BeliefMdpExplorer.cpp

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#include "storm-pomdp/builder/BeliefMdpExplorer.h"
 
#include "storm-parsers/api/properties.h"
#include "storm/api/properties.h"
#include "storm/api/verification.h"
 
#include "storm/modelchecker/hints/ExplicitModelCheckerHint.h"
#include "storm/modelchecker/results/CheckResult.h"
#include "storm/modelchecker/results/ExplicitQualitativeCheckResult.h"
#include "storm/modelchecker/results/ExplicitQuantitativeCheckResult.h"
#include "storm/models/sparse/Pomdp.h"
#include "storm/storage/SparseMatrix.h"
#include "storm/storage/jani/Property.h"
#include "storm/utility/SignalHandler.h"
#include "storm/utility/constants.h"
#include "storm/utility/graph.h"
#include "storm/utility/macros.h"
#include "storm/utility/vector.h"
 
namespace storm {
namespace builder {
template<typename PomdpType, typename BeliefValueType>
BeliefMdpExplorer<PomdpType, BeliefValueType>::SuccessorObservationInformation::SuccessorObservationInformation(ValueType const &obsProb,
                                                                                                                ValueType const &maxProb, uint64_t const &count)
    : observationProbability(obsProb), maxProbabilityToSuccessorWithObs(maxProb), successorWithObsCount(count) {
    // Intentionally left empty.
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::SuccessorObservationInformation::join(
    SuccessorObservationInformation other) {  
    observationProbability += other.observationProbability;
    maxProbabilityToSuccessorWithObs = std::max(maxProbabilityToSuccessorWithObs, other.maxProbabilityToSuccessorWithObs);
    successorWithObsCount += other.successorWithObsCount;
}
 
template<typename PomdpType, typename BeliefValueType>
BeliefMdpExplorer<PomdpType, BeliefValueType>::BeliefMdpExplorer(std::shared_ptr<BeliefManagerType> beliefManager,
                                                                 storm::pomdp::storage::PreprocessingPomdpValueBounds<ValueType> const &pomdpValueBounds,
                                                                 ExplorationHeuristic explorationHeuristic)
    : beliefManager(beliefManager), pomdpValueBounds(pomdpValueBounds), explHeuristic(explorationHeuristic), status(Status::Uninitialized) {
    // Intentionally left empty
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::BeliefManagerType const &BeliefMdpExplorer<PomdpType, BeliefValueType>::getBeliefManager() const {
    return *beliefManager;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::startNewExploration(std::optional<ValueType> extraTargetStateValue,
                                                                        std::optional<ValueType> extraBottomStateValue) {
    status = Status::Exploring;
    // Reset data from potential previous explorations
    prio = storm::utility::zero<ValueType>();
    nextId = 0;
    mdpStateToBeliefIdMap.clear();
    beliefIdToMdpStateMap.clear();
    exploredBeliefIds.clear();
    exploredBeliefIds.grow(beliefManager->getNumberOfBeliefIds(), false);
    mdpStatesToExplorePrioState.clear();
    mdpStatesToExploreStatePrio.clear();
    stateRemapping.clear();
    lowerValueBounds.clear();
    upperValueBounds.clear();
    values.clear();
    exploredMdpTransitions.clear();
    exploredChoiceIndices.clear();
    previousChoiceIndices.clear();
    probabilityEstimation.clear();
    mdpActionRewards.clear();
    targetStates.clear();
    truncatedStates.clear();
    clippedStates.clear();
    delayedExplorationChoices.clear();
    clippingTransitionRewards.clear();
    mdpStateToChoiceLabelsMap.clear();
    optimalChoices = std::nullopt;
    optimalChoicesReachableMdpStates = std::nullopt;
    scheduler = nullptr;
    exploredMdp = nullptr;
    internalAddRowGroupIndex();  // Mark the start of the first row group
 
    // Add some states with special treatment (if requested)
    if (extraBottomStateValue) {
        currentMdpState = getCurrentNumberOfMdpStates();
        extraBottomState = currentMdpState;
        mdpStateToBeliefIdMap.push_back(beliefManager->noId());
        probabilityEstimation.push_back(storm::utility::zero<ValueType>());
        insertValueHints(extraBottomStateValue.value(), extraBottomStateValue.value());
 
        internalAddTransition(getStartOfCurrentRowGroup(), extraBottomState.value(), storm::utility::one<ValueType>());
        mdpStateToChoiceLabelsMap[getStartOfCurrentRowGroup()][0] = "loop";
        internalAddRowGroupIndex();
        ++nextId;
    } else {
        extraBottomState = std::nullopt;
    }
    if (extraTargetStateValue) {
        currentMdpState = getCurrentNumberOfMdpStates();
        extraTargetState = currentMdpState;
        mdpStateToBeliefIdMap.push_back(beliefManager->noId());
        probabilityEstimation.push_back(storm::utility::zero<ValueType>());
        insertValueHints(extraTargetStateValue.value(), extraTargetStateValue.value());
 
        internalAddTransition(getStartOfCurrentRowGroup(), extraTargetState.value(), storm::utility::one<ValueType>());
        mdpStateToChoiceLabelsMap[getStartOfCurrentRowGroup()][0] = "loop";
        internalAddRowGroupIndex();
 
        targetStates.grow(getCurrentNumberOfMdpStates(), false);
        targetStates.set(extraTargetState.value(), true);
        ++nextId;
    } else {
        extraTargetState = std::nullopt;
    }
    currentMdpState = noState();
 
    // Set up the initial state.
    initialMdpState = getOrAddMdpState(beliefManager->getInitialBelief());
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::restartExploration() {
    STORM_LOG_ASSERT(status == Status::ModelChecked || status == Status::ModelFinished, "Method call is invalid in current status.");
    status = Status::Exploring;
    // We will not erase old states during the exploration phase, so most state-based data (like mappings between MDP and Belief states) remain valid.
    prio = storm::utility::zero<ValueType>();
    stateRemapping.clear();
    exploredBeliefIds.clear();
    exploredBeliefIds.grow(beliefManager->getNumberOfBeliefIds(), false);
    exploredMdpTransitions.clear();
    exploredMdpTransitions.resize(exploredMdp->getNumberOfChoices());
    clippingTransitionRewards.clear();
    previousChoiceIndices = exploredMdp->getNondeterministicChoiceIndices();
    exploredChoiceIndices = exploredMdp->getNondeterministicChoiceIndices();
    mdpActionRewards.clear();
    probabilityEstimation.clear();
    if (exploredMdp->hasRewardModel()) {
        // Can be overwritten during exploration
        mdpActionRewards = exploredMdp->getUniqueRewardModel().getStateActionRewardVector();
    }
    targetStates = storm::storage::BitVector(getCurrentNumberOfMdpStates(), false);
    truncatedStates = storm::storage::BitVector(getCurrentNumberOfMdpStates(), false);
    clippedStates = storm::storage::BitVector(getCurrentNumberOfMdpStates(), false);
    delayedExplorationChoices.clear();
    mdpStatesToExplorePrioState.clear();
    mdpStatesToExploreStatePrio.clear();
 
    // The extra states are not changed
    if (extraBottomState) {
        currentMdpState = extraBottomState.value();
        restoreOldBehaviorAtCurrentState(0);
    }
    if (extraTargetState) {
        currentMdpState = extraTargetState.value();
        restoreOldBehaviorAtCurrentState(0);
        targetStates.set(extraTargetState.value(), true);
    }
    currentMdpState = noState();
 
    // Set up the initial state.
    initialMdpState = getOrAddMdpState(beliefManager->getInitialBelief());
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::storeExplorationState() {
    explorationStorage.storedMdpStateToBeliefIdMap = std::vector<BeliefId>(mdpStateToBeliefIdMap);
    explorationStorage.storedBeliefIdToMdpStateMap = std::map<BeliefId, MdpStateType>(beliefIdToMdpStateMap);
    explorationStorage.storedExploredBeliefIds = storm::storage::BitVector(exploredBeliefIds);
    explorationStorage.storedMdpStateToChoiceLabelsMap = std::map<BeliefId, std::map<uint64_t, std::string>>(mdpStateToChoiceLabelsMap);
    explorationStorage.storedMdpStatesToExplorePrioState = std::multimap<ValueType, uint64_t>(mdpStatesToExplorePrioState);
    explorationStorage.storedMdpStatesToExploreStatePrio = std::map<uint64_t, ValueType>(mdpStatesToExploreStatePrio);
    explorationStorage.storedProbabilityEstimation = std::vector<ValueType>(probabilityEstimation);
    explorationStorage.storedExploredMdpTransitions = std::vector<std::map<MdpStateType, ValueType>>(exploredMdpTransitions);
    explorationStorage.storedExploredChoiceIndices = std::vector<MdpStateType>(exploredChoiceIndices);
    explorationStorage.storedMdpActionRewards = std::vector<ValueType>(mdpActionRewards);
    explorationStorage.storedClippingTransitionRewards = std::map<MdpStateType, ValueType>(clippingTransitionRewards);
    explorationStorage.storedCurrentMdpState = currentMdpState;
    explorationStorage.storedStateRemapping = std::map<MdpStateType, MdpStateType>(stateRemapping);
    explorationStorage.storedNextId = nextId;
    explorationStorage.storedPrio = ValueType(prio);
    explorationStorage.storedLowerValueBounds = std::vector<ValueType>(lowerValueBounds);
    explorationStorage.storedUpperValueBounds = std::vector<ValueType>(upperValueBounds);
    explorationStorage.storedValues = std::vector<ValueType>(values);
 
    explorationStorage.storedTargetStates = storm::storage::BitVector(targetStates);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::restoreExplorationState() {
    mdpStateToBeliefIdMap = std::vector<BeliefId>(explorationStorage.storedMdpStateToBeliefIdMap);
    beliefIdToMdpStateMap = std::map<BeliefId, MdpStateType>(explorationStorage.storedBeliefIdToMdpStateMap);
    exploredBeliefIds = storm::storage::BitVector(explorationStorage.storedExploredBeliefIds);
    mdpStateToChoiceLabelsMap = std::map<BeliefId, std::map<uint64_t, std::string>>(explorationStorage.storedMdpStateToChoiceLabelsMap);
    mdpStatesToExplorePrioState = std::multimap<ValueType, uint64_t>(explorationStorage.storedMdpStatesToExplorePrioState);
    mdpStatesToExploreStatePrio = std::map<uint64_t, ValueType>(explorationStorage.storedMdpStatesToExploreStatePrio);
    probabilityEstimation = std::vector<ValueType>(explorationStorage.storedProbabilityEstimation);
    exploredMdpTransitions = std::vector<std::map<MdpStateType, ValueType>>(explorationStorage.storedExploredMdpTransitions);
    exploredChoiceIndices = std::vector<MdpStateType>(explorationStorage.storedExploredChoiceIndices);
    mdpActionRewards = std::vector<ValueType>(explorationStorage.storedMdpActionRewards);
    clippingTransitionRewards = std::map<MdpStateType, ValueType>(explorationStorage.storedClippingTransitionRewards);
    currentMdpState = explorationStorage.storedCurrentMdpState;
    stateRemapping = std::map<MdpStateType, MdpStateType>(explorationStorage.storedStateRemapping);
    nextId = explorationStorage.storedNextId;
    prio = ValueType(explorationStorage.storedPrio);
    lowerValueBounds = explorationStorage.storedLowerValueBounds;
    upperValueBounds = explorationStorage.storedUpperValueBounds;
    values = explorationStorage.storedValues;
    status = Status::Exploring;
    targetStates = explorationStorage.storedTargetStates;
 
    truncatedStates.clear();
    clippedStates.clear();
    delayedExplorationChoices.clear();
    optimalChoices = std::nullopt;
    optimalChoicesReachableMdpStates = std::nullopt;
    exploredMdp = nullptr;
    scheduler = nullptr;
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::hasUnexploredState() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    return !mdpStatesToExploreStatePrio.empty();
}
 
template<typename PomdpType, typename BeliefValueType>
std::vector<uint64_t> BeliefMdpExplorer<PomdpType, BeliefValueType>::getUnexploredStates() {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    std::vector<uint64_t> res;
    res.reserve(mdpStatesToExploreStatePrio.size());
    for (auto const &entry : mdpStatesToExploreStatePrio) {
        res.push_back(entry.first);
    }
    return res;
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::BeliefId BeliefMdpExplorer<PomdpType, BeliefValueType>::exploreNextState() {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    // Mark the end of the previously explored row group.
    if (currentMdpState != noState() && mdpStatesToExplorePrioState.rbegin()->second == exploredChoiceIndices.size()) {
        internalAddRowGroupIndex();
    }
 
    // Pop from the queue.
    currentMdpState = mdpStatesToExplorePrioState.rbegin()->second;
    auto currprio = mdpStatesToExplorePrioState.rbegin()->first;
    auto range = mdpStatesToExplorePrioState.equal_range(currprio);
    for (auto i = range.first; i != range.second; ++i) {
        if (i->second == currentMdpState) {
            mdpStatesToExplorePrioState.erase(i);
            break;
        }
    }
    mdpStatesToExploreStatePrio.erase(currentMdpState);
    if (currentMdpState != nextId && !currentStateHasOldBehavior()) {
        stateRemapping[currentMdpState] = nextId;
        STORM_LOG_DEBUG("Explore state " << currentMdpState << " [Bel " << getCurrentBeliefId() << " " << beliefManager->toString(getCurrentBeliefId())
                                         << "] as state with ID " << nextId << " (Prio: " << storm::utility::to_string(currprio) << ")");
    } else {
        STORM_LOG_DEBUG("Explore state " << currentMdpState << " [Bel " << getCurrentBeliefId() << " " << beliefManager->toString(getCurrentBeliefId()) << "]"
                                         << " (Prio: " << storm::utility::to_string(currprio) << ")");
    }
 
    if (!currentStateHasOldBehavior()) {
        ++nextId;
    }
    if (explHeuristic == ExplorationHeuristic::ProbabilityPrio) {
        probabilityEstimation.push_back(currprio);
    }
 
    return mdpStateToBeliefIdMap[currentMdpState];
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::addTransitionsToExtraStates(uint64_t const &localActionIndex, ValueType const &targetStateValue,
                                                                                ValueType const &bottomStateValue) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(!currentStateHasOldBehavior() || localActionIndex < previousChoiceIndices[currentMdpState + 1] - previousChoiceIndices[currentMdpState] ||
                         getCurrentStateWasTruncated(),
                     "Action index " << localActionIndex << " was not valid at non-truncated state " << currentMdpState << " of the previously explored MDP.");
    uint64_t row = getStartOfCurrentRowGroup() + localActionIndex;
    if (!storm::utility::isZero(bottomStateValue)) {
        STORM_LOG_ASSERT(extraBottomState.has_value(), "Requested a transition to the extra bottom state but there is none.");
        internalAddTransition(row, extraBottomState.value(), bottomStateValue);
    }
    if (!storm::utility::isZero(targetStateValue)) {
        STORM_LOG_ASSERT(extraTargetState.has_value(), "Requested a transition to the extra target state but there is none.");
        internalAddTransition(row, extraTargetState.value(), targetStateValue);
    }
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::addSelfloopTransition(uint64_t const &localActionIndex, ValueType const &value) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(!currentStateHasOldBehavior() || localActionIndex < previousChoiceIndices[currentMdpState + 1] - previousChoiceIndices[currentMdpState] ||
                         getCurrentStateWasTruncated(),
                     "Action index " << localActionIndex << " was not valid at non-truncated state " << currentMdpState << " of the previously explored MDP.");
    uint64_t row = getStartOfCurrentRowGroup() + localActionIndex;
    internalAddTransition(row, getCurrentMdpState(), value);
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::addTransitionToBelief(uint64_t const &localActionIndex, BeliefId const &transitionTarget,
                                                                          ValueType const &value, bool ignoreNewBeliefs) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(!currentStateHasOldBehavior() || localActionIndex < previousChoiceIndices[currentMdpState + 1] - previousChoiceIndices[currentMdpState] ||
                         getCurrentStateWasTruncated(),
                     "Action index " << localActionIndex << " was not valid at non-truncated state " << currentMdpState << " of the previously explored MDP.");
 
    MdpStateType column;
    if (ignoreNewBeliefs) {
        column = getExploredMdpState(transitionTarget);
        if (column == noState()) {
            return false;
        }
    } else {
        column = getOrAddMdpState(transitionTarget, value);
    }
    if (getCurrentMdpState() == exploredChoiceIndices.size()) {
        internalAddRowGroupIndex();
    }
    uint64_t row = getStartOfCurrentRowGroup() + localActionIndex;
    internalAddTransition(row, column, value);
    return true;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::computeRewardAtCurrentState(uint64_t const &localActionIndex, ValueType extraReward) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    if (getCurrentNumberOfMdpChoices() > mdpActionRewards.size()) {
        mdpActionRewards.resize(getCurrentNumberOfMdpChoices(), storm::utility::zero<ValueType>());
    }
    uint64_t row = getStartOfCurrentRowGroup() + localActionIndex;
    mdpActionRewards[row] = beliefManager->getBeliefActionReward(getCurrentBeliefId(), localActionIndex) + extraReward;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::addRewardToCurrentState(uint64_t const &localActionIndex, ValueType rewardValue) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    if (getCurrentNumberOfMdpChoices() > mdpActionRewards.size()) {
        mdpActionRewards.resize(getCurrentNumberOfMdpChoices(), storm::utility::zero<ValueType>());
    }
    uint64_t row = getStartOfCurrentRowGroup() + localActionIndex;
    mdpActionRewards[row] = rewardValue;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::addClippingRewardToCurrentState(uint64_t const &localActionIndex, ValueType rewardValue) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    uint64_t row = getStartOfCurrentRowGroup() + localActionIndex;
    clippingTransitionRewards[row] = rewardValue;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::setCurrentStateIsTarget() {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    targetStates.grow(getCurrentNumberOfMdpStates(), false);
    targetStates.set(getCurrentMdpState(), true);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::setCurrentStateIsTruncated() {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    truncatedStates.grow(getCurrentNumberOfMdpStates(), false);
    truncatedStates.set(getCurrentMdpState(), true);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::setCurrentStateIsClipped() {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    setCurrentStateIsTruncated();
    clippedStates.grow(getCurrentNumberOfMdpStates(), false);
    clippedStates.set(getCurrentMdpState(), true);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::setCurrentChoiceIsDelayed(uint64_t const &localActionIndex) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    delayedExplorationChoices.grow(getCurrentNumberOfMdpChoices(), false);
    delayedExplorationChoices.set(getStartOfCurrentRowGroup() + localActionIndex, true);
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::currentStateHasOldBehavior() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(getCurrentMdpState() != noState(), "Method 'currentStateHasOldBehavior' called but there is no current state.");
    return exploredMdp && getCurrentMdpState() < exploredMdp->getNumberOfStates();
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::getCurrentStateWasTruncated() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(getCurrentMdpState() != noState(), "Method 'actionAtCurrentStateWasOptimal' called but there is no current state.");
    STORM_LOG_ASSERT(currentStateHasOldBehavior(), "Method 'actionAtCurrentStateWasOptimal' called but current state has no old behavior");
    STORM_LOG_ASSERT(exploredMdp, "No 'old' mdp available");
    return exploredMdp->getStateLabeling().getStateHasLabel("truncated", getCurrentMdpState());
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::getCurrentStateWasClipped() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(getCurrentMdpState() != noState(), "Method 'actionAtCurrentStateWasOptimal' called but there is no current state.");
    STORM_LOG_ASSERT(currentStateHasOldBehavior(), "Method 'actionAtCurrentStateWasOptimal' called but current state has no old behavior");
    STORM_LOG_ASSERT(exploredMdp, "No 'old' mdp available");
    return exploredMdp->getStateLabeling().getStateHasLabel("clipped", getCurrentMdpState());
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::stateIsOptimalSchedulerReachable(MdpStateType mdpState) const {
    STORM_LOG_ASSERT(status == Status::ModelChecked, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(optimalChoicesReachableMdpStates.has_value(),
                     "Method 'stateIsOptimalSchedulerReachable' called but 'computeOptimalChoicesAndReachableMdpStates' was not called before.");
    return optimalChoicesReachableMdpStates->get(mdpState);
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::actionIsOptimal(uint64_t const &globalActionIndex) const {
    STORM_LOG_ASSERT(status == Status::ModelChecked, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(optimalChoices.has_value(), "Method 'actionIsOptimal' called but 'computeOptimalChoicesAndReachableMdpStates' was not called before.");
    return optimalChoices->get(globalActionIndex);
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::currentStateIsOptimalSchedulerReachable() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(getCurrentMdpState() != noState(), "Method 'currentStateIsOptimalSchedulerReachable' called but there is no current state.");
    STORM_LOG_ASSERT(currentStateHasOldBehavior(), "Method 'currentStateIsOptimalSchedulerReachable' called but current state has no old behavior");
    STORM_LOG_ASSERT(optimalChoicesReachableMdpStates.has_value(),
                     "Method 'currentStateIsOptimalSchedulerReachable' called but 'computeOptimalChoicesAndReachableMdpStates' was not called before.");
    return optimalChoicesReachableMdpStates->get(getCurrentMdpState());
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::actionAtCurrentStateWasOptimal(uint64_t const &localActionIndex) const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(getCurrentMdpState() != noState(), "Method 'actionAtCurrentStateWasOptimal' called but there is no current state.");
    STORM_LOG_ASSERT(currentStateHasOldBehavior(), "Method 'actionAtCurrentStateWasOptimal' called but current state has no old behavior");
    STORM_LOG_ASSERT(optimalChoices.has_value(),
                     "Method 'currentStateIsOptimalSchedulerReachable' called but 'computeOptimalChoicesAndReachableMdpStates' was not called before.");
    uint64_t choice = previousChoiceIndices.at(getCurrentMdpState()) + localActionIndex;
    return optimalChoices->get(choice);
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::getCurrentStateActionExplorationWasDelayed(uint64_t const &localActionIndex) const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(getCurrentMdpState() != noState(), "Method 'actionAtCurrentStateWasOptimal' called but there is no current state.");
    STORM_LOG_ASSERT(currentStateHasOldBehavior(), "Method 'actionAtCurrentStateWasOptimal' called but current state has no old behavior");
    STORM_LOG_ASSERT(exploredMdp, "No 'old' mdp available");
    uint64_t choice = exploredMdp->getNondeterministicChoiceIndices()[getCurrentMdpState()] + localActionIndex;
    return exploredMdp->hasChoiceLabeling() && exploredMdp->getChoiceLabeling().getLabels().count("delayed") > 0 &&
           exploredMdp->getChoiceLabeling().getChoiceHasLabel("delayed", choice);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::restoreOldBehaviorAtCurrentState(uint64_t const &localActionIndex) {
    STORM_LOG_ASSERT(currentStateHasOldBehavior(), "Cannot restore old behavior as the current state does not have any.");
    STORM_LOG_ASSERT(localActionIndex < previousChoiceIndices[currentMdpState + 1] - previousChoiceIndices[currentMdpState],
                     "Action index " << localActionIndex << " was not valid at state " << currentMdpState << " of the previously explored MDP.");
 
    if (getCurrentMdpState() == exploredChoiceIndices.size()) {
        internalAddRowGroupIndex();
    }
 
    assert(getCurrentMdpState() < previousChoiceIndices.size());
    assert(getCurrentMdpState() < exploredChoiceIndices.size());
    uint64_t oldChoiceIndex = previousChoiceIndices.at(getCurrentMdpState()) + localActionIndex;
    uint64_t newChoiceIndex = exploredChoiceIndices.at(getCurrentMdpState()) + localActionIndex;
 
    // Insert the transitions
    for (auto const &transition : exploredMdp->getTransitionMatrix().getRow(oldChoiceIndex)) {
        internalAddTransition(newChoiceIndex, transition.getColumn(), transition.getValue());
        // Check whether exploration is needed
        auto beliefId = getBeliefId(transition.getColumn());
        if (beliefId != beliefManager->noId()) {  // Not the extra target or bottom state
            if (!exploredBeliefIds.get(beliefId)) {
                // This belief needs exploration
                exploredBeliefIds.set(beliefId, true);
                ValueType currentPrio;
                switch (explHeuristic) {
                    case ExplorationHeuristic::BreadthFirst:
                        currentPrio = prio;
                        prio = prio - storm::utility::one<ValueType>();
                        break;
                    case ExplorationHeuristic::LowerBoundPrio:
                        currentPrio = getLowerValueBoundAtCurrentState();
                        break;
                    case ExplorationHeuristic::UpperBoundPrio:
                        currentPrio = getUpperValueBoundAtCurrentState();
                        break;
                    case ExplorationHeuristic::GapPrio:
                        currentPrio = getUpperValueBoundAtCurrentState() - getLowerValueBoundAtCurrentState();
                        break;
                    case ExplorationHeuristic::ProbabilityPrio:
                        if (getCurrentMdpState() != noState()) {
                            currentPrio = probabilityEstimation[getCurrentMdpState()] * transition.getValue();
                        } else {
                            currentPrio = storm::utility::one<ValueType>();
                        }
                        break;
                    default:
                        STORM_LOG_THROW(false, storm::exceptions::NotImplementedException, "Other heuristics not implemented yet");
                }
                mdpStatesToExploreStatePrio[transition.getColumn()] = currentPrio;
                mdpStatesToExplorePrioState.emplace(currentPrio, transition.getColumn());
            }
        }
    }
 
    // Actually, nothing needs to be done for rewards since we already initialize the vector with the "old" values
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::finishExploration() {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(!hasUnexploredState(), "Finishing exploration not possible if there are still unexplored states.");
 
    // Complete the exploration
    // Finish the last row grouping in case the last explored state was new
    if (!currentStateHasOldBehavior() || exploredChoiceIndices.back() < getCurrentNumberOfMdpChoices()) {
        internalAddRowGroupIndex();
    }
    // Resize state- and choice based vectors to the correct size
    targetStates.resize(getCurrentNumberOfMdpStates(), false);
    truncatedStates.resize(getCurrentNumberOfMdpStates(), false);
    clippedStates.resize(getCurrentNumberOfMdpStates(), false);
    if (!mdpActionRewards.empty()) {
        mdpActionRewards.resize(getCurrentNumberOfMdpChoices(), storm::utility::zero<ValueType>());
    }
 
    // We are not exploring anymore
    currentMdpState = noState();
 
    // If this was a restarted exploration, we might still have unexplored states (which were only reachable and explored in a previous build).
    // We get rid of these before rebuilding the model
    if (exploredMdp) {
        dropUnexploredStates();
    }
 
    // The potentially computed optimal choices and the set of states that are reachable under these choices are not valid anymore.
    optimalChoices = std::nullopt;
    optimalChoicesReachableMdpStates = std::nullopt;
 
    // Apply state remapping to the Belief-State maps
    if (!stateRemapping.empty()) {
        std::vector<BeliefId> remappedStateToBeliefIdMap(mdpStateToBeliefIdMap);
        for (auto const &entry : stateRemapping) {
            remappedStateToBeliefIdMap[entry.second] = mdpStateToBeliefIdMap[entry.first];
        }
        mdpStateToBeliefIdMap = remappedStateToBeliefIdMap;
        for (auto const &beliefMdpState : beliefIdToMdpStateMap) {
            if (stateRemapping.find(beliefMdpState.second) != stateRemapping.end()) {
                beliefIdToMdpStateMap[beliefMdpState.first] = stateRemapping[beliefMdpState.second];
            }
        }
        if (!mdpStateToChoiceLabelsMap.empty()) {
            std::map<BeliefId, std::map<uint64_t, std::string>> temp(mdpStateToChoiceLabelsMap);
            for (auto const &entry : stateRemapping) {
                temp[entry.second] = mdpStateToChoiceLabelsMap[entry.first];
            }
            mdpStateToChoiceLabelsMap = temp;
        }
    }
 
    // Create the transition matrix
    uint64_t entryCount = 0;
    for (auto const &row : exploredMdpTransitions) {
        entryCount += row.size();
    }
    storm::storage::SparseMatrixBuilder<ValueType> builder(getCurrentNumberOfMdpChoices(), getCurrentNumberOfMdpStates(), entryCount, true, true,
                                                           getCurrentNumberOfMdpStates());
    for (uint64_t groupIndex = 0; groupIndex < exploredChoiceIndices.size() - 1; ++groupIndex) {
        uint64_t rowIndex = exploredChoiceIndices[groupIndex];
        uint64_t groupEnd = exploredChoiceIndices[groupIndex + 1];
        builder.newRowGroup(rowIndex);
        for (; rowIndex < groupEnd; ++rowIndex) {
            for (auto const &entry : exploredMdpTransitions[rowIndex]) {
                if (stateRemapping.find(entry.first) == stateRemapping.end()) {
                    builder.addNextValue(rowIndex, entry.first, entry.second);
                } else {
                    builder.addNextValue(rowIndex, stateRemapping[entry.first], entry.second);
                }
            }
        }
    }
    auto mdpTransitionMatrix = builder.build();
 
    // Create a standard labeling
    storm::models::sparse::StateLabeling mdpLabeling(getCurrentNumberOfMdpStates());
    mdpLabeling.addLabel("init");
    mdpLabeling.addLabelToState("init", initialMdpState);
    targetStates.resize(getCurrentNumberOfMdpStates(), false);
    mdpLabeling.addLabel("target", std::move(targetStates));
    truncatedStates.resize(getCurrentNumberOfMdpStates(), false);
    mdpLabeling.addLabel("truncated", std::move(truncatedStates));
    clippedStates.resize(getCurrentNumberOfMdpStates(), false);
    mdpLabeling.addLabel("clipped", std::move(clippedStates));
 
    for (uint64_t state = 0; state < getCurrentNumberOfMdpStates(); ++state) {
        if (state == extraBottomState || state == extraTargetState) {
            if (!mdpLabeling.containsLabel("__extra")) {
                mdpLabeling.addLabel("__extra");
            }
            mdpLabeling.addLabelToState("__extra", state);
        } else {
            STORM_LOG_DEBUG("Observation of MDP state " << state << " : " << beliefManager->getObservationLabel(mdpStateToBeliefIdMap[state]) << "\n");
            std::string obsLabel = beliefManager->getObservationLabel(mdpStateToBeliefIdMap[state]);
            uint32_t obsId = beliefManager->getBeliefObservation(mdpStateToBeliefIdMap[state]);
            if (!obsLabel.empty()) {
                if (!mdpLabeling.containsLabel(obsLabel)) {
                    mdpLabeling.addLabel(obsLabel);
                }
                mdpLabeling.addLabelToState(obsLabel, state);
            } else if (mdpStateToBeliefIdMap[state] != beliefManager->noId()) {
                std::string obsIdLabel = "obs_" + std::to_string(obsId);
                if (!mdpLabeling.containsLabel(obsIdLabel)) {
                    mdpLabeling.addLabel(obsIdLabel);
                }
                mdpLabeling.addLabelToState(obsIdLabel, state);
            }
        }
    }
 
    // Create a standard reward model (if rewards are available)
    std::unordered_map<std::string, storm::models::sparse::StandardRewardModel<ValueType>> mdpRewardModels;
    if (!mdpActionRewards.empty()) {
        mdpActionRewards.resize(getCurrentNumberOfMdpChoices(), storm::utility::zero<ValueType>());
        if (!clippingTransitionRewards.empty()) {
            storm::storage::SparseMatrixBuilder<ValueType> rewardBuilder(getCurrentNumberOfMdpChoices(), getCurrentNumberOfMdpStates(),
                                                                         clippingTransitionRewards.size(), true, true, getCurrentNumberOfMdpStates());
            for (uint64_t groupIndex = 0; groupIndex < exploredChoiceIndices.size() - 1; ++groupIndex) {
                uint64_t rowIndex = exploredChoiceIndices[groupIndex];
                uint64_t groupEnd = exploredChoiceIndices[groupIndex + 1];
                rewardBuilder.newRowGroup(rowIndex);
                for (; rowIndex < groupEnd; ++rowIndex) {
                    if (clippingTransitionRewards.find(rowIndex) != clippingTransitionRewards.end()) {
                        STORM_LOG_ASSERT(extraTargetState.has_value(), "Requested a transition to the extra target state but there is none.");
                        rewardBuilder.addNextValue(rowIndex, extraTargetState.value(), clippingTransitionRewards[rowIndex]);
                    }
                }
            }
            auto transitionRewardMatrix = rewardBuilder.build();
            mdpRewardModels.emplace("default", storm::models::sparse::StandardRewardModel<ValueType>(
                                                   std::optional<std::vector<ValueType>>(), std::move(mdpActionRewards), std::move(transitionRewardMatrix)));
        } else {
            mdpRewardModels.emplace(
                "default", storm::models::sparse::StandardRewardModel<ValueType>(std::optional<std::vector<ValueType>>(), std::move(mdpActionRewards)));
        }
    }
 
    // Create model components
    storm::storage::sparse::ModelComponents<ValueType> modelComponents(std::move(mdpTransitionMatrix), std::move(mdpLabeling), std::move(mdpRewardModels));
 
    // Potentially create a choice labeling
    if (!mdpStateToChoiceLabelsMap.empty()) {
        modelComponents.choiceLabeling = storm::models::sparse::ChoiceLabeling(getCurrentNumberOfMdpChoices());
        for (auto const &stateMap : mdpStateToChoiceLabelsMap) {
            auto rowGroup = stateMap.first;
            for (auto const &actionLabel : stateMap.second) {
                if (!modelComponents.choiceLabeling->containsLabel(actionLabel.second)) {
                    modelComponents.choiceLabeling->addLabel(actionLabel.second);
                }
                modelComponents.choiceLabeling->addLabelToChoice(actionLabel.second, exploredChoiceIndices.at(rowGroup) + actionLabel.first);
            }
        }
    }
 
    if (!delayedExplorationChoices.empty()) {
        modelComponents.choiceLabeling = storm::models::sparse::ChoiceLabeling(getCurrentNumberOfMdpChoices());
        delayedExplorationChoices.resize(getCurrentNumberOfMdpChoices(), false);
        modelComponents.choiceLabeling->addLabel("delayed", std::move(delayedExplorationChoices));
    }
 
    // Create the final model.
    exploredMdp = std::make_shared<storm::models::sparse::Mdp<ValueType>>(std::move(modelComponents));
    status = Status::ModelFinished;
    STORM_LOG_DEBUG("Explored Mdp with " << exploredMdp->getNumberOfStates() << " states (" << clippedStates.getNumberOfSetBits()
                                         << " of which were clipped and " << truncatedStates.getNumberOfSetBits() - clippedStates.getNumberOfSetBits()
                                         << " of which were flagged as truncated).");
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::dropUnexploredStates() {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(!hasUnexploredState(), "Finishing exploration not possible if there are still unexplored states.");
 
    STORM_LOG_ASSERT(exploredMdp, "Method called although no 'old' MDP is available.");
    // Find the states (and corresponding choices) that were not explored.
    // These correspond to "empty" MDP transitions
    storm::storage::BitVector relevantMdpStates(getCurrentNumberOfMdpStates(), true), relevantMdpChoices(getCurrentNumberOfMdpChoices(), true);
    std::vector<MdpStateType> toRelevantStateIndexMap(getCurrentNumberOfMdpStates(), noState());
    MdpStateType nextRelevantIndex = 0;
    for (uint64_t groupIndex = 0; groupIndex < exploredChoiceIndices.size() - 1; ++groupIndex) {
        uint64_t rowIndex = exploredChoiceIndices[groupIndex];
        // Check first row in group
        if (exploredMdpTransitions[rowIndex].empty()) {
            relevantMdpChoices.set(rowIndex, false);
            relevantMdpStates.set(groupIndex, false);
        } else {
            toRelevantStateIndexMap[groupIndex] = nextRelevantIndex;
            ++nextRelevantIndex;
        }
        uint64_t groupEnd = exploredChoiceIndices[groupIndex + 1];
        // process remaining rows in group
        for (++rowIndex; rowIndex < groupEnd; ++rowIndex) {
            // Assert that all actions at the current state were consistently explored or unexplored.
            STORM_LOG_ASSERT(exploredMdpTransitions[rowIndex].empty() != relevantMdpStates.get(groupIndex),
                             "Actions at 'old' MDP state " << groupIndex << " were only partly explored.");
            if (exploredMdpTransitions[rowIndex].empty()) {
                relevantMdpChoices.set(rowIndex, false);
            }
        }
    }
 
    if (relevantMdpStates.full()) {
        // All states are relevant so nothing to do
        return;
    }
 
    nextId -= (relevantMdpStates.size() - relevantMdpStates.getNumberOfSetBits());
 
    // Translate various components to the "new" MDP state set
    storm::utility::vector::filterVectorInPlace(mdpStateToBeliefIdMap, relevantMdpStates);
    {  // beliefIdToMdpStateMap
        for (auto belIdToMdpStateIt = beliefIdToMdpStateMap.begin(); belIdToMdpStateIt != beliefIdToMdpStateMap.end();) {
            if (relevantMdpStates.get(belIdToMdpStateIt->second)) {
                // Translate current entry and move on to the next one.
                belIdToMdpStateIt->second = toRelevantStateIndexMap[belIdToMdpStateIt->second];
                ++belIdToMdpStateIt;
            } else {
                STORM_LOG_ASSERT(!exploredBeliefIds.get(belIdToMdpStateIt->first),
                                 "Inconsistent exploration information: Unexplored MDPState corresponds to explored beliefId");
                // Delete current entry and move on to the next one.
                // This works because std::map::erase does not invalidate other iterators within the map!
                beliefIdToMdpStateMap.erase(belIdToMdpStateIt++);
            }
        }
    }
    {  // exploredMdpTransitions
        storm::utility::vector::filterVectorInPlace(exploredMdpTransitions, relevantMdpChoices);
        // Adjust column indices. Unfortunately, the fastest way seems to be to "rebuild" the map
        // It might pay off to do this when building the matrix.
        for (auto &transitions : exploredMdpTransitions) {
            std::map<MdpStateType, ValueType> newTransitions;
            for (auto const &entry : transitions) {
                STORM_LOG_ASSERT(relevantMdpStates.get(entry.first), "Relevant state has transition to irrelevant state.");
                newTransitions.emplace_hint(newTransitions.end(), toRelevantStateIndexMap[entry.first], entry.second);
            }
            transitions = std::move(newTransitions);
        }
    }
    {  // exploredChoiceIndices
        MdpStateType newState = 0;
        assert(exploredChoiceIndices[0] == 0u);
        // Loop invariant: all indices up to exploredChoiceIndices[newState] consider the new row indices and all other entries are not touched.
        for (auto const oldState : relevantMdpStates) {
            if (oldState != newState) {
                assert(oldState > newState);
                uint64_t groupSize = getRowGroupSizeOfState(oldState);
                exploredChoiceIndices.at(newState + 1) = exploredChoiceIndices.at(newState) + groupSize;
            }
            ++newState;
        }
        exploredChoiceIndices.resize(newState + 1);
    }
    if (!mdpActionRewards.empty()) {
        storm::utility::vector::filterVectorInPlace(mdpActionRewards, relevantMdpChoices);
    }
    if (extraBottomState) {
        extraBottomState = toRelevantStateIndexMap[extraBottomState.value()];
    }
    if (extraTargetState) {
        extraTargetState = toRelevantStateIndexMap[extraTargetState.value()];
    }
    targetStates = targetStates % relevantMdpStates;
    truncatedStates = truncatedStates % relevantMdpStates;
    clippedStates = clippedStates % relevantMdpStates;
    initialMdpState = toRelevantStateIndexMap[initialMdpState];
 
    storm::utility::vector::filterVectorInPlace(lowerValueBounds, relevantMdpStates);
    storm::utility::vector::filterVectorInPlace(upperValueBounds, relevantMdpStates);
    storm::utility::vector::filterVectorInPlace(values, relevantMdpStates);
 
    {  // mdpStateToChoiceLabelsMap
        if (!mdpStateToChoiceLabelsMap.empty()) {
            auto temp = std::map<BeliefId, std::map<uint64_t, std::string>>();
            for (auto const relevantState : relevantMdpStates) {
                temp[toRelevantStateIndexMap[relevantState]] = mdpStateToChoiceLabelsMap[relevantState];
            }
            mdpStateToChoiceLabelsMap = temp;
        }
    }
}
 
template<typename PomdpType, typename BeliefValueType>
std::shared_ptr<storm::models::sparse::Mdp<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType>>
BeliefMdpExplorer<PomdpType, BeliefValueType>::getExploredMdp() const {
    STORM_LOG_ASSERT(status == Status::ModelFinished || status == Status::ModelChecked, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(exploredMdp, "Tried to get the explored MDP but exploration was not finished yet.");
    return exploredMdp;
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::getCurrentNumberOfMdpStates() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    return mdpStateToBeliefIdMap.size();
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::getCurrentNumberOfMdpChoices() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    return exploredMdpTransitions.size();
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::getStartOfCurrentRowGroup() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    assert(getCurrentMdpState() < exploredChoiceIndices.size());
    return exploredChoiceIndices.at(getCurrentMdpState());
}
 
template<typename PomdpType, typename BeliefValueType>
uint64_t BeliefMdpExplorer<PomdpType, BeliefValueType>::getSizeOfCurrentRowGroup() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    assert(getCurrentMdpState() < exploredChoiceIndices.size() - 1);
    return exploredChoiceIndices.at(getCurrentMdpState() + 1) - exploredChoiceIndices.at(getCurrentMdpState());
}
 
template<typename PomdpType, typename BeliefValueType>
uint64_t BeliefMdpExplorer<PomdpType, BeliefValueType>::getRowGroupSizeOfState(uint64_t state) const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    assert(state < exploredChoiceIndices.size());
    if (state < exploredChoiceIndices.size() - 1) {
        return exploredChoiceIndices.at(state + 1) - exploredChoiceIndices.at(state);
    } else if (state == exploredChoiceIndices.size() - 1) {
        return exploredMdpTransitions.size() - exploredChoiceIndices.at(state);
    } else {
        return 0;
    }
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::needsActionAdjustment(uint64_t numActionsNeeded) {
    return (currentStateHasOldBehavior() && getCurrentStateWasTruncated() && getCurrentMdpState() < exploredChoiceIndices.size() - 1 &&
            getSizeOfCurrentRowGroup() != numActionsNeeded);
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::getLowerValueBoundAtCurrentState() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    return lowerValueBounds[getCurrentMdpState()];
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::getUpperValueBoundAtCurrentState() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    return upperValueBounds[getCurrentMdpState()];
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::computeLowerValueBoundAtBelief(
    BeliefId const &beliefId) const {
    STORM_LOG_ASSERT(!pomdpValueBounds.lower.empty(), "Requested lower value bounds but none were available.");
    auto it = pomdpValueBounds.lower.begin();
    ValueType result = beliefManager->getWeightedSum(beliefId, *it);
    for (++it; it != pomdpValueBounds.lower.end(); ++it) {
        result = std::max(result, beliefManager->getWeightedSum(beliefId, *it));
    }
    return result;
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::computeUpperValueBoundAtBelief(
    BeliefId const &beliefId) const {
    STORM_LOG_ASSERT(!pomdpValueBounds.upper.empty(), "Requested upper value bounds but none were available.");
    auto it = pomdpValueBounds.upper.begin();
    ValueType result = beliefManager->getWeightedSum(beliefId, *it);
    for (++it; it != pomdpValueBounds.upper.end(); ++it) {
        result = std::min(result, beliefManager->getWeightedSum(beliefId, *it));
    }
    return result;
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::computeLowerValueBoundForScheduler(
    BeliefId const &beliefId, uint64_t schedulerId) const {
    STORM_LOG_ASSERT(!pomdpValueBounds.lower.empty(), "Requested lower value bounds but none were available.");
    STORM_LOG_ASSERT(pomdpValueBounds.lower.size() > schedulerId, "Requested lower value bound for scheduler with ID " << schedulerId << " not available.");
    return beliefManager->getWeightedSum(beliefId, pomdpValueBounds.lower[schedulerId]);
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::computeUpperValueBoundForScheduler(
    BeliefId const &beliefId, uint64_t schedulerId) const {
    STORM_LOG_ASSERT(!pomdpValueBounds.upper.empty(), "Requested upper value bounds but none were available.");
    STORM_LOG_ASSERT(pomdpValueBounds.upper.size() > schedulerId, "Requested upper value bound for scheduler with ID " << schedulerId << " not available.");
    return beliefManager->getWeightedSum(beliefId, pomdpValueBounds.upper[schedulerId]);
}
 
template<typename PomdpType, typename BeliefValueType>
std::pair<bool, typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType>
BeliefMdpExplorer<PomdpType, BeliefValueType>::computeFMSchedulerValueForMemoryNode(BeliefId const &beliefId, uint64_t memoryNode) const {
    STORM_LOG_ASSERT(!fmSchedulerValueList.empty(), "Requested finite memory scheduler value bounds but none were available.");
    auto obs = beliefManager->getBeliefObservation(beliefId);
    STORM_LOG_ASSERT(fmSchedulerValueList.size() > obs, "Requested value bound for observation " << obs << " not available.");
    STORM_LOG_ASSERT(fmSchedulerValueList.at(obs).size() > memoryNode,
                     "Requested value bound for observation " << obs << " and memory node " << memoryNode << " not available.");
    return beliefManager->getWeightedSum(beliefId, fmSchedulerValueList.at(obs).at(memoryNode));
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::computeValuesOfExploredMdp(storm::Environment const &env, storm::solver::OptimizationDirection const &dir) {
    STORM_LOG_ASSERT(status == Status::ModelFinished, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(exploredMdp, "Tried to compute values but the MDP is not explored");
    auto property = createStandardProperty(dir, exploredMdp->hasRewardModel());
    auto task = createStandardCheckTask(property);
 
    std::unique_ptr<storm::modelchecker::CheckResult> res(storm::api::verifyWithSparseEngine<ValueType>(env, exploredMdp, task));
    if (res) {
        values = std::move(res->asExplicitQuantitativeCheckResult<ValueType>().getValueVector());
        scheduler = std::make_shared<storm::storage::Scheduler<ValueType>>(res->asExplicitQuantitativeCheckResult<ValueType>().getScheduler());
        STORM_LOG_WARN_COND_DEBUG(storm::utility::vector::compareElementWise(lowerValueBounds, values, std::less_equal<ValueType>()),
                                  "Computed values are smaller than the lower bound.");
        STORM_LOG_WARN_COND_DEBUG(storm::utility::vector::compareElementWise(upperValueBounds, values, std::greater_equal<ValueType>()),
                                  "Computed values are larger than the upper bound.");
    } else {
        STORM_LOG_ASSERT(storm::utility::resources::isTerminate(), "Empty check result!");
        STORM_LOG_ERROR("No result obtained while checking.");
    }
    status = Status::ModelChecked;
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::hasComputedValues() const {
    return status == Status::ModelChecked;
}
 
template<typename PomdpType, typename BeliefValueType>
std::vector<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType> const &BeliefMdpExplorer<PomdpType, BeliefValueType>::getValuesOfExploredMdp()
    const {
    STORM_LOG_ASSERT(status == Status::ModelChecked, "Method call is invalid in current status.");
    return values;
}
 
template<typename PomdpType, typename BeliefValueType>
const std::shared_ptr<storm::storage::Scheduler<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType>> &
BeliefMdpExplorer<PomdpType, BeliefValueType>::getSchedulerForExploredMdp() const {
    STORM_LOG_ASSERT(status == Status::ModelChecked, "Method call is invalid in current status.");
    return scheduler;
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType const &BeliefMdpExplorer<PomdpType, BeliefValueType>::getComputedValueAtInitialState() const {
    STORM_LOG_ASSERT(status == Status::ModelChecked, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(exploredMdp, "Tried to get a value but no MDP was explored.");
    return getValuesOfExploredMdp()[exploredMdp->getInitialStates().getNextSetIndex(0)];
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::getBeliefId(
    MdpStateType exploredMdpState) const {
    STORM_LOG_ASSERT(status != Status::Uninitialized, "Method call is invalid in current status.");
    return mdpStateToBeliefIdMap[exploredMdpState];
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::gatherSuccessorObservationInformationAtCurrentState(
    uint64_t localActionIndex, std::map<uint32_t, SuccessorObservationInformation> &gatheredSuccessorObservations) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(currentStateHasOldBehavior(), "Method call is invalid since the current state has no old behavior");
    uint64_t mdpChoice = getStartOfCurrentRowGroup() + localActionIndex;
    gatherSuccessorObservationInformationAtMdpChoice(mdpChoice, gatheredSuccessorObservations);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::gatherSuccessorObservationInformationAtMdpChoice(
    uint64_t mdpChoice, std::map<uint32_t, SuccessorObservationInformation> &gatheredSuccessorObservations) {
    STORM_LOG_ASSERT(exploredMdp, "Method call is invalid if no MDP has been explored before");
    for (auto const &entry : exploredMdp->getTransitionMatrix().getRow(mdpChoice)) {
        auto const &beliefId = getBeliefId(entry.getColumn());
        if (beliefId != beliefManager->noId()) {
            auto const &obs = beliefManager->getBeliefObservation(beliefId);
            SuccessorObservationInformation info(entry.getValue(), entry.getValue(), 1);
            auto obsInsertion = gatheredSuccessorObservations.emplace(obs, info);
            if (!obsInsertion.second) {
                // There already is an entry for this observation, so join the two information constructs
                obsInsertion.first->second.join(info);
            }
            beliefManager->joinSupport(beliefId, obsInsertion.first->second.support);
        }
    }
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::currentStateHasSuccessorObservationInObservationSet(uint64_t localActionIndex,
                                                                                                        storm::storage::BitVector const &observationSet) {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(currentStateHasOldBehavior(), "Method call is invalid since the current state has no old behavior");
    uint64_t mdpChoice = previousChoiceIndices.at(getCurrentMdpState()) + localActionIndex;
    return std::any_of(exploredMdp->getTransitionMatrix().getRow(mdpChoice).begin(), exploredMdp->getTransitionMatrix().getRow(mdpChoice).end(),
                       [this, &observationSet](typename storm::storage::MatrixEntry<uint_fast64_t, ValueType> i) {
                           return observationSet.get(beliefManager->getBeliefObservation(getBeliefId(i.getColumn())));
                       });
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::takeCurrentValuesAsUpperBounds() {
    STORM_LOG_ASSERT(status == Status::ModelChecked, "Method call is invalid in current status.");
    upperValueBounds = values;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::takeCurrentValuesAsLowerBounds() {
    STORM_LOG_ASSERT(status == Status::ModelChecked, "Method call is invalid in current status.");
    lowerValueBounds = values;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::computeOptimalChoicesAndReachableMdpStates(ValueType const &ancillaryChoicesEpsilon,
                                                                                               bool relativeDifference) {
    STORM_LOG_ASSERT(status == Status::ModelChecked, "Method call is invalid in current status.");
    STORM_LOG_ASSERT(exploredMdp, "Method call is invalid in if no MDP is available.");
    STORM_LOG_ASSERT(!optimalChoices.has_value(), "Tried to compute optimal scheduler but this has already been done before.");
    STORM_LOG_ASSERT(!optimalChoicesReachableMdpStates.has_value(),
                     "Tried to compute states that are reachable under an optimal scheduler but this has already been done before.");
 
    // First find the choices that are optimal
    optimalChoices = storm::storage::BitVector(exploredMdp->getNumberOfChoices(), false);
    auto const &choiceIndices = exploredMdp->getNondeterministicChoiceIndices();
    auto const &transitions = exploredMdp->getTransitionMatrix();
    auto const &targetStatesExploredMDP = exploredMdp->getStates("target");
    for (uint64_t mdpState = 0; mdpState < exploredMdp->getNumberOfStates(); ++mdpState) {
        if (targetStatesExploredMDP.get(mdpState)) {
            // Target states can be skipped.
            continue;
        } else {
            auto const &stateValue = values[mdpState];
            for (uint64_t globalChoice = choiceIndices[mdpState]; globalChoice < choiceIndices[mdpState + 1]; ++globalChoice) {
                ValueType choiceValue = transitions.multiplyRowWithVector(globalChoice, values);
                if (exploredMdp->hasRewardModel()) {
                    choiceValue += exploredMdp->getUniqueRewardModel().getStateActionReward(globalChoice);
                }
                auto absDiff = storm::utility::abs<ValueType>((choiceValue - stateValue));
                if ((relativeDifference && absDiff <= ancillaryChoicesEpsilon * stateValue) || (!relativeDifference && absDiff <= ancillaryChoicesEpsilon)) {
                    optimalChoices->set(globalChoice, true);
                }
            }
            STORM_LOG_ASSERT(optimalChoices->getNextSetIndex(choiceIndices[mdpState]) < optimalChoices->size(), "Could not find an optimal choice.");
        }
    }
 
    // Then, find the states that are reachable via these choices
    optimalChoicesReachableMdpStates = storm::utility::graph::getReachableStates(transitions, exploredMdp->getInitialStates(), ~targetStatesExploredMDP,
                                                                                 targetStatesExploredMDP, false, 0, optimalChoices.value());
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::beliefHasMdpState(BeliefId const &beliefId) const {
    return getExploredMdpState(beliefId) != noState();
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::noState() const {
    return std::numeric_limits<MdpStateType>::max();
}
 
template<typename PomdpType, typename BeliefValueType>
std::shared_ptr<storm::logic::Formula const> BeliefMdpExplorer<PomdpType, BeliefValueType>::createStandardProperty(
    storm::solver::OptimizationDirection const &dir, bool computeRewards) {
    std::string propertyString = computeRewards ? "R" : "P";
    propertyString += storm::solver::minimize(dir) ? "min" : "max";
    propertyString += "=? [F \"target\"]";
    std::vector<storm::jani::Property> propertyVector = storm::api::parseProperties(propertyString);
    return storm::api::extractFormulasFromProperties(propertyVector).front();
}
 
template<typename PomdpType, typename BeliefValueType>
storm::modelchecker::CheckTask<storm::logic::Formula, typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType>
BeliefMdpExplorer<PomdpType, BeliefValueType>::createStandardCheckTask(std::shared_ptr<storm::logic::Formula const> &property) {
    // Note: The property should not run out of scope after calling this because the task only stores the property by reference.
    //  Therefore, this method needs the property by reference (and not const reference)
    auto task = storm::api::createTask<ValueType>(property, false);
    auto hint = storm::modelchecker::ExplicitModelCheckerHint<ValueType>();
    hint.setResultHint(values);
    auto hintPtr = std::make_shared<storm::modelchecker::ExplicitModelCheckerHint<ValueType>>(hint);
    task.setHint(hintPtr);
    task.setProduceSchedulers();
    return task;
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::getCurrentMdpState() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    if (stateRemapping.find(currentMdpState) != stateRemapping.end()) {
        return stateRemapping.at(currentMdpState);
    } else {
        return currentMdpState;
    }
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::getCurrentBeliefId() const {
    STORM_LOG_ASSERT(status == Status::Exploring, "Method call is invalid in current status.");
    return getBeliefId(currentMdpState);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::internalAddTransition(uint64_t const &row, MdpStateType const &column, ValueType const &value) {
    STORM_LOG_ASSERT(row <= exploredMdpTransitions.size(), "Skipped at least one row.");
    if (row == exploredMdpTransitions.size()) {
        exploredMdpTransitions.emplace_back();
    }
    STORM_LOG_ASSERT(exploredMdpTransitions[row].count(column) == 0, "Trying to insert multiple transitions to the same state.");
    exploredMdpTransitions[row][column] = value;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::internalAddRowGroupIndex() {
    exploredChoiceIndices.push_back(getCurrentNumberOfMdpChoices());
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::markAsGridBelief(BeliefId const &beliefId) {
    gridBeliefs.insert(beliefId);
}
 
template<typename PomdpType, typename BeliefValueType>
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::isMarkedAsGridBelief(BeliefId const &beliefId) {
    return gridBeliefs.count(beliefId) > 0;
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::getExploredMdpState(
    BeliefId const &beliefId) const {
    if (beliefId < exploredBeliefIds.size() && exploredBeliefIds.get(beliefId)) {
        return beliefIdToMdpStateMap.at(beliefId);
    } else {
        return noState();
    }
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::insertValueHints(ValueType const &lowerBound, ValueType const &upperBound) {
    lowerValueBounds.push_back(lowerBound);
    upperValueBounds.push_back(upperBound);
    // Take the middle value as a hint
    values.push_back((lowerBound + upperBound) / storm::utility::convertNumber<ValueType, uint64_t>(2));
    STORM_LOG_ASSERT(lowerValueBounds.size() == getCurrentNumberOfMdpStates(), "Value vectors have different size then number of available states.");
    STORM_LOG_ASSERT(lowerValueBounds.size() == upperValueBounds.size() && values.size() == upperValueBounds.size(), "Value vectors have inconsistent size.");
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::MdpStateType BeliefMdpExplorer<PomdpType, BeliefValueType>::getOrAddMdpState(
    BeliefId const &beliefId, ValueType const &transitionValue) {
    exploredBeliefIds.grow(beliefId + 1, false);
    if (exploredBeliefIds.get(beliefId)) {
        if (explHeuristic == ExplorationHeuristic::ProbabilityPrio &&
            mdpStatesToExploreStatePrio.find(beliefIdToMdpStateMap[beliefId]) != mdpStatesToExploreStatePrio.end()) {
            // We check if the value is higher than the current priority and update if necessary
            auto newPrio = probabilityEstimation[getCurrentMdpState()] * transitionValue;
            if (newPrio > mdpStatesToExploreStatePrio[beliefIdToMdpStateMap[beliefId]]) {
                // Erase the state from the "queue" map and re-insert it with the new value
                auto range = mdpStatesToExplorePrioState.equal_range(mdpStatesToExploreStatePrio[beliefIdToMdpStateMap[beliefId]]);
                for (auto i = range.first; i != range.second; ++i) {
                    if (i->second == beliefIdToMdpStateMap[beliefId]) {
                        mdpStatesToExplorePrioState.erase(i);
                        break;
                    }
                }
                mdpStatesToExplorePrioState.emplace(newPrio, beliefIdToMdpStateMap[beliefId]);
                mdpStatesToExploreStatePrio[beliefIdToMdpStateMap[beliefId]] = newPrio;
            }
        }
        return beliefIdToMdpStateMap[beliefId];
    } else {
        // This state needs exploration
        exploredBeliefIds.set(beliefId, true);
 
        // If this is a restart of the exploration, we still might have an MDP state for the belief
        if (exploredMdp) {
            auto findRes = beliefIdToMdpStateMap.find(beliefId);
            if (findRes != beliefIdToMdpStateMap.end()) {
                ValueType currentPrio;
                switch (explHeuristic) {
                    case ExplorationHeuristic::BreadthFirst:
                        currentPrio = prio;
                        prio = prio - storm::utility::one<ValueType>();
                        break;
                    case ExplorationHeuristic::LowerBoundPrio:
                        currentPrio = getLowerValueBoundAtCurrentState();
                        break;
                    case ExplorationHeuristic::UpperBoundPrio:
                        currentPrio = getUpperValueBoundAtCurrentState();
                        break;
                    case ExplorationHeuristic::GapPrio:
                        currentPrio = getUpperValueBoundAtCurrentState() - getLowerValueBoundAtCurrentState();
                        break;
                    case ExplorationHeuristic::ProbabilityPrio:
                        if (getCurrentMdpState() != noState()) {
                            currentPrio = probabilityEstimation[getCurrentMdpState()] * transitionValue;
                        } else {
                            currentPrio = storm::utility::one<ValueType>();
                        }
                        break;
                    default:
                        STORM_LOG_THROW(false, storm::exceptions::NotImplementedException, "Other heuristics not implemented yet");
                }
                mdpStatesToExploreStatePrio[findRes->second] = currentPrio;
                mdpStatesToExplorePrioState.emplace(currentPrio, findRes->second);
                return findRes->second;
            }
        }
        // At this point we need to add a new MDP state
        MdpStateType result = getCurrentNumberOfMdpStates();
        assert(getCurrentNumberOfMdpStates() == mdpStateToBeliefIdMap.size());
        mdpStateToBeliefIdMap.push_back(beliefId);
        beliefIdToMdpStateMap[beliefId] = result;
        insertValueHints(computeLowerValueBoundAtBelief(beliefId), computeUpperValueBoundAtBelief(beliefId));
        ValueType currentPrio;
        switch (explHeuristic) {
            case ExplorationHeuristic::BreadthFirst:
                currentPrio = prio;
                prio = prio - storm::utility::one<ValueType>();
                break;
            case ExplorationHeuristic::LowerBoundPrio:
                currentPrio = getLowerValueBoundAtCurrentState();
                break;
            case ExplorationHeuristic::UpperBoundPrio:
                currentPrio = getUpperValueBoundAtCurrentState();
                break;
            case ExplorationHeuristic::GapPrio:
                currentPrio = getUpperValueBoundAtCurrentState() - getLowerValueBoundAtCurrentState();
                break;
            case ExplorationHeuristic::ProbabilityPrio:
                if (getCurrentMdpState() != noState()) {
                    currentPrio = probabilityEstimation[getCurrentMdpState()] * transitionValue;
                } else {
                    currentPrio = storm::utility::one<ValueType>();
                }
                break;
            default:
                STORM_LOG_THROW(false, storm::exceptions::NotImplementedException, "Other heuristics not implemented yet");
        }
        mdpStatesToExploreStatePrio[result] = currentPrio;
        mdpStatesToExplorePrioState.emplace(currentPrio, result);
        return result;
    }
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::addChoiceLabelToCurrentState(uint64_t const &localActionIndex, std::string const &label) {
    mdpStateToChoiceLabelsMap[currentMdpState][localActionIndex] = label;
}
 
template<typename PomdpType, typename BeliefValueType>
std::vector<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::BeliefId> BeliefMdpExplorer<PomdpType, BeliefValueType>::getBeliefsInMdp() {
    return mdpStateToBeliefIdMap;
}
 
template<typename PomdpType, typename BeliefValueType>
std::vector<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::BeliefId> BeliefMdpExplorer<PomdpType, BeliefValueType>::getBeliefsWithObservationInMdp(
    uint32_t obs) const {
    std::vector<BeliefId> res;
    for (auto const &belief : mdpStateToBeliefIdMap) {
        if (belief != beliefManager->noId()) {
            if (beliefManager->getBeliefObservation(belief) == obs) {
                res.push_back(belief);
            }
        }
    }
    return res;
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::getTrivialUpperBoundAtPOMDPState(
    uint64_t const &pomdpState) {
    return pomdpValueBounds.getSmallestUpperBound(pomdpState);
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::getTrivialLowerBoundAtPOMDPState(
    uint64_t const &pomdpState) {
    return pomdpValueBounds.getHighestLowerBound(pomdpState);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::setExtremeValueBound(storm::pomdp::storage::ExtremePOMDPValueBound<ValueType> valueBound) {
    extremeValueBound = valueBound;
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::setFMSchedValueList(std::vector<std::vector<std::unordered_map<uint64_t, ValueType>>> valueList) {
    fmSchedulerValueList = valueList;
}
 
template<typename PomdpType, typename BeliefValueType>
uint64_t BeliefMdpExplorer<PomdpType, BeliefValueType>::getNrOfMemoryNodesForObservation(uint32_t observation) const {
    return fmSchedulerValueList.at(observation).size();
}
 
template<typename PomdpType, typename BeliefValueType>
typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType BeliefMdpExplorer<PomdpType, BeliefValueType>::getExtremeValueBoundAtPOMDPState(
    const uint64_t &pomdpState) {
    return extremeValueBound.getValueForState(pomdpState);
}
 
template<typename PomdpType, typename BeliefValueType>
storm::storage::BitVector BeliefMdpExplorer<PomdpType, BeliefValueType>::getStateExtremeBoundIsInfinite() {
    return extremeValueBound.isInfinite;
}
 
template<typename PomdpType, typename BeliefValueType>
uint64_t BeliefMdpExplorer<PomdpType, BeliefValueType>::getNrSchedulersForUpperBounds() {
    return pomdpValueBounds.upper.size();
}
 
template<typename PomdpType, typename BeliefValueType>
uint64_t BeliefMdpExplorer<PomdpType, BeliefValueType>::getNrSchedulersForLowerBounds() {
    return pomdpValueBounds.lower.size();
}
 
template<typename PomdpType, typename BeliefValueType>
storm::storage::Scheduler<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType>
BeliefMdpExplorer<PomdpType, BeliefValueType>::getLowerValueBoundScheduler(uint64_t schedulerId) const {
    STORM_LOG_ASSERT(!pomdpValueBounds.lowerSchedulers.empty(), "Requested lower bound scheduler but none were available.");
    STORM_LOG_ASSERT(pomdpValueBounds.lowerSchedulers.size() > schedulerId,
                     "Requested lower value bound scheduler with ID " << schedulerId << " not available.");
    return pomdpValueBounds.lowerSchedulers[schedulerId];
}
 
template<typename PomdpType, typename BeliefValueType>
storm::storage::Scheduler<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType>
BeliefMdpExplorer<PomdpType, BeliefValueType>::getUpperValueBoundScheduler(uint64_t schedulerId) const {
    STORM_LOG_ASSERT(!pomdpValueBounds.upperSchedulers.empty(), "Requested upper bound scheduler but none were available.");
    STORM_LOG_ASSERT(pomdpValueBounds.upperSchedulers.size() > schedulerId,
                     "Requested upper value bound scheduler with ID " << schedulerId << " not available.");
    return pomdpValueBounds.upperSchedulers[schedulerId];
}
 
template<typename PomdpType, typename BeliefValueType>
std::vector<storm::storage::Scheduler<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType>>
BeliefMdpExplorer<PomdpType, BeliefValueType>::getLowerValueBoundSchedulers() const {
    STORM_LOG_ASSERT(!pomdpValueBounds.lowerSchedulers.empty(), "Requested lower bound schedulers but none were available.");
    return pomdpValueBounds.lowerSchedulers;
}
 
template<typename PomdpType, typename BeliefValueType>
std::vector<storm::storage::Scheduler<typename BeliefMdpExplorer<PomdpType, BeliefValueType>::ValueType>>
BeliefMdpExplorer<PomdpType, BeliefValueType>::getUpperValueBoundSchedulers() const {
    STORM_LOG_ASSERT(!pomdpValueBounds.upperSchedulers.empty(), "Requested upper bound schedulers but none were available.");
    return pomdpValueBounds.upperSchedulers;
}
 
template<typename PomdpType, typename BeliefValueType>
 
bool BeliefMdpExplorer<PomdpType, BeliefValueType>::hasFMSchedulerValues() const {
    return !fmSchedulerValueList.empty();
}
 
template<typename PomdpType, typename BeliefValueType>
std::vector<BeliefValueType> BeliefMdpExplorer<PomdpType, BeliefValueType>::computeProductWithSparseMatrix(
    BeliefId const &beliefId, storm::storage::SparseMatrix<BeliefValueType> &matrix) const {
    return beliefManager->computeMatrixBeliefProduct(beliefId, matrix);
}
 
template<typename PomdpType, typename BeliefValueType>
void BeliefMdpExplorer<PomdpType, BeliefValueType>::adjustActions(uint64_t totalNumberOfActions) {
    uint64_t currentRowGroupSize = getSizeOfCurrentRowGroup();
    assert(totalNumberOfActions != currentRowGroupSize);
    if (totalNumberOfActions > currentRowGroupSize) {
        uint64_t numberOfActionsToAdd = totalNumberOfActions - currentRowGroupSize;
        exploredMdpTransitions.insert(exploredMdpTransitions.begin() + (exploredChoiceIndices[getCurrentMdpState() + 1]), numberOfActionsToAdd,
                                      std::map<MdpStateType, ValueType>());
        for (uint64_t i = getCurrentMdpState() + 1; i < exploredChoiceIndices.size(); i++) {
            exploredChoiceIndices[i] += numberOfActionsToAdd;
        }
        return;
    }
    if (totalNumberOfActions < currentRowGroupSize) {
        uint64_t numberOfActionsToRemove = currentRowGroupSize - totalNumberOfActions;
        exploredMdpTransitions.erase(exploredMdpTransitions.begin() + (exploredChoiceIndices[getCurrentMdpState() + 1]) - numberOfActionsToRemove,
                                     exploredMdpTransitions.begin() + (exploredChoiceIndices[getCurrentMdpState() + 1]));
        for (uint64_t i = getCurrentMdpState() + 1; i < exploredChoiceIndices.size(); i++) {
            exploredChoiceIndices[i] -= numberOfActionsToRemove;
        }
    }
}
 
template class BeliefMdpExplorer<storm::models::sparse::Pomdp<double>>;
 
template class BeliefMdpExplorer<storm::models::sparse::Pomdp<double>, storm::RationalNumber>;
 
template class BeliefMdpExplorer<storm::models::sparse::Pomdp<storm::RationalNumber>, double>;
 
template class BeliefMdpExplorer<storm::models::sparse::Pomdp<storm::RationalNumber>>;
}  // namespace builder
}  // namespace storm