask.getBoundComparisonType()) ? storm::OptimizationDirection::Minimize : storm::OptimizationDirection::Maximize;
|
|
}
|
|
STORM_LOG_THROW(false, storm::exceptions::InvalidPropertyException, "Could not derive player 1 optimization direction.");
|
|
return storm::OptimizationDirection::Maximize;
|
|
}
|
|
|
|
template<storm::dd::DdType Type, typename ModelType>
|
|
std::unique_ptr<CheckResult> GameBasedMdpModelChecker<Type, ModelType>::computeProb01States(CheckTask<storm::logic::Formula> const& checkTask, detail::GameProb01ResultMinMax<Type>& qualitativeResult, storm::abstraction::MenuGame<Type, ValueType> const& game, storm::OptimizationDirection player1Direction, storm::dd::Bdd<Type> const& transitionMatrixBdd, storm::dd::Bdd<Type> const& initialStates, storm::dd::Bdd<Type> const& constraintStates, storm::dd::Bdd<Type> const& targetStates) {
|
|
qualitativeResult.prob0Min = computeProb01States(true, player1Direction, storm::OptimizationDirection::Minimize, game, transitionMatrixBdd, constraintStates, targetStates);
|
|
qualitativeResult.prob1Min = computeProb01States(false, player1Direction, storm::OptimizationDirection::Minimize, game, transitionMatrixBdd, constraintStates, targetStates);
|
|
std::unique_ptr<CheckResult> result = checkForResultAfterQualitativeCheck<Type, ValueType>(checkTask, storm::OptimizationDirection::Minimize, initialStates, qualitativeResult.prob0Min.getPlayer1States(), qualitativeResult.prob1Min.getPlayer1States());
|
|
if (result) {
|
|
return result;
|
|
}
|
|
|
|
qualitativeResult.prob0Max = computeProb01States(true, player1Direction, storm::OptimizationDirection::Maximize, game, transitionMatrixBdd, constraintStates, targetStates);
|
|
qualitativeResult.prob1Max = computeProb01States(false, player1Direction, storm::OptimizationDirection::Maximize, game, transitionMatrixBdd, constraintStates, targetStates);
|
|
result = checkForResultAfterQualitativeCheck<Type, ValueType>(checkTask, storm::OptimizationDirection::Maximize, initialStates, qualitativeResult.prob0Max.getPlayer1States(), qualitativeResult.prob1Max.getPlayer1States());
|
|
if (result) {
|
|
return result;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
template<storm::dd::DdType Type, typename ModelType>
|
|
storm::utility::graph::GameProb01Result<Type> GameBasedMdpModelChecker<Type, ModelType>::computeProb01States(bool prob0, storm::OptimizationDirection player1Direction, storm::OptimizationDirection player2Direction, storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& transitionMatrixBdd, storm::dd::Bdd<Type> const& constraintStates, storm::dd::Bdd<Type> const& targetStates) {
|
|
storm::utility::graph::GameProb01Result<Type> result;
|
|
if (prob0) {
|
|
result = storm::utility::graph::performProb0(game, transitionMatrixBdd, constraintStates, targetStates, player1Direction, player2Direction, true, true);
|
|
} else {
|
|
result = storm::utility::graph::performProb1(game, transitionMatrixBdd, constraintStates, targetStates, player1Direction, player2Direction, true, true);
|
|
}
|
|
|
|
STORM_LOG_ASSERT(result.hasPlayer1Strategy() && (result.getPlayer1States().isZero() || !result.getPlayer1Strategy().isZero()), "Unable to proceed without strategy.");
|
|
STORM_LOG_ASSERT(result.hasPlayer2Strategy() && (result.getPlayer2States().isZero() || !result.getPlayer2Strategy().isZero()), "Unable to proceed without strategy.");
|
|
|
|
STORM_LOG_TRACE("Computed states with probability " << (prob0 ? "0" : "1") << " (player 1: " << player1Direction << ", player 2: " << player2Direction << "): " << result.getPlayer1States().getNonZeroCount() << " '" << (prob0 ? "no" : "yes") << "' states.");
|
|
|
|
return result;
|
|
}
|
|
|
|
template<storm::dd::DdType Type, typename ModelType>
|
|
storm::expressions::Expression GameBasedMdpModelChecker<Type, ModelType>::getExpression(storm::logic::Formula const& formula) {
|
|
STORM_LOG_THROW(formula.isBooleanLiteralFormula() || formula.isAtomicExpressionFormula() || formula.isAtomicLabelFormula(), storm::exceptions::InvalidPropertyException, "The target states have to be given as label or an expression.");
|
|
storm::expressions::Expression result;
|
|
if (formula.isAtomicLabelFormula()) {
|
|
result = preprocessedModel.asPrismProgram().getLabelExpression(formula.asAtomicLabelFormula().getLabel());
|
|
} else if (formula.isAtomicExpressionFormula()) {
|
|
result = formula.asAtomicExpressionFormula().getExpression();
|
|
} else {
|
|
result = formula.asBooleanLiteralFormula().isTrueFormula() ? preprocessedModel.getManager().boolean(true) : preprocessedModel.getManager().boolean(false);
|
|
}
|
|
return result;
|
|
}
|
|
|
|
template class GameBasedMdpModelChecker<storm::dd::DdType::CUDD, storm::models::symbolic::Dtmc<storm::dd::DdType::CUDD, double>>;
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template class GameBasedMdpModelChecker<storm::dd::DdType::CUDD, storm::models::symbolic::Mdp<storm::dd::DdType::CUDD, double>>;
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template class GameBasedMdpModelChecker<storm::dd::DdType::Sylvan, storm::models::symbolic::Dtmc<storm::dd::DdType::Sylvan, double>>;
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template class GameBasedMdpModelChecker<storm::dd::DdType::Sylvan, storm::models::symbolic::Mdp<storm::dd::DdType::Sylvan, double>>;
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}
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}
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