tempest/src/storm/abstraction/jani/EdgeAbstractor.cpp

#include "storm/abstraction/jani/EdgeAbstractor.h"

#include <chrono>

#include <boost/iterator/transform_iterator.hpp>

#include "storm/abstraction/BottomStateResult.h"
#include "storm/abstraction/AbstractionInformation.h"

#include "storm/storage/dd/DdManager.h"
#include "storm/storage/dd/Add.h"

#include "storm/storage/jani/Edge.h"
#include "storm/storage/jani/EdgeDestination.h"

#include "storm/utility/solver.h"
#include "storm/utility/macros.h"

#include "storm-config.h"
#include "storm/adapters/CarlAdapter.h"

namespace storm {
    namespace abstraction {
        namespace jani {
            template <storm::dd::DdType DdType, typename ValueType>
            EdgeAbstractor<DdType, ValueType>::EdgeAbstractor(uint64_t edgeId, storm::jani::Edge const& edge, AbstractionInformation<DdType>& abstractionInformation, std::shared_ptr<storm::utility::solver::SmtSolverFactory> const& smtSolverFactory, bool useDecomposition) : smtSolver(smtSolverFactory->create(abstractionInformation.getExpressionManager())), abstractionInformation(abstractionInformation), edgeId(edgeId), edge(edge), localExpressionInformation(abstractionInformation), evaluator(abstractionInformation.getExpressionManager()), relevantPredicatesAndVariables(), cachedDd(abstractionInformation.getDdManager().getBddZero(), 0), decisionVariables(), useDecomposition(useDecomposition), skipBottomStates(false), forceRecomputation(true), abstractGuard(abstractionInformation.getDdManager().getBddZero()), bottomStateAbstractor(abstractionInformation, {!edge.getGuard()}, smtSolverFactory) {
                
                // Make the second component of relevant predicates have the right size.
                relevantPredicatesAndVariables.second.resize(edge.getNumberOfDestinations());
                
                // Assert all constraints to enforce legal variable values.
                for (auto const& constraint : abstractionInformation.getConstraints()) {
                    smtSolver->add(constraint);
                    bottomStateAbstractor.constrain(constraint);
                }
                
                // Assert the guard of the command.
                smtSolver->add(edge.getGuard());
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            void EdgeAbstractor<DdType, ValueType>::refine(std::vector<uint_fast64_t> const& predicates) {
                // Add all predicates to the variable partition.
                for (auto predicateIndex : predicates) {
                    localExpressionInformation.addExpression(predicateIndex);
                }
                
                // Next, we check whether there is work to be done by recomputing the relevant predicates and checking
                // whether they changed.
                std::pair<std::set<uint_fast64_t>, std::vector<std::set<uint_fast64_t>>> newRelevantPredicates = this->computeRelevantPredicates();
                
                // Check whether we need to recompute the abstraction.
                bool relevantPredicatesChanged = this->relevantPredicatesChanged(newRelevantPredicates);
                if (relevantPredicatesChanged) {
                    addMissingPredicates(newRelevantPredicates);
                }
                forceRecomputation |= relevantPredicatesChanged;
                
                // Refine bottom state abstractor. Note that this does not trigger a recomputation yet.
                bottomStateAbstractor.refine(predicates);
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            storm::expressions::Expression const& EdgeAbstractor<DdType, ValueType>::getGuard() const {
                return edge.get().getGuard();
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            std::map<storm::expressions::Variable, storm::expressions::Expression> EdgeAbstractor<DdType, ValueType>::getVariableUpdates(uint64_t auxiliaryChoice) const {
                return edge.get().getDestination(auxiliaryChoice).getAsVariableToExpressionMap();
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            void EdgeAbstractor<DdType, ValueType>::recomputeCachedBdd() {
                if (useDecomposition) {
                    recomputeCachedBddWithDecomposition();
                } else {
                    recomputeCachedBddWithoutDecomposition();
                }
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            void EdgeAbstractor<DdType, ValueType>::recomputeCachedBddWithDecomposition() {
                STORM_LOG_TRACE("Recomputing BDD for edge with id " << edgeId << " and guard " << edge.get().getGuard() << " using the decomposition.");
                auto start = std::chrono::high_resolution_clock::now();
                
                // compute a decomposition of the command
                //  * start with all relevant blocks: blocks of assignment variables and variables in the rhs of assignments
                //  * go through all assignments of all updates and merge relevant blocks that are related via an assignment
                //  * repeat this until nothing changes anymore
                //  * the resulting blocks are the decomposition
                
                // Start by constructing the relevant blocks.
                std::set<uint64_t> allRelevantBlocks;
                std::map<storm::expressions::Variable, uint64_t> variableToBlockIndex;
                for (auto const& destination : edge.get().getDestinations()) {
                    for (auto const& assignment : destination.getOrderedAssignments().getAllAssignments()) {
                        allRelevantBlocks.insert(localExpressionInformation.getBlockIndexOfVariable(assignment.getExpressionVariable()));
                        
                        auto rhsVariableBlocks = localExpressionInformation.getBlockIndicesOfVariables(assignment.getAssignedExpression().getVariables());
                        allRelevantBlocks.insert(rhsVariableBlocks.begin(), rhsVariableBlocks.end());
                    }
                }
                STORM_LOG_TRACE("Found " << allRelevantBlocks.size() << " relevant block(s).");
                
                // Create a block partition.
                std::vector<std::set<uint64_t>> relevantBlockPartition;
                std::map<storm::expressions::Variable, uint64_t> variableToLocalBlockIndex;
                uint64_t index = 0;
                for (auto const& blockIndex : allRelevantBlocks) {
                    relevantBlockPartition.emplace_back(std::set<uint64_t>({blockIndex}));
                    for (auto const& variable : localExpressionInformation.getVariableBlockWithIndex(blockIndex)) {
                        variableToLocalBlockIndex[variable] = index;
                    }
                    ++index;
                }
                
                // Merge all blocks that are related via the right-hand side of assignments.
                for (auto const& destination : edge.get().getDestinations()) {
                    for (auto const& assignment : destination.getOrderedAssignments().getAllAssignments()) {
                        std::set<storm::expressions::Variable> rhsVariables = assignment.getAssignedExpression().getVariables();
                        
                        if (!rhsVariables.empty()) {
                            uint64_t blockToKeep = variableToLocalBlockIndex.at(*rhsVariables.begin());
                            for (auto const& variable : rhsVariables) {
                                uint64_t block = variableToLocalBlockIndex.at(variable);
                                if (block != blockToKeep) {
                                    for (auto const& blockIndex : relevantBlockPartition[block]) {
                                        for (auto const& variable : localExpressionInformation.getVariableBlockWithIndex(blockIndex)) {
                                            variableToLocalBlockIndex[variable] = blockToKeep;
                                        }
                                    }
                                    relevantBlockPartition[blockToKeep].insert(relevantBlockPartition[block].begin(), relevantBlockPartition[block].end());
                                    relevantBlockPartition[block].clear();
                                }
                            }
                        }
                    }
                }
                
                // Proceed by relating the blocks via assignment-variables and the expressions of their assigned expressions.
                bool changed = false;
                do {
                    changed = false;
                    for (auto const& destination : edge.get().getDestinations()) {
                        for (auto const& assignment : destination.getOrderedAssignments().getAllAssignments()) {
                            std::set<storm::expressions::Variable> rhsVariables = assignment.getAssignedExpression().getVariables();
                            
                            if (!rhsVariables.empty()) {
                                storm::expressions::Variable const& representativeVariable = *rhsVariables.begin();
                                uint64_t representativeBlock = variableToLocalBlockIndex.at(representativeVariable);
                                uint64_t assignmentVariableBlock = variableToLocalBlockIndex.at(assignment.getExpressionVariable());
                                
                                // If the blocks are different, we merge them now
                                if (assignmentVariableBlock != representativeBlock) {
                                    changed = true;
                                    
                                    for (auto const& blockIndex : relevantBlockPartition[assignmentVariableBlock]) {
                                        for (auto const& variable : localExpressionInformation.getVariableBlockWithIndex(blockIndex)) {
                                            variableToLocalBlockIndex[variable] = representativeBlock;
                                        }
                                    }
                                    relevantBlockPartition[representativeBlock].insert(relevantBlockPartition[assignmentVariableBlock].begin(), relevantBlockPartition[assignmentVariableBlock].end());
                                    relevantBlockPartition[assignmentVariableBlock].clear();
                                    
                                }
                            }
                        }
                    }
                } while (changed);
                
                // Now remove all blocks that are empty and obtain the partition.
                std::vector<std::set<uint64_t>> cleanedRelevantBlockPartition;
                for (auto& element : relevantBlockPartition) {
                    if (!element.empty()) {
                        cleanedRelevantBlockPartition.emplace_back(std::move(element));
                    }
                }
                relevantBlockPartition = std::move(cleanedRelevantBlockPartition);
                
                // if the decomposition has size 1, use the plain technique from before
                if (relevantBlockPartition.size() == 1) {
                    STORM_LOG_TRACE("Relevant block partition size is one, falling back to regular computation.");
                    recomputeCachedBddWithoutDecomposition();
                } else {
                    std::set<storm::expressions::Variable> variablesContainedInGuard = edge.get().getGuard().getVariables();
                    
                    // Check whether we need to enumerate the guard. This is the case if the blocks related by the guard
                    // are not contained within a single block of our decomposition.
                    bool enumerateAbstractGuard = true;
                    std::set<uint64_t> guardBlocks = localExpressionInformation.getBlockIndicesOfVariables(variablesContainedInGuard);
                    for (auto const& block : relevantBlockPartition) {
                        bool allContained = true;
                        for (auto const& guardBlock : guardBlocks) {
                            if (block.find(guardBlock) == block.end()) {
                                allContained = false;
                                break;
                            }
                        }
                        if (allContained) {
                            enumerateAbstractGuard = false;
                        }
                    }
                    
                    uint64_t numberOfSolutions = 0;
                    
                    if (enumerateAbstractGuard) {
                        // otherwise, enumerate the abstract guard so we do this only once
                        std::set<uint64_t> relatedGuardPredicates = localExpressionInformation.getRelatedExpressions(variablesContainedInGuard);
                        std::vector<storm::expressions::Variable> guardDecisionVariables;
                        std::vector<std::pair<storm::expressions::Variable, uint_fast64_t>> guardVariablesAndPredicates;
                        for (auto const& element : relevantPredicatesAndVariables.first) {
                            if (relatedGuardPredicates.find(element.second) != relatedGuardPredicates.end()) {
                                guardDecisionVariables.push_back(element.first);
                                guardVariablesAndPredicates.push_back(element);
                            }
                        }
                        abstractGuard = this->getAbstractionInformation().getDdManager().getBddZero();
                        smtSolver->allSat(guardDecisionVariables, [this,&guardVariablesAndPredicates,&numberOfSolutions] (storm::solver::SmtSolver::ModelReference const& model) {
                            abstractGuard |= getSourceStateBdd(model, guardVariablesAndPredicates);
                            ++numberOfSolutions;
                            return true;
                        });
                        STORM_LOG_TRACE("Enumerated " << numberOfSolutions << " for abstract guard.");
                        
                        // now that we have the abstract guard, we can add it as an assertion to the solver before enumerating
                        // the other solutions.
                        
                        // Create a new backtracking point before adding the guard.
                        smtSolver->push();
                        
                        // Create the guard constraint.
                        std::pair<std::vector<storm::expressions::Expression>, std::unordered_map<uint_fast64_t, storm::expressions::Variable>> result = abstractGuard.toExpression(this->getAbstractionInformation().getExpressionManager());
                        
                        // Then add it to the solver.
                        for (auto const& expression : result.first) {
                            smtSolver->add(expression);
                        }
                        
                        // Finally associate the level variables with the predicates.
                        for (auto const& indexVariablePair : result.second) {
                            smtSolver->add(storm::expressions::iff(indexVariablePair.second, this->getAbstractionInformation().getPredicateForDdVariableIndex(indexVariablePair.first)));
                        }
                    }
                    
                    // then enumerate the solutions for each of the blocks of the decomposition
                    uint64_t usedNondeterminismVariables = 0;
                    uint64_t blockCounter = 0;
                    std::vector<storm::dd::Bdd<DdType>> blockBdds;
                    for (auto const& block : relevantBlockPartition) {
                        std::set<uint64_t> relevantPredicates;
                        for (auto const& innerBlock : block) {
                            relevantPredicates.insert(localExpressionInformation.getExpressionBlock(innerBlock).begin(), localExpressionInformation.getExpressionBlock(innerBlock).end());
                        }
                        
                        std::vector<storm::expressions::Variable> transitionDecisionVariables;
                        std::vector<std::pair<storm::expressions::Variable, uint_fast64_t>> sourceVariablesAndPredicates;
                        for (auto const& element : relevantPredicatesAndVariables.first) {
                            if (relevantPredicates.find(element.second) != relevantPredicates.end()) {
                                transitionDecisionVariables.push_back(element.first);
                                sourceVariablesAndPredicates.push_back(element);
                            }
                        }
                        
                        std::vector<std::vector<std::pair<storm::expressions::Variable, uint_fast64_t>>> destinationVariablesAndPredicates;
                        for (uint64_t destinationIndex = 0; destinationIndex < edge.get().getNumberOfDestinations(); ++destinationIndex) {
                            destinationVariablesAndPredicates.emplace_back();
                            for (auto const& assignment : edge.get().getDestination(destinationIndex).getOrderedAssignments().getAllAssignments()) {
                                uint64_t assignmentVariableBlockIndex = localExpressionInformation.getBlockIndexOfVariable(assignment.getExpressionVariable());
                                std::set<uint64_t> const& assignmentVariableBlock = localExpressionInformation.getExpressionBlock(assignmentVariableBlockIndex);
                                if (block.find(assignmentVariableBlockIndex) != block.end()) {
                                    for (auto const& element : relevantPredicatesAndVariables.second[destinationIndex]) {
                                        if (assignmentVariableBlock.find(element.second) != assignmentVariableBlock.end()) {
                                            destinationVariablesAndPredicates.back().push_back(element);
                                            transitionDecisionVariables.push_back(element.first);
                                        }
                                    }
                                }
                            }
                        }
                        
                        std::unordered_map<storm::dd::Bdd<DdType>, std::vector<storm::dd::Bdd<DdType>>> sourceToDistributionsMap;
                        numberOfSolutions = 0;
                        smtSolver->allSat(transitionDecisionVariables, [&sourceToDistributionsMap,this,&numberOfSolutions,&sourceVariablesAndPredicates,&destinationVariablesAndPredicates] (storm::solver::SmtSolver::ModelReference const& model) {
                            sourceToDistributionsMap[getSourceStateBdd(model, sourceVariablesAndPredicates)].push_back(getDistributionBdd(model, destinationVariablesAndPredicates));
                            ++numberOfSolutions;
                            return true;
                        });
                        STORM_LOG_TRACE("Enumerated " << numberOfSolutions << " solutions for block " << blockCounter << ".");
                        numberOfSolutions = 0;
                        
                        // Now we search for the maximal number of choices of player 2 to determine how many DD variables we
                        // need to encode the nondeterminism.
                        uint_fast64_t maximalNumberOfChoices = 0;
                        for (auto const& sourceDistributionsPair : sourceToDistributionsMap) {
                            maximalNumberOfChoices = std::max(maximalNumberOfChoices, static_cast<uint_fast64_t>(sourceDistributionsPair.second.size()));
                        }
                        
                        // We now compute how many variables we need to encode the choices. We add one to the maximal number of
                        // choices to account for a possible transition to a bottom state.
                        uint_fast64_t numberOfVariablesNeeded = static_cast<uint_fast64_t>(std::ceil(std::log2(maximalNumberOfChoices + 1)));
                        
                        // Finally, build overall result.
                        storm::dd::Bdd<DdType> resultBdd = this->getAbstractionInformation().getDdManager().getBddZero();
                        
                        uint_fast64_t sourceStateIndex = 0;
                        for (auto const& sourceDistributionsPair : sourceToDistributionsMap) {
                            STORM_LOG_ASSERT(!sourceDistributionsPair.first.isZero(), "The source BDD must not be empty.");
                            STORM_LOG_ASSERT(!sourceDistributionsPair.second.empty(), "The distributions must not be empty.");
                            // We start with the distribution index of 1, becase 0 is reserved for a potential bottom choice.
                            uint_fast64_t distributionIndex = 1;
                            storm::dd::Bdd<DdType> allDistributions = this->getAbstractionInformation().getDdManager().getBddZero();
                            for (auto const& distribution : sourceDistributionsPair.second) {
                                allDistributions |= distribution && this->getAbstractionInformation().encodePlayer2Choice(distributionIndex, usedNondeterminismVariables, usedNondeterminismVariables + numberOfVariablesNeeded);
                                ++distributionIndex;
                                STORM_LOG_ASSERT(!allDistributions.isZero(), "The BDD must not be empty.");
                            }
                            resultBdd |= sourceDistributionsPair.first && allDistributions;
                            ++sourceStateIndex;
                            STORM_LOG_ASSERT(!resultBdd.isZero(), "The BDD must not be empty.");
                        }
                        usedNondeterminismVariables += numberOfVariablesNeeded;
                        
                        blockBdds.push_back(resultBdd);
                        ++blockCounter;
                    }
                    
                    if (enumerateAbstractGuard) {
                        smtSolver->pop();
                    }
                    
                    // multiply the results
                    storm::dd::Bdd<DdType> resultBdd = getAbstractionInformation().getDdManager().getBddOne();
                    for (auto const& blockBdd : blockBdds) {
                        resultBdd &= blockBdd;
                    }
                    
                    // if we did not explicitly enumerate the guard, we can construct it from the result BDD.
                    if (!enumerateAbstractGuard) {
                        std::set<storm::expressions::Variable> allVariables(this->getAbstractionInformation().getSuccessorVariables());
                        auto player2Variables = this->getAbstractionInformation().getPlayer2VariableSet(usedNondeterminismVariables);
                        allVariables.insert(player2Variables.begin(), player2Variables.end());
                        auto auxVariables = this->getAbstractionInformation().getAuxVariableSet(0, this->getAbstractionInformation().getAuxVariableCount());
                        allVariables.insert(auxVariables.begin(), auxVariables.end());
                        
                        std::set<storm::expressions::Variable> variablesToAbstract;
                        std::set_intersection(allVariables.begin(), allVariables.end(), resultBdd.getContainedMetaVariables().begin(), resultBdd.getContainedMetaVariables().end(), std::inserter(variablesToAbstract, variablesToAbstract.begin()));
                        
                        abstractGuard = resultBdd.existsAbstract(variablesToAbstract);
                    } else {
                        // Multiply the abstract guard as it can contain predicates that are not mentioned in the blocks.
                        resultBdd &= abstractGuard;
                    }
                    
                    // multiply with missing identities
                    resultBdd &= computeMissingIdentities();
                    
                    // cache and return result
                    resultBdd &= this->getAbstractionInformation().encodePlayer1Choice(edgeId, this->getAbstractionInformation().getPlayer1VariableCount());
                    
                    // Cache the result.
                    cachedDd = GameBddResult<DdType>(resultBdd, usedNondeterminismVariables);
                    
                    auto end = std::chrono::high_resolution_clock::now();
                    STORM_LOG_TRACE("Enumerated " << numberOfSolutions << " solutions in " << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count() << "ms.");
                    forceRecomputation = false;
                }
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            void EdgeAbstractor<DdType, ValueType>::recomputeCachedBddWithoutDecomposition() {
                STORM_LOG_TRACE("Recomputing BDD for edge with id " << edgeId << " and guard " << edge.get().getGuard());
                auto start = std::chrono::high_resolution_clock::now();
                
                // Create a mapping from source state DDs to their distributions.
                std::unordered_map<storm::dd::Bdd<DdType>, std::vector<storm::dd::Bdd<DdType>>> sourceToDistributionsMap;
                uint64_t numberOfSolutions = 0;
                smtSolver->allSat(decisionVariables, [&sourceToDistributionsMap,this,&numberOfSolutions] (storm::solver::SmtSolver::ModelReference const& model) {
                    sourceToDistributionsMap[getSourceStateBdd(model, relevantPredicatesAndVariables.first)].push_back(getDistributionBdd(model, relevantPredicatesAndVariables.second));
                    ++numberOfSolutions;
                    return true;
                });
                
                // Now we search for the maximal number of choices of player 2 to determine how many DD variables we
                // need to encode the nondeterminism.
                uint_fast64_t maximalNumberOfChoices = 0;
                for (auto const& sourceDistributionsPair : sourceToDistributionsMap) {
                    maximalNumberOfChoices = std::max(maximalNumberOfChoices, static_cast<uint_fast64_t>(sourceDistributionsPair.second.size()));
                }
                
                // We now compute how many variables we need to encode the choices. We add one to the maximal number of
                // choices to account for a possible transition to a bottom state.
                uint_fast64_t numberOfVariablesNeeded = static_cast<uint_fast64_t>(std::ceil(std::log2(maximalNumberOfChoices + 1)));
                
                // Finally, build overall result.
                storm::dd::Bdd<DdType> resultBdd = this->getAbstractionInformation().getDdManager().getBddZero();
                if (!skipBottomStates) {
                    abstractGuard = this->getAbstractionInformation().getDdManager().getBddZero();
                }
                uint_fast64_t sourceStateIndex = 0;
                for (auto const& sourceDistributionsPair : sourceToDistributionsMap) {
                    if (!skipBottomStates) {
                        abstractGuard |= sourceDistributionsPair.first;
                    }
                    
                    STORM_LOG_ASSERT(!sourceDistributionsPair.first.isZero(), "The source BDD must not be empty.");
                    STORM_LOG_ASSERT(!sourceDistributionsPair.second.empty(), "The distributions must not be empty.");
                    // We start with the distribution index of 1, becase 0 is reserved for a potential bottom choice.
                    uint_fast64_t distributionIndex = 1;
                    storm::dd::Bdd<DdType> allDistributions = this->getAbstractionInformation().getDdManager().getBddZero();
                    for (auto const& distribution : sourceDistributionsPair.second) {
                        allDistributions |= distribution && this->getAbstractionInformation().encodePlayer2Choice(distributionIndex, 0, numberOfVariablesNeeded);
                        ++distributionIndex;
                        STORM_LOG_ASSERT(!allDistributions.isZero(), "The BDD must not be empty.");
                    }
                    resultBdd |= sourceDistributionsPair.first && allDistributions;
                    ++sourceStateIndex;
                    STORM_LOG_ASSERT(!resultBdd.isZero(), "The BDD must not be empty.");
                }
                
                resultBdd &= computeMissingIdentities();
                resultBdd &= this->getAbstractionInformation().encodePlayer1Choice(edgeId, this->getAbstractionInformation().getPlayer1VariableCount());
                STORM_LOG_ASSERT(sourceToDistributionsMap.empty() || !resultBdd.isZero(), "The BDD must not be empty, if there were distributions.");
                
                // Cache the result.
                cachedDd = GameBddResult<DdType>(resultBdd, numberOfVariablesNeeded);
                auto end = std::chrono::high_resolution_clock::now();
                
                STORM_LOG_TRACE("Enumerated " << numberOfSolutions << " solutions in " << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count() << "ms.");
                forceRecomputation = false;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            std::pair<std::set<uint_fast64_t>, std::set<uint_fast64_t>> EdgeAbstractor<DdType, ValueType>::computeRelevantPredicates(storm::jani::OrderedAssignments const& assignments) const {
                std::pair<std::set<uint_fast64_t>, std::set<uint_fast64_t>> result;
                
                std::set<storm::expressions::Variable> assignedVariables;
                for (auto const& assignment : assignments.getAllAssignments()) {
                    // Also, variables appearing on the right-hand side of an assignment are relevant for source state.
                    auto const& rightHandSidePredicates = localExpressionInformation.getExpressionsUsingVariables(assignment.getAssignedExpression().getVariables());
                    result.first.insert(rightHandSidePredicates.begin(), rightHandSidePredicates.end());
                    
                    // Variables that are being assigned are relevant for the successor state.
                    storm::expressions::Variable const& assignedVariable = assignment.getExpressionVariable();
                    auto const& leftHandSidePredicates = localExpressionInformation.getExpressionsUsingVariable(assignedVariable);
                    result.second.insert(leftHandSidePredicates.begin(), leftHandSidePredicates.end());
                    
                    // Keep track of all assigned variables, so we can find the related predicates later.
                    assignedVariables.insert(assignedVariable);
                }
                
                auto const& predicatesRelatedToAssignedVariable = localExpressionInformation.getRelatedExpressions(assignedVariables);
                result.first.insert(predicatesRelatedToAssignedVariable.begin(), predicatesRelatedToAssignedVariable.end());
                
                return result;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            std::pair<std::set<uint_fast64_t>, std::vector<std::set<uint_fast64_t>>> EdgeAbstractor<DdType, ValueType>::computeRelevantPredicates() const {
                std::pair<std::set<uint_fast64_t>, std::vector<std::set<uint_fast64_t>>> result;
                
                // To start with, all predicates related to the guard are relevant source predicates.
                result.first = localExpressionInformation.getExpressionsUsingVariables(edge.get().getGuard().getVariables());
                
                // Then, we add the predicates that become relevant, because of some update.
                for (auto const& destination : edge.get().getDestinations()) {
                    std::pair<std::set<uint_fast64_t>, std::set<uint_fast64_t>> relevantUpdatePredicates = computeRelevantPredicates(destination.getOrderedAssignments());
                    result.first.insert(relevantUpdatePredicates.first.begin(), relevantUpdatePredicates.first.end());
                    result.second.push_back(relevantUpdatePredicates.second);
                }
                
                return result;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            bool EdgeAbstractor<DdType, ValueType>::relevantPredicatesChanged(std::pair<std::set<uint_fast64_t>, std::vector<std::set<uint_fast64_t>>> const& newRelevantPredicates) const {
                if (newRelevantPredicates.first.size() > relevantPredicatesAndVariables.first.size()) {
                    return true;
                }
                
                for (uint_fast64_t index = 0; index < edge.get().getNumberOfDestinations(); ++index) {
                    if (newRelevantPredicates.second[index].size() > relevantPredicatesAndVariables.second[index].size()) {
                        return true;
                    }
                }
                
                return false;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            void EdgeAbstractor<DdType, ValueType>::addMissingPredicates(std::pair<std::set<uint_fast64_t>, std::vector<std::set<uint_fast64_t>>> const& newRelevantPredicates) {
                // Determine and add new relevant source predicates.
                std::vector<std::pair<storm::expressions::Variable, uint_fast64_t>> newSourceVariables = this->getAbstractionInformation().declareNewVariables(relevantPredicatesAndVariables.first, newRelevantPredicates.first);
                for (auto const& element : newSourceVariables) {
                    allRelevantPredicates.insert(element.second);
                    smtSolver->add(storm::expressions::iff(element.first, this->getAbstractionInformation().getPredicateByIndex(element.second)));
                    decisionVariables.push_back(element.first);
                }
                
                // Insert the new variables into the record of relevant source variables.
                relevantPredicatesAndVariables.first.insert(relevantPredicatesAndVariables.first.end(), newSourceVariables.begin(), newSourceVariables.end());
                std::sort(relevantPredicatesAndVariables.first.begin(), relevantPredicatesAndVariables.first.end(), [] (std::pair<storm::expressions::Variable, uint_fast64_t> const& first, std::pair<storm::expressions::Variable, uint_fast64_t> const& second) { return first.second < second.second; } );
                
                // Do the same for every update.
                for (uint_fast64_t index = 0; index < edge.get().getNumberOfDestinations(); ++index) {
                    std::vector<std::pair<storm::expressions::Variable, uint_fast64_t>> newSuccessorVariables = this->getAbstractionInformation().declareNewVariables(relevantPredicatesAndVariables.second[index], newRelevantPredicates.second[index]);
                    for (auto const& element : newSuccessorVariables) {
                        allRelevantPredicates.insert(element.second);
                        smtSolver->add(storm::expressions::iff(element.first, this->getAbstractionInformation().getPredicateByIndex(element.second).substitute(edge.get().getDestination(index).getAsVariableToExpressionMap())));
                        decisionVariables.push_back(element.first);
                    }
                    
                    relevantPredicatesAndVariables.second[index].insert(relevantPredicatesAndVariables.second[index].end(), newSuccessorVariables.begin(), newSuccessorVariables.end());
                    std::sort(relevantPredicatesAndVariables.second[index].begin(), relevantPredicatesAndVariables.second[index].end(), [] (std::pair<storm::expressions::Variable, uint_fast64_t> const& first, std::pair<storm::expressions::Variable, uint_fast64_t> const& second) { return first.second < second.second; } );
                }
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            storm::dd::Bdd<DdType> EdgeAbstractor<DdType, ValueType>::getSourceStateBdd(storm::solver::SmtSolver::ModelReference const& model, std::vector<std::pair<storm::expressions::Variable, uint_fast64_t>> const& variablePredicates) const {
                storm::dd::Bdd<DdType> result = this->getAbstractionInformation().getDdManager().getBddOne();
                for (auto const& variableIndexPair : variablePredicates) {
                    if (model.getBooleanValue(variableIndexPair.first)) {
                        result &= this->getAbstractionInformation().encodePredicateAsSource(variableIndexPair.second);
                    } else {
                        result &= !this->getAbstractionInformation().encodePredicateAsSource(variableIndexPair.second);
                    }
                }
                
                STORM_LOG_ASSERT(!result.isZero(), "Source must not be empty.");
                return result;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            storm::dd::Bdd<DdType> EdgeAbstractor<DdType, ValueType>::getDistributionBdd(storm::solver::SmtSolver::ModelReference const& model, std::vector<std::vector<std::pair<storm::expressions::Variable, uint_fast64_t>>> const& variablePredicates) const {
                storm::dd::Bdd<DdType> result = this->getAbstractionInformation().getDdManager().getBddZero();
                
                for (uint_fast64_t destinationIndex = 0; destinationIndex < edge.get().getNumberOfDestinations(); ++destinationIndex) {
                    storm::dd::Bdd<DdType> updateBdd = this->getAbstractionInformation().getDdManager().getBddOne();
                    
                    // Translate block variables for this update into a successor block.
                    for (auto const& variableIndexPair : variablePredicates[destinationIndex]) {
                        if (model.getBooleanValue(variableIndexPair.first)) {
                            updateBdd &= this->getAbstractionInformation().encodePredicateAsSuccessor(variableIndexPair.second);
                        } else {
                            updateBdd &= !this->getAbstractionInformation().encodePredicateAsSuccessor(variableIndexPair.second);
                        }
                        updateBdd &= this->getAbstractionInformation().encodeAux(destinationIndex, 0, this->getAbstractionInformation().getAuxVariableCount());
                    }
                    
                    result |= updateBdd;
                }
                
                STORM_LOG_ASSERT(!result.isZero(), "Distribution must not be empty.");
                return result;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            storm::dd::Bdd<DdType> EdgeAbstractor<DdType, ValueType>::computeMissingIdentities() const {
                storm::dd::Bdd<DdType> identities = computeMissingGlobalIdentities();
                identities &= computeMissingUpdateIdentities();
                return identities;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            storm::dd::Bdd<DdType> EdgeAbstractor<DdType, ValueType>::computeMissingUpdateIdentities() const {
                storm::dd::Bdd<DdType> result = this->getAbstractionInformation().getDdManager().getBddZero();
                
                for (uint_fast64_t updateIndex = 0; updateIndex < edge.get().getNumberOfDestinations(); ++updateIndex) {
                    // Compute the identities that are missing for this update.
                    auto updateRelevantIt = relevantPredicatesAndVariables.second[updateIndex].begin();
                    auto updateRelevantIte = relevantPredicatesAndVariables.second[updateIndex].end();
                    
                    storm::dd::Bdd<DdType> updateIdentity = this->getAbstractionInformation().getDdManager().getBddOne();
                    auto sourceRelevantIt = relevantPredicatesAndVariables.first.begin();
                    auto sourceRelevantIte = relevantPredicatesAndVariables.first.end();
                    
                    // Go through all relevant source predicates. This is guaranteed to be a superset of the set of
                    // relevant successor predicates for any update.
                    for (; sourceRelevantIt != sourceRelevantIte; ++sourceRelevantIt) {
                        // If the predicates do not match, there is a predicate missing, so we need to add its identity.
                        if (updateRelevantIt == updateRelevantIte || sourceRelevantIt->second != updateRelevantIt->second) {
                            updateIdentity &= this->getAbstractionInformation().getPredicateIdentity(sourceRelevantIt->second);
                        } else {
                            ++updateRelevantIt;
                        }
                    }
                    
                    result |= updateIdentity && this->getAbstractionInformation().encodeAux(updateIndex, 0, this->getAbstractionInformation().getAuxVariableCount());
                }
                return result;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            storm::dd::Bdd<DdType> EdgeAbstractor<DdType, ValueType>::computeMissingGlobalIdentities() const {
                storm::dd::Bdd<DdType> result = this->getAbstractionInformation().getDdManager().getBddOne();
                
                auto relevantIt = relevantPredicatesAndVariables.first.begin();
                auto relevantIte = relevantPredicatesAndVariables.first.end();
                
                for (uint_fast64_t predicateIndex = 0; predicateIndex < this->getAbstractionInformation().getNumberOfPredicates(); ++predicateIndex) {
                    if (relevantIt == relevantIte || relevantIt->second != predicateIndex) {
                        result &= this->getAbstractionInformation().getPredicateIdentity(predicateIndex);
                    } else {
                        ++relevantIt;
                    }
                }
                
                return result;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            GameBddResult<DdType> EdgeAbstractor<DdType, ValueType>::abstract() {
                if (forceRecomputation) {
                    this->recomputeCachedBdd();
                } else {
                    cachedDd.bdd &= computeMissingGlobalIdentities();
                }
                
                return cachedDd;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            BottomStateResult<DdType> EdgeAbstractor<DdType, ValueType>::getBottomStateTransitions(storm::dd::Bdd<DdType> const& reachableStates, uint_fast64_t numberOfPlayer2Variables, boost::optional<std::pair<storm::expressions::Variable, storm::expressions::Variable>> const& locationVariables) {
                // Compute the reachable states that have this edge enabled.
                storm::dd::Bdd<DdType> reachableStatesWithEdge = (reachableStates && abstractGuard && this->getAbstractionInformation().encodeLocation(locationVariables.get().first, edge.get().getSourceLocationIndex())).existsAbstract(this->getAbstractionInformation().getSourceLocationVariables());
                
                STORM_LOG_TRACE("Computing bottom state transitions of edge with guard " << edge.get().getGuard());
                BottomStateResult<DdType> result(this->getAbstractionInformation().getDdManager().getBddZero(), this->getAbstractionInformation().getDdManager().getBddZero());
                
                // If the guard of this edge is a predicate, there are not bottom states/transitions.
                if (skipBottomStates) {
                    STORM_LOG_TRACE("Skipping bottom state computation for this edge.");
                    return result;
                }
                
                // Use the state abstractor to compute the set of abstract states that has this edge enabled but still
                // has a transition to a bottom state.
                bottomStateAbstractor.constrain(reachableStatesWithEdge);
                result.states = bottomStateAbstractor.getAbstractStates() && reachableStatesWithEdge && this->getAbstractionInformation().encodeLocation(locationVariables.get().first, edge.get().getSourceLocationIndex());
                
                // If the result is empty one time, we can skip the bottom state computation from now on.
                if (result.states.isZero()) {
                    skipBottomStates = true;
                }
                
                // Now equip all these states with an actual transition to a bottom state.
                result.transitions = result.states && this->getAbstractionInformation().getAllPredicateIdentities() && this->getAbstractionInformation().getBottomStateBdd(false, false);
                
                // Mark the states as bottom states and add source location information.
                result.states &= this->getAbstractionInformation().getBottomStateBdd(true, false);
                
                // Add the edge encoding.
                result.transitions &= this->getAbstractionInformation().encodePlayer1Choice(edgeId, this->getAbstractionInformation().getPlayer1VariableCount()) && this->getAbstractionInformation().encodePlayer2Choice(0, 0,numberOfPlayer2Variables) && this->getAbstractionInformation().encodeAux(0, 0, this->getAbstractionInformation().getAuxVariableCount());
                
                // Add the location identity to the transitions.
                result.transitions &= this->getAbstractionInformation().getAllLocationIdentities();
                
                return result;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            storm::dd::Add<DdType, ValueType> EdgeAbstractor<DdType, ValueType>::getEdgeDecoratorAdd(boost::optional<std::pair<storm::expressions::Variable, storm::expressions::Variable>> const& locationVariables) const {
                storm::dd::Add<DdType, ValueType> result = this->getAbstractionInformation().getDdManager().template getAddZero<ValueType>();
                for (uint_fast64_t destinationIndex = 0; destinationIndex < edge.get().getNumberOfDestinations(); ++destinationIndex) {
                    storm::dd::Add<DdType, ValueType> tmp = this->getAbstractionInformation().encodeAux(destinationIndex, 0, this->getAbstractionInformation().getAuxVariableCount()).template toAdd<ValueType>() * this->getAbstractionInformation().getDdManager().getConstant(evaluator.asRational(edge.get().getDestination(destinationIndex).getProbability()));
                    if (locationVariables) {
                        tmp *= this->getAbstractionInformation().encodeLocation(locationVariables.get().second, edge.get().getDestination(destinationIndex).getLocationIndex()).template toAdd<ValueType>();
                    }
                    result += tmp;
                }
                
                storm::dd::Add<DdType, ValueType> tmp = this->getAbstractionInformation().getDdManager().template getAddOne<ValueType>();
                if (locationVariables) {
                    tmp *= this->getAbstractionInformation().encodeLocation(locationVariables.get().first, edge.get().getSourceLocationIndex()).template toAdd<ValueType>();
                }
                tmp *= this->getAbstractionInformation().encodePlayer1Choice(edgeId, this->getAbstractionInformation().getPlayer1VariableCount()).template toAdd<ValueType>();
                
                result *= tmp;
                
                return result;
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            storm::jani::Edge const& EdgeAbstractor<DdType, ValueType>::getConcreteEdge() const {
                return edge.get();
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            AbstractionInformation<DdType> const& EdgeAbstractor<DdType, ValueType>::getAbstractionInformation() const {
                return abstractionInformation.get();
            }
            
            template <storm::dd::DdType DdType, typename ValueType>
            AbstractionInformation<DdType>& EdgeAbstractor<DdType, ValueType>::getAbstractionInformation() {
                return abstractionInformation.get();
            }
            
            template class EdgeAbstractor<storm::dd::DdType::CUDD, double>;
            template class EdgeAbstractor<storm::dd::DdType::Sylvan, double>;
#ifdef STORM_HAVE_CARL
            template class EdgeAbstractor<storm::dd::DdType::Sylvan, storm::RationalFunction>;
#endif
        }
    }
}