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308 lines
22 KiB
308 lines
22 KiB
#include "storm/abstraction/MenuGameRefiner.h"
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#include "storm/abstraction/AbstractionInformation.h"
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#include "storm/abstraction/MenuGameAbstractor.h"
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#include "storm/utility/dd.h"
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#include "storm/settings/SettingsManager.h"
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#include "storm/settings/modules/AbstractionSettings.h"
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namespace storm {
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namespace abstraction {
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template<storm::dd::DdType Type, typename ValueType>
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MenuGameRefiner<Type, ValueType>::MenuGameRefiner(MenuGameAbstractor<Type, ValueType>& abstractor, std::unique_ptr<storm::solver::SmtSolver>&& smtSolver) : abstractor(abstractor), splitPredicates(storm::settings::getModule<storm::settings::modules::AbstractionSettings>().isSplitPredicatesSet()), splitter(), equivalenceChecker(std::move(smtSolver)) {
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// Intentionally left empty.
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}
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template<storm::dd::DdType Type, typename ValueType>
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void MenuGameRefiner<Type, ValueType>::refine(std::vector<storm::expressions::Expression> const& predicates) const {
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abstractor.get().refine(predicates);
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}
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template<storm::dd::DdType Type, typename ValueType>
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storm::dd::Bdd<Type> pickPivotStateWithMinimalDistance(storm::dd::Bdd<Type> const& initialStates, storm::dd::Bdd<Type> const& transitionsMin, storm::dd::Bdd<Type> const& transitionsMax, std::set<storm::expressions::Variable> const& rowVariables, std::set<storm::expressions::Variable> const& columnVariables, storm::dd::Bdd<Type> const& pivotStates, boost::optional<QuantitativeResultMinMax<Type, ValueType>> const& quantitativeResult = boost::none) {
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// Set up used variables.
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storm::dd::Bdd<Type> frontierMin = initialStates;
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storm::dd::Bdd<Type> frontierMax = initialStates;
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storm::dd::Bdd<Type> frontierPivotStates = frontierMin && pivotStates;
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// Check whether we have pivot states on the very first level.
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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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STORM_LOG_TRACE("Picked pivot state from " << frontierPivotStates.getNonZeroCount() << " candidates on level " << level << ", " << pivotStates.getNonZeroCount() << " candidates in total.");
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return frontierPivotStates.existsAbstractRepresentative(rowVariables);
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} else {
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// Otherwise, we perform a simulatenous BFS in the sense that we make one step in both the min and max
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// transitions and check for pivot states we encounter.
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while (!foundPivotState) {
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frontierMin = frontierMin.relationalProduct(transitionsMin, rowVariables, columnVariables);
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frontierMax = frontierMax.relationalProduct(transitionsMax, rowVariables, columnVariables);
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frontierPivotStates = (frontierMin && pivotStates) || (frontierMax && pivotStates);
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if (!frontierPivotStates.isZero()) {
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if (quantitativeResult) {
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storm::dd::Add<Type, ValueType> frontierPivotStatesAdd = frontierPivotStates.template toAdd<ValueType>();
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storm::dd::Add<Type, ValueType> diff = frontierPivotStatesAdd * quantitativeResult.get().max.values - frontierPivotStatesAdd * quantitativeResult.get().min.values;
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STORM_LOG_TRACE("Picked pivot state with difference " << diff.getMax() << " from " << frontierPivotStates.getNonZeroCount() << " candidates on level " << level << ", " << pivotStates.getNonZeroCount() << " candidates in total.");
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return diff.maxAbstractRepresentative(rowVariables);
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} else {
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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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return frontierPivotStates.existsAbstractRepresentative(rowVariables);
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}
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}
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++level;
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}
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}
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STORM_LOG_ASSERT(false, "This point must not be reached, because then no pivot state could be found.");
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return storm::dd::Bdd<Type>();
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}
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template <storm::dd::DdType Type, typename ValueType>
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storm::expressions::Expression MenuGameRefiner<Type, ValueType>::derivePredicateFromDifferingChoices(storm::dd::Bdd<Type> const& pivotState, storm::dd::Bdd<Type> const& player1Choice, storm::dd::Bdd<Type> const& lowerChoice, storm::dd::Bdd<Type> const& upperChoice) const {
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// Prepare result.
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storm::expressions::Expression newPredicate;
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// Get abstraction informatin for easier access.
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AbstractionInformation<Type> const& abstractionInformation = abstractor.get().getAbstractionInformation();
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// Decode the index of the command chosen by player 1.
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storm::dd::Add<Type, ValueType> player1ChoiceAsAdd = player1Choice.template toAdd<ValueType>();
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auto pl1It = player1ChoiceAsAdd.begin();
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uint_fast64_t player1Index = abstractionInformation.decodePlayer1Choice((*pl1It).first, abstractionInformation.getPlayer1VariableCount());
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// Check whether there are bottom states in the game and whether one of the choices actually picks the
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// bottom state as the successor.
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bool buttomStateSuccessor = !((abstractionInformation.getBottomStateBdd(false, false) && lowerChoice) || (abstractionInformation.getBottomStateBdd(false, false) && upperChoice)).isZero();
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// If one of the choices picks the bottom state, the new predicate is based on the guard of the appropriate
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// command (that is the player 1 choice).
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if (buttomStateSuccessor) {
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STORM_LOG_TRACE("One of the successors is a bottom state, taking a guard as a new predicate.");
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newPredicate = abstractor.get().getGuard(player1Index);
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STORM_LOG_DEBUG("Derived new predicate (based on guard): " << newPredicate);
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} else {
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STORM_LOG_TRACE("No bottom state successor. Deriving a new predicate using weakest precondition.");
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// Decode both choices to explicit mappings.
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std::map<uint_fast64_t, storm::storage::BitVector> lowerChoiceUpdateToSuccessorMapping = abstractionInformation.decodeChoiceToUpdateSuccessorMapping(lowerChoice);
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std::map<uint_fast64_t, storm::storage::BitVector> upperChoiceUpdateToSuccessorMapping = abstractionInformation.decodeChoiceToUpdateSuccessorMapping(upperChoice);
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STORM_LOG_ASSERT(lowerChoiceUpdateToSuccessorMapping.size() == upperChoiceUpdateToSuccessorMapping.size(), "Mismatching sizes after decode (" << lowerChoiceUpdateToSuccessorMapping.size() << " vs. " << upperChoiceUpdateToSuccessorMapping.size() << ").");
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// Now go through the mappings and find points of deviation. Currently, we take the first deviation.
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auto lowerIt = lowerChoiceUpdateToSuccessorMapping.begin();
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auto lowerIte = lowerChoiceUpdateToSuccessorMapping.end();
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auto upperIt = upperChoiceUpdateToSuccessorMapping.begin();
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for (; lowerIt != lowerIte; ++lowerIt, ++upperIt) {
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STORM_LOG_ASSERT(lowerIt->first == upperIt->first, "Update indices mismatch.");
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uint_fast64_t updateIndex = lowerIt->first;
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bool deviates = lowerIt->second != upperIt->second;
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if (deviates) {
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for (uint_fast64_t predicateIndex = 0; predicateIndex < lowerIt->second.size(); ++predicateIndex) {
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if (lowerIt->second.get(predicateIndex) != upperIt->second.get(predicateIndex)) {
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// Now we know the point of the deviation (command, update, predicate).
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newPredicate = abstractionInformation.getPredicateByIndex(predicateIndex).substitute(abstractor.get().getVariableUpdates(player1Index, updateIndex)).simplify();
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break;
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}
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}
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}
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}
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STORM_LOG_ASSERT(newPredicate.isInitialized(), "Could not derive new predicate as there is no deviation.");
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STORM_LOG_DEBUG("Derived new predicate (based on weakest-precondition): " << newPredicate);
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}
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STORM_LOG_TRACE("Current set of predicates:");
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for (auto const& predicate : abstractionInformation.getPredicates()) {
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STORM_LOG_TRACE(predicate);
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}
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return newPredicate;
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}
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template<storm::dd::DdType Type>
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struct PivotStateResult {
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storm::dd::Bdd<Type> reachableTransitionsMin;
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storm::dd::Bdd<Type> reachableTransitionsMax;
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storm::dd::Bdd<Type> pivotStates;
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};
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template<storm::dd::DdType Type, typename ValueType>
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PivotStateResult<Type> computePivotStates(storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& transitionMatrixBdd, storm::dd::Bdd<Type> const& minPlayer1Strategy, storm::dd::Bdd<Type> const& minPlayer2Strategy, storm::dd::Bdd<Type> const& maxPlayer1Strategy, storm::dd::Bdd<Type> const& maxPlayer2Strategy) {
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PivotStateResult<Type> result;
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// Build the fragment of transitions that is reachable by either the min or the max strategies.
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result.reachableTransitionsMin = (transitionMatrixBdd && minPlayer1Strategy && minPlayer2Strategy).existsAbstract(game.getNondeterminismVariables());
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result.reachableTransitionsMax = (transitionMatrixBdd && maxPlayer1Strategy && maxPlayer2Strategy).existsAbstract(game.getNondeterminismVariables());
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// Start with all reachable states as potential pivot states.
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result.pivotStates = storm::utility::dd::computeReachableStates(game.getInitialStates(), result.reachableTransitionsMin, game.getRowVariables(), game.getColumnVariables()) ||
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storm::utility::dd::computeReachableStates(game.getInitialStates(), result.reachableTransitionsMax, game.getRowVariables(), game.getColumnVariables());
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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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result.pivotStates &= ((minPlayer1Strategy && maxPlayer1Strategy) && constraint).existsAbstract(game.getNondeterminismVariables());
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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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storm::expressions::Expression MenuGameRefiner<Type, ValueType>::derivePredicateFromPivotState(storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& pivotState, storm::dd::Bdd<Type> const& minPlayer1Strategy, storm::dd::Bdd<Type> const& minPlayer2Strategy, storm::dd::Bdd<Type> const& maxPlayer1Strategy, storm::dd::Bdd<Type> const& maxPlayer2Strategy) const {
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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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storm::expressions::Expression newPredicate = derivePredicateFromDifferingChoices(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 newPredicate;
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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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storm::expressions::Expression newPredicate = derivePredicateFromDifferingChoices(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 newPredicate;
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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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}
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template<storm::dd::DdType Type, typename ValueType>
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bool MenuGameRefiner<Type, ValueType>::refine(storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& transitionMatrixBdd, QualitativeResultMinMax<Type> const& qualitativeResult) const {
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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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// Compute all reached pivot states.
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PivotStateResult<Type> pivotStateResult = computePivotStates(game, transitionMatrixBdd, minPlayer1Strategy, minPlayer2Strategy, maxPlayer1Strategy, maxPlayer2Strategy);
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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 prob1 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 (pivotStateResult.pivotStates.isZero()) {
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return false;
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}
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STORM_LOG_ASSERT(!pivotStateResult.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 = pickPivotStateWithMinimalDistance<Type, ValueType>(game.getInitialStates(), pivotStateResult.reachableTransitionsMin, pivotStateResult.reachableTransitionsMax, game.getRowVariables(), game.getColumnVariables(), pivotStateResult.pivotStates);
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// Derive predicate based on the selected pivot state.
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storm::expressions::Expression newPredicate = derivePredicateFromPivotState(game, pivotState, minPlayer1Strategy, minPlayer2Strategy, maxPlayer1Strategy, maxPlayer2Strategy);
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performRefinement({newPredicate});
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return true;
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}
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template<storm::dd::DdType Type, typename ValueType>
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bool MenuGameRefiner<Type, ValueType>::refine(storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& transitionMatrixBdd, QuantitativeResultMinMax<Type, ValueType> const& quantitativeResult) const {
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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 = quantitativeResult.min.player1Strategy;
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storm::dd::Bdd<Type> minPlayer2Strategy = quantitativeResult.min.player2Strategy;
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storm::dd::Bdd<Type> maxPlayer1Strategy = quantitativeResult.max.player1Strategy;
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storm::dd::Bdd<Type> maxPlayer2Strategy = quantitativeResult.max.player2Strategy;
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// Compute all reached pivot states.
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PivotStateResult<Type> pivotStateResult = computePivotStates(game, transitionMatrixBdd, minPlayer1Strategy, minPlayer2Strategy, maxPlayer1Strategy, maxPlayer2Strategy);
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// TODO: required?
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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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pivotStateResult.pivotStates &= quantitativeResult.min.values.less(quantitativeResult.max.values);
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STORM_LOG_ASSERT(!pivotStateResult.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 = pickPivotStateWithMinimalDistance<Type, ValueType>(game.getInitialStates(), pivotStateResult.reachableTransitionsMin, pivotStateResult.reachableTransitionsMax, game.getRowVariables(), game.getColumnVariables(), pivotStateResult.pivotStates);
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// Derive predicate based on the selected pivot state.
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storm::expressions::Expression newPredicate = derivePredicateFromPivotState(game, pivotState, minPlayer1Strategy, minPlayer2Strategy, maxPlayer1Strategy, maxPlayer2Strategy);
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performRefinement({newPredicate});
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return true;
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}
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template<storm::dd::DdType Type, typename ValueType>
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bool MenuGameRefiner<Type, ValueType>::performRefinement(std::vector<storm::expressions::Expression> const& predicates) const {
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if (splitPredicates) {
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std::vector<storm::expressions::Expression> cleanedAtoms;
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for (auto const& predicate : predicates) {
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AbstractionInformation<Type> const& abstractionInformation = abstractor.get().getAbstractionInformation();
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// Split the predicates.
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std::vector<storm::expressions::Expression> atoms = splitter.split(predicate);
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// Check which of the atoms are redundant in the sense that they are equivalent to a predicate we already have.
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for (auto const& atom : atoms) {
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// Check whether the newly found atom is equivalent to an atom we already have in the predicate
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// set or in the set that is to be added.
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bool addAtom = true;
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for (auto const& oldPredicate : abstractionInformation.getPredicates()) {
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if (equivalenceChecker.areEquivalent(atom, oldPredicate)) {
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addAtom = false;
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break;
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}
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}
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for (auto const& addedAtom : cleanedAtoms) {
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if (equivalenceChecker.areEquivalent(addedAtom, atom)) {
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addAtom = false;
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break;
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}
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}
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if (addAtom) {
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cleanedAtoms.push_back(atom);
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}
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}
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}
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abstractor.get().refine(cleanedAtoms);
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} else {
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// If no splitting of the predicates is required, just forward the refinement request to the abstractor.
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abstractor.get().refine(predicates);
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}
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return true;
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}
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template class MenuGameRefiner<storm::dd::DdType::CUDD, double>;
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template class MenuGameRefiner<storm::dd::DdType::Sylvan, double>;
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}
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}
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