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Added timing and caching of subsimplex computation results

tempestpy_adaptions
Alexander Bork 5 years ago
parent
d814942997
commit
3bd910f42b
5 changed files with 117 additions and 41 deletions
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  1. 17
      src/storm-pomdp-cli/settings/modules/POMDPSettings.cpp
  2. 4
      src/storm-pomdp-cli/settings/modules/POMDPSettings.h
  3. 42
      src/storm-pomdp-cli/storm-pomdp.cpp
  4. 81
      src/storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.cpp
  5. 10
      src/storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.h

17
src/storm-pomdp-cli/settings/modules/POMDPSettings.cpp
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@ -14,6 +14,7 @@ namespace storm {
const std::string POMDPSettings::moduleName = "pomdp"; const std::string POMDPSettings::moduleName = "pomdp";
const std::string exportAsParametricModelOption = "parametric-drn"; const std::string exportAsParametricModelOption = "parametric-drn";
const std::string gridApproximationOption = "gridapproximation";
const std::string qualitativeReductionOption = "qualitativereduction"; const std::string qualitativeReductionOption = "qualitativereduction";
const std::string analyzeUniqueObservationsOption = "uniqueobservations"; const std::string analyzeUniqueObservationsOption = "uniqueobservations";
const std::string mecReductionOption = "mecreduction"; const std::string mecReductionOption = "mecreduction";
@ -37,6 +38,13 @@ namespace storm {
this->addOption(storm::settings::OptionBuilder(moduleName, fscmode, false, "Sets the way the pMC is obtained").addArgument(storm::settings::ArgumentBuilder::createStringArgument("type", "type name").addValidatorString(ArgumentValidatorFactory::createMultipleChoiceValidator(fscModes)).setDefaultValueString("standard").build()).build()); this->addOption(storm::settings::OptionBuilder(moduleName, fscmode, false, "Sets the way the pMC is obtained").addArgument(storm::settings::ArgumentBuilder::createStringArgument("type", "type name").addValidatorString(ArgumentValidatorFactory::createMultipleChoiceValidator(fscModes)).setDefaultValueString("standard").build()).build());
this->addOption(storm::settings::OptionBuilder(moduleName, transformBinaryOption, false, "Transforms the pomdp to a binary pomdp.").build()); this->addOption(storm::settings::OptionBuilder(moduleName, transformBinaryOption, false, "Transforms the pomdp to a binary pomdp.").build());
this->addOption(storm::settings::OptionBuilder(moduleName, transformSimpleOption, false, "Transforms the pomdp to a binary and simple pomdp.").build()); this->addOption(storm::settings::OptionBuilder(moduleName, transformSimpleOption, false, "Transforms the pomdp to a binary and simple pomdp.").build());
this->addOption(storm::settings::OptionBuilder(moduleName, gridApproximationOption, false,
"Analyze the POMDP using grid approximation.").addArgument(
storm::settings::ArgumentBuilder::createUnsignedIntegerArgument("resolution",
"the resolution of the grid").setDefaultValueUnsignedInteger(
10).addValidatorUnsignedInteger(
storm::settings::ArgumentValidatorFactory::createUnsignedGreaterValidator(
0)).build()).build());
} }
bool POMDPSettings::isExportToParametricSet() const { bool POMDPSettings::isExportToParametricSet() const {
@ -63,6 +71,15 @@ namespace storm {
return this->getOption(selfloopReductionOption).getHasOptionBeenSet(); return this->getOption(selfloopReductionOption).getHasOptionBeenSet();
} }
bool POMDPSettings::isGridApproximationSet() const {
return this->getOption(gridApproximationOption).getHasOptionBeenSet();
}
uint64_t POMDPSettings::getGridResolution() const {
return this->getOption(gridApproximationOption).getArgumentByName(
"resolution").getValueAsUnsignedInteger();
}
uint64_t POMDPSettings::getMemoryBound() const { uint64_t POMDPSettings::getMemoryBound() const {
return this->getOption(memoryBoundOption).getArgumentByName("bound").getValueAsUnsignedInteger(); return this->getOption(memoryBoundOption).getArgumentByName("bound").getValueAsUnsignedInteger();
} }

4
src/storm-pomdp-cli/settings/modules/POMDPSettings.h
View File

@ -25,6 +25,8 @@ namespace storm {
std::string getExportToParametricFilename() const; std::string getExportToParametricFilename() const;
bool isQualitativeReductionSet() const; bool isQualitativeReductionSet() const;
bool isGridApproximationSet() const;
bool isAnalyzeUniqueObservationsSet() const; bool isAnalyzeUniqueObservationsSet() const;
bool isMecReductionSet() const; bool isMecReductionSet() const;
bool isSelfloopReductionSet() const; bool isSelfloopReductionSet() const;
@ -32,6 +34,8 @@ namespace storm {
bool isTransformBinarySet() const; bool isTransformBinarySet() const;
std::string getFscApplicationTypeString() const; std::string getFscApplicationTypeString() const;
uint64_t getMemoryBound() const; uint64_t getMemoryBound() const;
uint64_t getGridResolution() const;
storm::storage::PomdpMemoryPattern getMemoryPattern() const; storm::storage::PomdpMemoryPattern getMemoryPattern() const;
bool check() const override; bool check() const override;

42
src/storm-pomdp-cli/storm-pomdp.cpp
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@ -42,6 +42,8 @@
#include "storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.h" #include "storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.h"
#include "storm/api/storm.h" #include "storm/api/storm.h"
#include <typeinfo>
/*! /*!
* Initialize the settings manager. * Initialize the settings manager.
*/ */
@ -113,10 +115,6 @@ int main(const int argc, const char** argv) {
STORM_LOG_THROW(model && model->getType() == storm::models::ModelType::Pomdp, storm::exceptions::WrongFormatException, "Expected a POMDP."); STORM_LOG_THROW(model && model->getType() == storm::models::ModelType::Pomdp, storm::exceptions::WrongFormatException, "Expected a POMDP.");
std::shared_ptr<storm::models::sparse::Pomdp<storm::RationalNumber>> pomdp = model->template as<storm::models::sparse::Pomdp<storm::RationalNumber>>(); std::shared_ptr<storm::models::sparse::Pomdp<storm::RationalNumber>> pomdp = model->template as<storm::models::sparse::Pomdp<storm::RationalNumber>>();
// For ease of testing
storm::pomdp::modelchecker::ApproximatePOMDPModelchecker<storm::RationalNumber> checker = storm::pomdp::modelchecker::ApproximatePOMDPModelchecker<storm::RationalNumber>();
checker.computeReachabilityProbability(*pomdp, std::set<uint32_t>({7}), false, 10);
std::shared_ptr<storm::logic::Formula const> formula; std::shared_ptr<storm::logic::Formula const> formula;
if (!symbolicInput.properties.empty()) { if (!symbolicInput.properties.empty()) {
formula = symbolicInput.properties.front().getRawFormula(); formula = symbolicInput.properties.front().getRawFormula();
@ -149,6 +147,42 @@ int main(const int argc, const char** argv) {
STORM_PRINT_AND_LOG(" done." << std::endl); STORM_PRINT_AND_LOG(" done." << std::endl);
std::cout << "actual reduction not yet implemented..." << std::endl; std::cout << "actual reduction not yet implemented..." << std::endl;
} }
if (pomdpSettings.isGridApproximationSet()) {
storm::logic::ProbabilityOperatorFormula const &probFormula = formula->asProbabilityOperatorFormula();
storm::logic::Formula const &subformula1 = probFormula.getSubformula();
std::set<uint32_t> targetObservationSet;
//TODO refactor
bool validFormula = false;
if (subformula1.isEventuallyFormula()) {
storm::logic::EventuallyFormula const &eventuallyFormula = subformula1.asEventuallyFormula();
storm::logic::Formula const &subformula2 = eventuallyFormula.getSubformula();
if (subformula2.isAtomicLabelFormula()) {
storm::logic::AtomicLabelFormula const &alFormula = subformula2.asAtomicLabelFormula();
validFormula = true;
std::string targetLabel = alFormula.getLabel();
auto labeling = pomdp->getStateLabeling();
for (size_t state = 0; state < pomdp->getNumberOfStates(); ++state) {
if (labeling.getStateHasLabel(targetLabel, state)) {
targetObservationSet.insert(pomdp->getObservation(state));
}
}
}
}
STORM_LOG_THROW(validFormula, storm::exceptions::InvalidPropertyException,
"The formula is not supported by the grid approximation");
storm::pomdp::modelchecker::ApproximatePOMDPModelchecker<storm::RationalNumber> checker = storm::pomdp::modelchecker::ApproximatePOMDPModelchecker<storm::RationalNumber>();
storm::RationalNumber overRes = storm::utility::one<storm::RationalNumber>();
storm::RationalNumber underRes = storm::utility::zero<storm::RationalNumber>();
std::unique_ptr<storm::pomdp::modelchecker::POMDPCheckResult<storm::RationalNumber>> result;
result = checker.computeReachabilityProbability(*pomdp, targetObservationSet,
probFormula.getOptimalityType() ==
storm::OptimizationDirection::Minimize,
pomdpSettings.getGridResolution() + gridIncrease);
overRes = result->OverapproximationValue;
underRes = result->UnderapproximationValue;
}
} else if (formula->isRewardOperatorFormula()) { } else if (formula->isRewardOperatorFormula()) {
if (pomdpSettings.isSelfloopReductionSet() && storm::solver::minimize(formula->asRewardOperatorFormula().getOptimalityType())) { if (pomdpSettings.isSelfloopReductionSet() && storm::solver::minimize(formula->asRewardOperatorFormula().getOptimalityType())) {
STORM_PRINT_AND_LOG("Eliminating self-loop choices ..."); STORM_PRINT_AND_LOG("Eliminating self-loop choices ...");

81
src/storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.cpp
View File

@ -22,11 +22,11 @@ namespace storm {
} }
template<typename ValueType, typename RewardModelType> template<typename ValueType, typename RewardModelType>
/*std::unique_ptr<POMDPCheckResult>*/ void
std::unique_ptr<POMDPCheckResult<ValueType>>
ApproximatePOMDPModelchecker<ValueType, RewardModelType>::computeReachabilityProbability( ApproximatePOMDPModelchecker<ValueType, RewardModelType>::computeReachabilityProbability(
storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp, storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::set<uint32_t> targetObservations, bool min, uint64_t gridResolution) { std::set<uint32_t> targetObservations, bool min, uint64_t gridResolution) {
//TODO add timing
storm::utility::Stopwatch beliefGridTimer(true);
uint64_t maxIterations = 100; uint64_t maxIterations = 100;
bool finished = false; bool finished = false;
uint64_t iteration = 0; uint64_t iteration = 0;
@ -46,7 +46,9 @@ namespace storm {
constructBeliefGrid(pomdp, targetObservations, gridResolution, beliefList, beliefGrid, beliefIsTarget, constructBeliefGrid(pomdp, targetObservations, gridResolution, beliefList, beliefGrid, beliefIsTarget,
nextId); nextId);
nextId = beliefList.size(); nextId = beliefList.size();
beliefGridTimer.stop();
storm::utility::Stopwatch overApproxTimer(true);
// ID -> Value // ID -> Value
std::map<uint64_t, ValueType> result; std::map<uint64_t, ValueType> result;
std::map<uint64_t, ValueType> result_backup; std::map<uint64_t, ValueType> result_backup;
@ -58,6 +60,7 @@ namespace storm {
// current ID -> action -> next ID // current ID -> action -> next ID
std::map<uint64_t, std::vector<std::map<uint32_t, uint64_t>>> nextBelieves; std::map<uint64_t, std::vector<std::map<uint32_t, uint64_t>>> nextBelieves;
storm::utility::Stopwatch nextBeliefGeneration(true);
for (size_t i = 0; i < beliefGrid.size(); ++i) { for (size_t i = 0; i < beliefGrid.size(); ++i) {
auto currentBelief = beliefGrid[i]; auto currentBelief = beliefGrid[i];
bool isTarget = beliefIsTarget[currentBelief.id]; bool isTarget = beliefIsTarget[currentBelief.id];
@ -68,6 +71,7 @@ namespace storm {
result.emplace(std::make_pair(currentBelief.id, storm::utility::zero<ValueType>())); result.emplace(std::make_pair(currentBelief.id, storm::utility::zero<ValueType>()));
result_backup.emplace(std::make_pair(currentBelief.id, storm::utility::zero<ValueType>())); result_backup.emplace(std::make_pair(currentBelief.id, storm::utility::zero<ValueType>()));
//TODO put this in extra function
std::vector<std::map<uint32_t, ValueType>> observationProbabilitiesInAction; std::vector<std::map<uint32_t, ValueType>> observationProbabilitiesInAction;
std::vector<std::map<uint32_t, uint64_t>> nextBelievesInAction; std::vector<std::map<uint32_t, uint64_t>> nextBelievesInAction;
@ -98,9 +102,17 @@ namespace storm {
nextBelieves.emplace(std::make_pair(currentBelief.id, nextBelievesInAction)); nextBelieves.emplace(std::make_pair(currentBelief.id, nextBelievesInAction));
} }
} }
nextBeliefGeneration.stop();
//Use chaching to avoid multiple computation of the subsimplices and lambdas
std::map<uint64_t, std::vector<std::vector<ValueType>>> subSimplexCache;
std::map<uint64_t, std::vector<ValueType>> lambdaCache;
STORM_PRINT("Time generation of next believes: " << nextBeliefGeneration << std::endl)
// Value Iteration // Value Iteration
auto cc = storm::utility::ConstantsComparator<ValueType>(); auto cc = storm::utility::ConstantsComparator<ValueType>();
while (!finished && iteration < maxIterations) { while (!finished && iteration < maxIterations) {
storm::utility::Stopwatch iterationTimer(true);
STORM_LOG_DEBUG("Iteration " << iteration + 1); STORM_LOG_DEBUG("Iteration " << iteration + 1);
bool improvement = false; bool improvement = false;
for (size_t i = 0; i < beliefGrid.size(); ++i) { for (size_t i = 0; i < beliefGrid.size(); ++i) {
@ -123,10 +135,20 @@ namespace storm {
uint32_t observation = iter->first; uint32_t observation = iter->first;
storm::pomdp::Belief<ValueType> nextBelief = beliefList[nextBelieves[currentBelief.id][action][observation]]; storm::pomdp::Belief<ValueType> nextBelief = beliefList[nextBelieves[currentBelief.id][action][observation]];
// compute subsimplex and lambdas according to the Lovejoy paper to approximate the next belief // compute subsimplex and lambdas according to the Lovejoy paper to approximate the next belief
// cache the values to not always re-calculate
std::vector<std::vector<ValueType>> subSimplex;
std::vector<ValueType> lambdas;
if (subSimplexCache.count(nextBelief.id) > 0) {
subSimplex = subSimplexCache[nextBelief.id];
lambdas = lambdaCache[nextBelief.id];
} else {
std::pair<std::vector<std::vector<ValueType>>, std::vector<ValueType>> temp = computeSubSimplexAndLambdas( std::pair<std::vector<std::vector<ValueType>>, std::vector<ValueType>> temp = computeSubSimplexAndLambdas(
nextBelief.probabilities, gridResolution); nextBelief.probabilities, gridResolution);
std::vector<std::vector<ValueType>> subSimplex = temp.first;
std::vector<ValueType> lambdas = temp.second;
subSimplex = temp.first;
lambdas = temp.second;
subSimplexCache[nextBelief.id] = subSimplex;
lambdaCache[nextBelief.id] = lambdas;
}
auto sum = storm::utility::zero<ValueType>(); auto sum = storm::utility::zero<ValueType>();
for (size_t j = 0; j < lambdas.size(); ++j) { for (size_t j = 0; j < lambdas.size(); ++j) {
@ -138,17 +160,11 @@ namespace storm {
currentValue += iter->second * sum; currentValue += iter->second * sum;
} }
// Update the selected actions TODO make this nicer
// Update the selected actions
if ((min && cc.isLess(storm::utility::zero<ValueType>(), chosenValue - currentValue)) || if ((min && cc.isLess(storm::utility::zero<ValueType>(), chosenValue - currentValue)) ||
(!min && (!min &&
cc.isLess(storm::utility::zero<ValueType>(), currentValue - chosenValue))) {
chosenValue = currentValue;
chosenActionIndex = action;
} else if ((min && cc.isEqual(storm::utility::zero<ValueType>(),
chosenValue - currentValue)) ||
(!min &&
cc.isEqual(storm::utility::zero<ValueType>(),
currentValue - chosenValue))) {
cc.isLess(storm::utility::zero<ValueType>(), currentValue - chosenValue)) ||
cc.isEqual(storm::utility::zero<ValueType>(), chosenValue - currentValue)) {
chosenValue = currentValue; chosenValue = currentValue;
chosenActionIndex = action; chosenActionIndex = action;
} }
@ -171,9 +187,11 @@ namespace storm {
result_backup[iter->first] = result[iter->first]; result_backup[iter->first] = result[iter->first];
} }
++iteration; ++iteration;
iterationTimer.stop();
STORM_PRINT("Iteration " << iteration << ": " << iterationTimer << std::endl);
} }
STORM_PRINT("Grid approximation took " << iteration << " iterations" << std::endl);
STORM_PRINT("Overapproximation took " << iteration << " iterations" << std::endl);
beliefGrid.push_back(initialBelief); beliefGrid.push_back(initialBelief);
beliefIsTarget.push_back( beliefIsTarget.push_back(
@ -192,9 +210,10 @@ namespace storm {
initSubSimplex[j])]; initSubSimplex[j])];
} }
} }
overApproxTimer.stop();
// Now onto the under-approximation // Now onto the under-approximation
storm::utility::Stopwatch underApproxTimer(true);
std::set<uint64_t> visitedBelieves; std::set<uint64_t> visitedBelieves;
std::deque<uint64_t> believesToBeExpanded; std::deque<uint64_t> believesToBeExpanded;
std::map<uint64_t, uint64_t> beliefStateMap; std::map<uint64_t, uint64_t> beliefStateMap;
@ -243,12 +262,6 @@ namespace storm {
believesToBeExpanded.pop_front(); believesToBeExpanded.pop_front();
} }
for (size_t i = 0; i < transitions.size(); ++i) {
for (auto const &transition : transitions[i]) {
STORM_LOG_DEBUG(
"Transition: " << i << " -- " << transition.second << "--> " << transition.first);
}
}
storm::models::sparse::StateLabeling labeling(transitions.size()); storm::models::sparse::StateLabeling labeling(transitions.size());
labeling.addLabel("init"); labeling.addLabel("init");
labeling.addLabel("target"); labeling.addLabel("target");
@ -276,8 +289,17 @@ namespace storm {
ValueType resultValue = res->asExplicitQuantitativeCheckResult<ValueType>().getValueMap().begin()->second; ValueType resultValue = res->asExplicitQuantitativeCheckResult<ValueType>().getValueMap().begin()->second;
STORM_PRINT("Time Belief Grid Generation: " << beliefGridTimer << std::endl
<< "Time Overapproximation: " << overApproxTimer
<< std::endl
<< "Time Underapproximation: " << underApproxTimer
<< std::endl);
STORM_PRINT("Over-Approximation Result: " << overApprox << std::endl); STORM_PRINT("Over-Approximation Result: " << overApprox << std::endl);
STORM_PRINT("Under-Approximation Result: " << resultValue << std::endl); STORM_PRINT("Under-Approximation Result: " << resultValue << std::endl);
return std::make_unique<POMDPCheckResult<ValueType>>(
POMDPCheckResult<ValueType>{overApprox, resultValue});
} }
template<typename ValueType, typename RewardModelType> template<typename ValueType, typename RewardModelType>
@ -311,9 +333,10 @@ namespace storm {
uint64_t gridResolution, uint64_t currentBeliefId, uint64_t nextId, bool min) { uint64_t gridResolution, uint64_t currentBeliefId, uint64_t nextId, bool min) {
auto cc = storm::utility::ConstantsComparator<ValueType>(); auto cc = storm::utility::ConstantsComparator<ValueType>();
storm::pomdp::Belief<ValueType> currentBelief = beliefList[currentBeliefId]; storm::pomdp::Belief<ValueType> currentBelief = beliefList[currentBeliefId];
//TODO put this in extra function
std::vector<std::map<uint32_t, ValueType>> observationProbabilitiesInAction; std::vector<std::map<uint32_t, ValueType>> observationProbabilitiesInAction;
std::vector<std::map<uint32_t, uint64_t>> nextBelievesInAction; std::vector<std::map<uint32_t, uint64_t>> nextBelievesInAction;
uint64_t numChoices = pomdp.getNumberOfChoices( uint64_t numChoices = pomdp.getNumberOfChoices(
pomdp.getStatesWithObservation(currentBelief.observation).front()); pomdp.getStatesWithObservation(currentBelief.observation).front());
for (uint64_t action = 0; action < numChoices; ++action) { for (uint64_t action = 0; action < numChoices; ++action) {
@ -354,8 +377,7 @@ namespace storm {
storm::pomdp::Belief<ValueType> nextBelief = beliefList[nextBelieves[currentBelief.id][action][observation]]; storm::pomdp::Belief<ValueType> nextBelief = beliefList[nextBelieves[currentBelief.id][action][observation]];
// compute subsimplex and lambdas according to the Lovejoy paper to approximate the next belief // compute subsimplex and lambdas according to the Lovejoy paper to approximate the next belief
auto temp = computeSubSimplexAndLambdas(
nextBelief.probabilities, gridResolution);
auto temp = computeSubSimplexAndLambdas(nextBelief.probabilities, gridResolution);
std::vector<std::vector<ValueType>> subSimplex = temp.first; std::vector<std::vector<ValueType>> subSimplex = temp.first;
std::vector<ValueType> lambdas = temp.second; std::vector<ValueType> lambdas = temp.second;
@ -369,15 +391,11 @@ namespace storm {
currentValue += iter->second * sum; currentValue += iter->second * sum;
} }
// Update the selected actions TODO make this nicer
// Update the selected actions
if ((min && cc.isLess(storm::utility::zero<ValueType>(), chosenValue - currentValue)) || if ((min && cc.isLess(storm::utility::zero<ValueType>(), chosenValue - currentValue)) ||
(!min && (!min &&
cc.isLess(storm::utility::zero<ValueType>(), currentValue - chosenValue))) {
chosenValue = currentValue;
chosenActionIndex = action;
} else if ((min && cc.isEqual(storm::utility::zero<ValueType>(), chosenValue - currentValue)) ||
(!min &&
cc.isEqual(storm::utility::zero<ValueType>(), currentValue - chosenValue))) {
cc.isLess(storm::utility::zero<ValueType>(), currentValue - chosenValue)) ||
cc.isEqual(storm::utility::zero<ValueType>(), chosenValue - currentValue)) {
chosenValue = currentValue; chosenValue = currentValue;
chosenActionIndex = action; chosenActionIndex = action;
} }
@ -561,7 +579,6 @@ namespace storm {
} }
lambdas[0] = storm::utility::one<ValueType>() - sum; lambdas[0] = storm::utility::one<ValueType>() - sum;
//TODO add assertion that we are close enough
return std::make_pair(subSimplex, lambdas); return std::make_pair(subSimplex, lambdas);
} }

10
src/storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.h
View File

@ -9,19 +9,23 @@
namespace storm { namespace storm {
namespace pomdp { namespace pomdp {
namespace modelchecker { namespace modelchecker {
class POMDPCheckResult;
template<class ValueType>
struct POMDPCheckResult {
ValueType OverapproximationValue;
ValueType UnderapproximationValue;
};
template<class ValueType, typename RewardModelType = models::sparse::StandardRewardModel<ValueType>> template<class ValueType, typename RewardModelType = models::sparse::StandardRewardModel<ValueType>>
class ApproximatePOMDPModelchecker { class ApproximatePOMDPModelchecker {
public: public:
explicit ApproximatePOMDPModelchecker(); explicit ApproximatePOMDPModelchecker();
/*std::unique_ptr<POMDPCheckResult>*/ void
std::unique_ptr<POMDPCheckResult<ValueType>>
computeReachabilityProbability(storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp, computeReachabilityProbability(storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::set<uint32_t> targetObservations, bool min, std::set<uint32_t> targetObservations, bool min,
uint64_t gridResolution); uint64_t gridResolution);
std::unique_ptr<POMDPCheckResult>
std::unique_ptr<POMDPCheckResult<ValueType>>
computeReachabilityReward(storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp, computeReachabilityReward(storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::set<uint32_t> target_observations, uint64_t gridResolution); std::set<uint32_t> target_observations, uint64_t gridResolution);

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