#pragma once
#include <queue>
#include <chrono>
#include "storm/solver/Z3SmtSolver.h"
#include "storm-counterexamples/counterexamples/HighLevelCounterexample.h"
#include "storm/storage/prism/Program.h"
#include "storm/storage/expressions/Expression.h"
#include "storm/storage/sparse/PrismChoiceOrigins.h"
#include "storm/modelchecker/propositional/SparsePropositionalModelChecker.h"
#include "storm/modelchecker/prctl/helper/SparseDtmcPrctlHelper.h"
#include "storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.h"
#include "storm/modelchecker/results/ExplicitQuantitativeCheckResult.h"
#include "storm/settings/SettingsManager.h"
#include "storm/settings/modules/CoreSettings.h"
#include "storm/utility/macros.h"
#include "storm/exceptions/NotSupportedException.h"
#include "storm/utility/counterexamples.h"
#include "storm/utility/cli.h"
namespace storm {
class Environment;
namespace counterexamples {
/*!
* This class provides functionality to generate a minimal counterexample to a probabilistic reachability
* property in terms of used labels.
*/
template <class T>
class SMTMinimalLabelSetGenerator {
#ifdef STORM_HAVE_Z3
private:
struct RelevancyInformation {
// The set of relevant states in the model.
storm::storage::BitVector relevantStates;
// The set of relevant labels.
boost::container::flat_set<uint_fast64_t> relevantLabels;
// The set of relevant label sets.
boost::container::flat_set<boost::container::flat_set<uint_fast64_t>> relevantLabelSets;
// The set of labels that matter in terms of minimality.
boost::container::flat_set<uint_fast64_t> minimalityLabels;
// A set of labels that is definitely known to be taken in the final solution.
boost::container::flat_set<uint_fast64_t> knownLabels;
boost::container::flat_set<uint64_t> dontCareLabels;
// A list of relevant choices for each relevant state.
std::map<uint_fast64_t, std::list<uint_fast64_t>> relevantChoicesForRelevantStates;
};
struct VariableInformation {
// The manager responsible for the constraints we are building.
std::shared_ptr<storm::expressions::ExpressionManager> manager;
// The variables associated with the relevant labels.
std::vector<storm::expressions::Variable> labelVariables;
// The variables associated with the labels that matter in terms of minimality.
std::vector<storm::expressions::Variable> minimalityLabelVariables;
// A mapping from relevant labels to their indices in the variable vector.
std::map<uint_fast64_t, uint_fast64_t> labelToIndexMap;
// A set of original auxiliary variables needed for the Fu-Malik procedure.
std::vector<storm::expressions::Variable> originalAuxiliaryVariables;
// A set of auxiliary variables that may be modified by the MaxSAT procedure.
std::vector<storm::expressions::Variable> auxiliaryVariables;
// A vector of variables that can be used to constrain the number of variables that are set to true.
std::vector<storm::expressions::Variable> adderVariables;
// A flag whether or not there are variables reserved for encoding reachability of a target state.
bool hasReachabilityVariables;
// Starting from here, all structures hold information only if hasReachabilityVariables is true;
// A mapping from each pair of adjacent relevant states to their index in the corresponding variable vector.
std::map<std::pair<uint_fast64_t, uint_fast64_t>, uint_fast64_t> statePairToIndexMap;
// A vector of variables associated with each pair of relevant states (s, s') such that s' is
// a successor of s.
std::vector<storm::expressions::Variable> statePairVariables;
// A mapping from relevant states to the index with the corresponding order variable in the state order variable vector.
std::map<uint_fast64_t, uint_fast64_t> relevantStatesToOrderVariableIndexMap;
// A vector of variables that holds all state order variables.
std::vector<storm::expressions::Variable> stateOrderVariables;
};
/*!
* Computes the set of relevant labels in the model. Relevant labels are choice labels such that there exists
* a scheduler that satisfies phi until psi with a nonzero probability.
*
* @param model The model to search for relevant labels.
* @param phiStates A bit vector representing all states that satisfy phi.
* @param psiStates A bit vector representing all states that satisfy psi.
* @param dontCareLabels A set of labels that are "don't care" labels wrt. minimality.
* @return A structure containing the relevant labels as well as states.
*/
static RelevancyInformation determineRelevantStatesAndLabels(storm::models::sparse::Model<T> const& model, std::vector<boost::container::flat_set<uint_fast64_t>> const& labelSets, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, boost::container::flat_set<uint_fast64_t> const& dontCareLabels) {
// Create result.
RelevancyInformation relevancyInformation;
// Compute all relevant states, i.e. states for which there exists a scheduler that has a non-zero
// probabilitiy of satisfying phi until psi.
storm::storage::SparseMatrix<T> backwardTransitions = model.getBackwardTransitions();
relevancyInformation.relevantStates = storm::utility::graph::performProbGreater0E(backwardTransitions, phiStates, psiStates);
relevancyInformation.relevantStates &= ~psiStates;
STORM_LOG_DEBUG("Found " << relevancyInformation.relevantStates.getNumberOfSetBits() << " relevant states.");
// Retrieve some references for convenient access.
storm::storage::SparseMatrix<T> const& transitionMatrix = model.getTransitionMatrix();
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
// Now traverse all choices of all relevant states and check whether there is a successor target state.
// If so, the associated labels become relevant. Also, if a choice of a relevant state has at least one
// relevant successor, the choice becomes relevant.
for (auto state : relevancyInformation.relevantStates) {
relevancyInformation.relevantChoicesForRelevantStates.emplace(state, std::list<uint_fast64_t>());
for (uint_fast64_t row = nondeterministicChoiceIndices[state]; row < nondeterministicChoiceIndices[state + 1]; ++row) {
for (auto const& entry : transitionMatrix.getRow(row)) {
// If there is a relevant successor, we need to add the labels of the current choice.
if (relevancyInformation.relevantStates.get(entry.getColumn()) || psiStates.get(entry.getColumn())) {
relevancyInformation.relevantChoicesForRelevantStates[state].push_back(row);
for (auto const& label : labelSets[row]) {
relevancyInformation.relevantLabels.insert(label);
}
relevancyInformation.relevantLabelSets.insert(labelSets[row]);
break;
}
}
}
}
// Compute the set of labels that are known to be taken in any case.
relevancyInformation.knownLabels = storm::utility::counterexamples::getGuaranteedLabelSet(model, labelSets, psiStates, relevancyInformation.relevantLabels);
if (!relevancyInformation.knownLabels.empty()) {
boost::container::flat_set<uint_fast64_t> remainingLabels;
std::set_difference(relevancyInformation.relevantLabels.begin(), relevancyInformation.relevantLabels.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(remainingLabels, remainingLabels.end()));
relevancyInformation.relevantLabels = remainingLabels;
}
relevancyInformation.dontCareLabels = dontCareLabels;
std::set_difference(relevancyInformation.relevantLabels.begin(), relevancyInformation.relevantLabels.end(), dontCareLabels.begin(), dontCareLabels.end(), std::inserter(relevancyInformation.minimalityLabels, relevancyInformation.minimalityLabels.begin()));
STORM_LOG_DEBUG("Found " << relevancyInformation.relevantLabels.size() << " relevant and " << relevancyInformation.knownLabels.size() << " known labels.");
STORM_LOG_DEBUG("Found " << relevancyInformation.minimalityLabels.size() << " labels to minize over.");
return relevancyInformation;
}
/*!
* Creates all necessary variables.
*
* @param manager The manager in which to create the variables.
* @param relevantCommands A set of relevant labels for which to create the expressions.
* @return A mapping from relevant labels to their corresponding expressions.
*/
static VariableInformation createVariables(std::shared_ptr<storm::expressions::ExpressionManager> const& manager, storm::models::sparse::Model<T> const& model, storm::storage::BitVector const& psiStates, RelevancyInformation const& relevancyInformation, bool createReachabilityVariables) {
VariableInformation variableInformation;
variableInformation.manager = manager;
// Create stringstream to build expression names.
std::stringstream variableName;
// Create the variables for the relevant labels.
for (auto label : relevancyInformation.relevantLabels) {
variableInformation.labelToIndexMap[label] = variableInformation.labelVariables.size();
// Clear contents of the stream to construct new expression name.
variableName.clear();
variableName.str("");
variableName << "c" << label;
variableInformation.labelVariables.push_back(manager->declareBooleanVariable(variableName.str()));
// Record if the label is among the ones that matter for minimality.
if (relevancyInformation.minimalityLabels.find(label) != relevancyInformation.minimalityLabels.end()) {
variableInformation.minimalityLabelVariables.push_back(variableInformation.labelVariables.back());
}
// Clear contents of the stream to construct new expression name.
variableName.clear();
variableName.str("");
variableName << "h" << label;
variableInformation.originalAuxiliaryVariables.push_back(manager->declareBooleanVariable(variableName.str()));
}
// A mapping from each pair of adjacent relevant states to their index in the corresponding variable vector.
std::map<std::pair<uint_fast64_t, uint_fast64_t>, uint_fast64_t> statePairToIndexMap;
// A vector of variables associated with each pair of relevant states (s, s') such that s' is
// a successor of s.
std::vector<storm::expressions::Variable> statePairVariables;
// Create variables needed for encoding reachability of a target state if requested.
if (createReachabilityVariables) {
variableInformation.hasReachabilityVariables = true;
storm::storage::SparseMatrix<T> const& transitionMatrix = model.getTransitionMatrix();
for (auto state : relevancyInformation.relevantStates) {
variableInformation.relevantStatesToOrderVariableIndexMap[state] = variableInformation.stateOrderVariables.size();
// Clear contents of the stream to construct new expression name.
variableName.clear();
variableName.str("");
variableName << "o" << state;
variableInformation.stateOrderVariables.push_back(manager->declareRationalVariable(variableName.str()));
for (auto const& relevantChoice : relevancyInformation.relevantChoicesForRelevantStates.at(state)) {
for (auto const& entry : transitionMatrix.getRow(relevantChoice)) {
// If the successor state is neither the state itself nor an irrelevant state, we need to add a variable for the transition.
if (state != entry.getColumn() && (relevancyInformation.relevantStates.get(entry.getColumn()) || psiStates.get(entry.getColumn()))) {
// Make sure that there is not already one variable for the state pair. This may happen because of several nondeterministic choices
// targeting the same state.
if (variableInformation.statePairToIndexMap.find(std::make_pair(state, entry.getColumn())) != variableInformation.statePairToIndexMap.end()) {
continue;
}
// At this point we know that the state-pair does not have an associated variable.
variableInformation.statePairToIndexMap[std::make_pair(state, entry.getColumn())] = variableInformation.statePairVariables.size();
// Clear contents of the stream to construct new expression name.
variableName.clear();
variableName.str("");
variableName << "t" << state << "_" << entry.getColumn();
variableInformation.statePairVariables.push_back(manager->declareBooleanVariable(variableName.str()));
}
}
}
}
for (auto psiState : psiStates) {
variableInformation.relevantStatesToOrderVariableIndexMap[psiState] = variableInformation.stateOrderVariables.size();
// Clear contents of the stream to construct new expression name.
variableName.clear();
variableName.str("");
variableName << "o" << psiState;
variableInformation.stateOrderVariables.push_back(manager->declareRationalVariable(variableName.str()));
}
}
return variableInformation;
}
static storm::expressions::Expression getOtherSynchronizationEnabledFormula(boost::container::flat_set<uint_fast64_t> const& labelSet, std::map<uint_fast64_t, std::set<boost::container::flat_set<uint_fast64_t>>> const& synchronizingLabels, boost::container::flat_map<boost::container::flat_set<uint_fast64_t>, storm::expressions::Expression> const& labelSetToFormula, VariableInformation const& variableInformation, RelevancyInformation const& relevancyInformation) {
// Taking all commands of a combination does not necessarily mean that a following label set needs to be taken.
// This is because it could be that the commands are taken to enable other synchronizations. Therefore, we need
// to add an additional clause that says that the right-hand side of the implication is also true if all commands
// of the current choice have enabled synchronization options.
if (labelSet.size() > 1) {
storm::expressions::Expression result = variableInformation.manager->boolean(true);
for (auto label : labelSet) {
storm::expressions::Expression alternativeExpressionForLabel = variableInformation.manager->boolean(false);
std::set<boost::container::flat_set<uint_fast64_t>> const& synchsForCommand = synchronizingLabels.at(label);
for (auto const& synchSet : synchsForCommand) {
storm::expressions::Expression alternativeExpression = variableInformation.manager->boolean(true);
// If the current synchSet is the same as left-hand side of the implication, we can to skip it.
if (synchSet == labelSet) continue;
// Build labels that are missing for this synchronization option.
std::set<uint_fast64_t> unknownSynchSetLabels;
std::set_difference(synchSet.begin(), synchSet.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(unknownSynchSetLabels, unknownSynchSetLabels.end()));
for (auto label : unknownSynchSetLabels) {
alternativeExpression = alternativeExpression && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label));
}
alternativeExpressionForLabel = alternativeExpressionForLabel || (alternativeExpression && labelSetToFormula.at(synchSet));
}
result = result && alternativeExpressionForLabel;
}
return result;
} else {
return variableInformation.manager->boolean(false);
}
}
/*!
* Asserts cuts that are derived from the explicit representation of the model and rule out a lot of
* suboptimal solutions.
*
* @param symbolicModel The symbolic model description used to build the model.
* @param model The labeled model for which to compute the cuts.
* @param context The Z3 context in which to build the expressions.
* @param solver The solver to use for the satisfiability evaluation.
*/
static void assertCuts(storm::storage::SymbolicModelDescription const& symbolicModel, storm::models::sparse::Model<T> const& model, std::vector<boost::container::flat_set<uint_fast64_t>> const& labelSets, storm::storage::BitVector const& psiStates, VariableInformation const& variableInformation, RelevancyInformation const& relevancyInformation, storm::solver::SmtSolver& solver) {
// Walk through the model and
// * identify labels enabled in initial states
// * identify labels that can directly precede a given action
// * identify labels that directly reach a target state
// * identify labels that can directly follow a given action
boost::container::flat_set<uint_fast64_t> initialLabels;
std::set<boost::container::flat_set<uint_fast64_t>> initialCombinations;
boost::container::flat_set<uint_fast64_t> targetLabels;
boost::container::flat_set<boost::container::flat_set<uint_fast64_t>> targetCombinations;
std::map<boost::container::flat_set<uint_fast64_t>, std::set<boost::container::flat_set<uint_fast64_t>>> precedingLabels;
std::map<boost::container::flat_set<uint_fast64_t>, std::set<boost::container::flat_set<uint_fast64_t>>> followingLabels;
std::map<uint_fast64_t, std::set<boost::container::flat_set<uint_fast64_t>>> synchronizingLabels;
// Get some data from the model for convenient access.
storm::storage::SparseMatrix<T> const& transitionMatrix = model.getTransitionMatrix();
storm::storage::SparseMatrix<T> backwardTransitions = model.getBackwardTransitions();
storm::storage::BitVector const& initialStates = model.getInitialStates();
for (auto currentState : relevancyInformation.relevantStates) {
for (auto currentChoice : relevancyInformation.relevantChoicesForRelevantStates.at(currentState)) {
// If the choice is a synchronization choice, we need to record it.
if (labelSets[currentChoice].size() > 1) {
for (auto label : labelSets[currentChoice]) {
synchronizingLabels[label].emplace(labelSets[currentChoice]);
}
}
// If the state is initial, we need to add all the choice labels to the initial label set.
if (initialStates.get(currentState)) {
initialLabels.insert(labelSets[currentChoice].begin(), labelSets[currentChoice].end());
initialCombinations.insert(labelSets[currentChoice]);
}
// Iterate over successors and add relevant choices of relevant successors to the following label set.
bool canReachTargetState = false;
for (auto const& entry : transitionMatrix.getRow(currentChoice)) {
if (relevancyInformation.relevantStates.get(entry.getColumn())) {
for (auto relevantChoice : relevancyInformation.relevantChoicesForRelevantStates.at(entry.getColumn())) {
if (labelSets[currentChoice] == labelSets[relevantChoice]) continue;
followingLabels[labelSets[currentChoice]].insert(labelSets[relevantChoice]);
}
} else if (psiStates.get(entry.getColumn())) {
canReachTargetState = true;
}
}
// If the choice can reach a target state directly, we add all the labels to the target label set.
if (canReachTargetState) {
targetLabels.insert(labelSets[currentChoice].begin(), labelSets[currentChoice].end());
targetCombinations.insert(labelSets[currentChoice]);
}
// Iterate over predecessors and add all choices that target the current state to the preceding
// label set of all labels of all relevant choices of the current state.
for (auto const& predecessorEntry : backwardTransitions.getRow(currentState)) {
if (relevancyInformation.relevantStates.get(predecessorEntry.getColumn())) {
for (auto predecessorChoice : relevancyInformation.relevantChoicesForRelevantStates.at(predecessorEntry.getColumn())) {
bool choiceTargetsCurrentState = false;
for (auto const& successorEntry : transitionMatrix.getRow(predecessorChoice)) {
if (successorEntry.getColumn() == currentState) {
choiceTargetsCurrentState = true;
}
}
if (choiceTargetsCurrentState) {
precedingLabels[labelSets.at(currentChoice)].insert(labelSets.at(predecessorChoice));
}
}
}
}
}
}
// Store the found implications in a container similar to the preceding label sets.
std::map<boost::container::flat_set<uint_fast64_t>, std::set<boost::container::flat_set<uint_fast64_t>>> backwardImplications;
if (!symbolicModel.isJaniModel() || !symbolicModel.asJaniModel().usesAssignmentLevels()) {
// Create a new solver over the same variables as the given symbolic model description to use it for
// determining the symbolic cuts.
std::unique_ptr<storm::solver::SmtSolver> localSolver;
if (symbolicModel.isPrismProgram()) {
storm::prism::Program const& program = symbolicModel.asPrismProgram();
localSolver = std::make_unique<storm::solver::Z3SmtSolver>(program.getManager());
// Then add the constraints for bounds of the integer variables.
for (auto const& integerVariable : program.getGlobalIntegerVariables()) {
localSolver->add(integerVariable.getExpressionVariable() >= integerVariable.getLowerBoundExpression());
localSolver->add(integerVariable.getExpressionVariable() <= integerVariable.getUpperBoundExpression());
}
for (auto const& module : program.getModules()) {
for (auto const& integerVariable : module.getIntegerVariables()) {
localSolver->add(integerVariable.getExpressionVariable() >= integerVariable.getLowerBoundExpression());
localSolver->add(integerVariable.getExpressionVariable() <= integerVariable.getUpperBoundExpression());
}
}
} else {
storm::jani::Model const& janiModel = symbolicModel.asJaniModel();
localSolver = std::make_unique<storm::solver::Z3SmtSolver>(janiModel.getManager());
for (auto const& integerVariable : janiModel.getGlobalVariables().getBoundedIntegerVariables()) {
if (integerVariable.isTransient()) {
continue;
}
localSolver->add(integerVariable.getExpressionVariable() >= integerVariable.getLowerBound());
localSolver->add(integerVariable.getExpressionVariable() <= integerVariable.getUpperBound());
}
for (auto const& automaton : janiModel.getAutomata()) {
for (auto const& integerVariable : automaton.getVariables().getBoundedIntegerVariables()) {
if (integerVariable.isTransient()) {
continue;
}
localSolver->add(integerVariable.getExpressionVariable() >= integerVariable.getLowerBound());
localSolver->add(integerVariable.getExpressionVariable() <= integerVariable.getUpperBound());
}
}
}
// Construct an expression that exactly characterizes the initial state.
storm::expressions::Expression initialStateExpression;
if (symbolicModel.isPrismProgram()) {
initialStateExpression = symbolicModel.asPrismProgram().getInitialStatesExpression();
} else {
initialStateExpression = symbolicModel.asJaniModel().getInitialStatesExpression();
}
// Now check for possible backward cuts.
for (auto const& labelSetAndPrecedingLabelSetsPair : precedingLabels) {
bool backwardImplicationAdded = false;
// std::cout << "labelSetAndPrecedingLabelSetsPair.first ";
// for (auto const& e : labelSetAndPrecedingLabelSetsPair.first) {
// std::cout << e << ", ";
// }
// std::cout << std::endl;
// Find out the commands for the currently considered label set.
storm::expressions::Expression guardConjunction;
if (symbolicModel.isPrismProgram()) {
storm::prism::Program const& program = symbolicModel.asPrismProgram();
for (uint_fast64_t moduleIndex = 0; moduleIndex < program.getNumberOfModules(); ++moduleIndex) {
storm::prism::Module const& module = program.getModule(moduleIndex);
for (uint_fast64_t commandIndex = 0; commandIndex < module.getNumberOfCommands(); ++commandIndex) {
storm::prism::Command const& command = module.getCommand(commandIndex);
// If the current command is one of the commands we need to consider, add its guard.
if (labelSetAndPrecedingLabelSetsPair.first.find(command.getGlobalIndex()) != labelSetAndPrecedingLabelSetsPair.first.end()) {
guardConjunction = guardConjunction && command.getGuardExpression();
}
}
}
} else {
storm::jani::Model const& janiModel = symbolicModel.asJaniModel();
for (uint_fast64_t automatonIndex = 0; automatonIndex < janiModel.getNumberOfAutomata(); ++automatonIndex) {
storm::jani::Automaton const& automaton = janiModel.getAutomaton(automatonIndex);
for (uint_fast64_t edgeIndex = 0; edgeIndex < automaton.getNumberOfEdges(); ++edgeIndex) {
// If the current edge is one of the edges we need to consider, add its guard.
if (labelSetAndPrecedingLabelSetsPair.first.find(janiModel.encodeAutomatonAndEdgeIndices(automatonIndex, edgeIndex)) != labelSetAndPrecedingLabelSetsPair.first.end()) {
storm::jani::Edge const& edge = automaton.getEdge(edgeIndex);
guardConjunction = guardConjunction && edge.getGuard();
}
}
}
}
// Save the state of the solver so we can easily backtrack.
localSolver->push();
// Push initial state expression.
STORM_LOG_DEBUG("About to assert that combination is not enabled in the current state.");
localSolver->add(initialStateExpression);
// Check if the label set is enabled in the initial state.
localSolver->add(guardConjunction);
storm::solver::SmtSolver::CheckResult checkResult = localSolver->check();
localSolver->pop();
localSolver->push();
// If the solver reports unsat, then we know that the current selection is not enabled in the initial state.
if (checkResult == storm::solver::SmtSolver::CheckResult::Unsat) {
STORM_LOG_DEBUG("Selection not enabled in initial state.");
//std::cout << "not gc: " << !guardConjunction << std::endl;
localSolver->add(!guardConjunction);
STORM_LOG_DEBUG("Asserted disjunction of negated guards.");
// Now check the possible preceding label sets for the essential ones.
for (auto const& precedingLabelSet : labelSetAndPrecedingLabelSetsPair.second) {
if (labelSetAndPrecedingLabelSetsPair.first == precedingLabelSet) continue;
//std::cout << "push" << std::endl;
// Create a restore point so we can easily pop-off all weakest precondition expressions.
localSolver->push();
// Find out the commands for the currently considered preceding label set.
std::vector<std::vector<boost::container::flat_map<storm::expressions::Variable, storm::expressions::Expression>>> currentPreceedingVariableUpdates;
storm::expressions::Expression preceedingGuardConjunction;
if (symbolicModel.isPrismProgram()) {
storm::prism::Program const& program = symbolicModel.asPrismProgram();
for (uint_fast64_t moduleIndex = 0; moduleIndex < program.getNumberOfModules(); ++moduleIndex) {
storm::prism::Module const& module = program.getModule(moduleIndex);
for (uint_fast64_t commandIndex = 0; commandIndex < module.getNumberOfCommands(); ++commandIndex) {
storm::prism::Command const& command = module.getCommand(commandIndex);
// If the current command is one of the commands we need to consider, store a reference to it in the container.
if (precedingLabelSet.find(command.getGlobalIndex()) != precedingLabelSet.end()) {
preceedingGuardConjunction = preceedingGuardConjunction && command.getGuardExpression();
currentPreceedingVariableUpdates.emplace_back();
for (uint64_t updateIndex = 0; updateIndex < command.getNumberOfUpdates(); ++updateIndex) {
storm::prism::Update const& update = command.getUpdate(updateIndex);
boost::container::flat_map<storm::expressions::Variable, storm::expressions::Expression> variableUpdates;
for (auto const& assignment : update.getAssignments()) {
variableUpdates.emplace(assignment.getVariable(), assignment.getExpression());
}
currentPreceedingVariableUpdates.back().emplace_back(std::move(variableUpdates));
}
}
}
}
} else {
storm::jani::Model const& janiModel = symbolicModel.asJaniModel();
for (uint_fast64_t automatonIndex = 0; automatonIndex < janiModel.getNumberOfAutomata(); ++automatonIndex) {
storm::jani::Automaton const& automaton = janiModel.getAutomaton(automatonIndex);
for (uint_fast64_t edgeIndex = 0; edgeIndex < automaton.getNumberOfEdges(); ++edgeIndex) {
// If the current command is one of the commands we need to consider, store a reference to it in the container.
if (precedingLabelSet.find(janiModel.encodeAutomatonAndEdgeIndices(automatonIndex, edgeIndex)) != precedingLabelSet.end()) {
storm::jani::Edge const& edge = automaton.getEdge(edgeIndex);
preceedingGuardConjunction = preceedingGuardConjunction && edge.getGuard();
currentPreceedingVariableUpdates.emplace_back();
for (uint64_t destinationIndex = 0; destinationIndex < edge.getNumberOfDestinations(); ++destinationIndex) {
storm::jani::EdgeDestination const& destination = edge.getDestination(destinationIndex);
boost::container::flat_map<storm::expressions::Variable, storm::expressions::Expression> variableUpdates;
for (auto const& assignment : destination.getOrderedAssignments().getNonTransientAssignments()) {
variableUpdates.emplace(assignment.getVariable().getExpressionVariable(), assignment.getAssignedExpression());
}
currentPreceedingVariableUpdates.back().emplace_back(std::move(variableUpdates));
}
}
}
}
}
//std::cout << "pgc: " << preceedingGuardConjunction << std::endl;
// Assert all the guards of the preceding command set.
localSolver->add(preceedingGuardConjunction);
std::vector<std::vector<boost::container::flat_map<storm::expressions::Variable, storm::expressions::Expression>>::const_iterator> iteratorVector;
for (auto const& variableUpdates : currentPreceedingVariableUpdates) {
iteratorVector.push_back(variableUpdates.begin());
}
// Iterate over all possible combinations of updates of the preceding command set.
std::vector<storm::expressions::Expression> formulae;
bool done = false;
while (!done) {
std::map<storm::expressions::Variable, storm::expressions::Expression> currentVariableUpdateCombinationMap;
for (auto const& updateIterator : iteratorVector) {
for (auto const& variableUpdatePair : *updateIterator) {
currentVariableUpdateCombinationMap.emplace(variableUpdatePair.first, variableUpdatePair.second);
}
}
STORM_LOG_DEBUG("About to assert a weakest precondition.");
storm::expressions::Expression wp = guardConjunction.substitute(currentVariableUpdateCombinationMap);
formulae.push_back(wp);
STORM_LOG_DEBUG("Asserted weakest precondition.");
// Now try to move iterators to the next position if possible. If we could properly
// move it, we can directly move on to the next combination of updates. If we have
// to reset it to the start, we do so unless there is no more iterator to reset.
uint_fast64_t k = iteratorVector.size();
for (; k > 0; --k) {
++iteratorVector[k - 1];
if (iteratorVector[k - 1] == currentPreceedingVariableUpdates[k - 1].end()) {
iteratorVector[k - 1] = currentPreceedingVariableUpdates[k - 1].begin();
} else {
break;
}
}
// If we had to reset all iterator to the start, we are done.
if (k == 0) {
done = true;
}
}
// Now assert the disjunction of all weakest preconditions of all considered update combinations.
assertDisjunction(*localSolver, formulae, symbolicModel.isPrismProgram() ? symbolicModel.asPrismProgram().getManager() : symbolicModel.asJaniModel().getManager());
STORM_LOG_DEBUG("Asserted disjunction of all weakest preconditions.");
storm::solver::SmtSolver::CheckResult result = localSolver->check();
if (result == storm::solver::SmtSolver::CheckResult::Sat) {
backwardImplications[labelSetAndPrecedingLabelSetsPair.first].insert(precedingLabelSet);
backwardImplicationAdded = true;
} else if (result == storm::solver::SmtSolver::CheckResult::Unknown) {
STORM_LOG_ERROR("The SMT solver does not come to a conclusive answer. Does your model contain integer division?");
}
localSolver->pop();
}
// Popping the disjunction of negated guards from the solver stack.
localSolver->pop();
STORM_LOG_ERROR_COND(backwardImplicationAdded, "Error in adding cuts for counterexample generation (backward implication misses a label set).");
} else {
STORM_LOG_DEBUG("Selection is enabled in initial state.");
}
}
} else if (symbolicModel.isJaniModel()) {
STORM_LOG_WARN("Model uses assignment levels, did not assert backward implications.");
}
STORM_LOG_DEBUG("Successfully gathered data for cuts.");
// Compute the sets of labels such that the transitions labeled with this set possess at least one known label.
boost::container::flat_set<boost::container::flat_set<uint_fast64_t>> hasKnownSuccessor;
for (auto const& labelSetFollowingSetsPair : followingLabels) {
for (auto const& set : labelSetFollowingSetsPair.second) {
if (std::includes(relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), set.begin(), set.end())) {
hasKnownSuccessor.insert(set);
break;
}
}
}
// Compute the sets of labels such that the transitions labeled with this set possess at least one known predecessor.
boost::container::flat_set<boost::container::flat_set<uint_fast64_t>> hasKnownPredecessor;
for (auto const& labelSetImplicationsPair : backwardImplications) {
for (auto const& set : labelSetImplicationsPair.second) {
if (std::includes(relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), set.begin(), set.end())) {
hasKnownPredecessor.insert(labelSetImplicationsPair.first);
break;
}
}
}
STORM_LOG_DEBUG("Asserting initial combination is taken.");
{
std::vector<storm::expressions::Expression> formulae;
// Start by asserting that we take at least one initial label. We may do so only if there is no initial
// combination that is already known. Otherwise this condition would be too strong.
bool initialCombinationKnown = false;
for (auto const& combination : initialCombinations) {
boost::container::flat_set<uint_fast64_t> tmpSet;
std::set_difference(combination.begin(), combination.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(tmpSet, tmpSet.end()));
if (tmpSet.size() == 0) {
initialCombinationKnown = true;
break;
} else {
storm::expressions::Expression conj = variableInformation.manager->boolean(true);
for (auto label : tmpSet) {
conj = conj && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label));
}
formulae.push_back(conj);
}
}
if (!initialCombinationKnown) {
assertDisjunction(solver, formulae, *variableInformation.manager);
}
}
STORM_LOG_DEBUG("Asserting target combination is taken.");
{
std::vector<storm::expressions::Expression> formulae;
// Likewise, if no target combination is known, we may assert that there is at least one.
bool targetCombinationKnown = false;
for (auto const& combination : targetCombinations) {
boost::container::flat_set<uint_fast64_t> tmpSet;
std::set_difference(combination.begin(), combination.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(tmpSet, tmpSet.end()));
if (tmpSet.size() == 0) {
targetCombinationKnown = true;
break;
} else {
storm::expressions::Expression conj = variableInformation.manager->boolean(true);
for (auto label : tmpSet) {
conj = conj && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label));
}
formulae.push_back(conj);
}
}
if (!targetCombinationKnown) {
assertDisjunction(solver, formulae, *variableInformation.manager);
}
}
STORM_LOG_DEBUG("Asserting taken labels are followed and preceeded by another label if they are not a target label or an initial label, respectively.");
boost::container::flat_map<boost::container::flat_set<uint_fast64_t>, storm::expressions::Expression> labelSetToFormula;
for (auto const& labelSet : relevancyInformation.relevantLabelSets) {
storm::expressions::Expression labelSetFormula = variableInformation.manager->boolean(false);
// Compute the set of unknown labels on the left-hand side of the implication.
boost::container::flat_set<uint_fast64_t> unknownLhsLabels;
std::set_difference(labelSet.begin(), labelSet.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(unknownLhsLabels, unknownLhsLabels.end()));
for (auto label : unknownLhsLabels) {
labelSetFormula = labelSetFormula || !variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label));
}
// Only build a constraint if the combination does not lead to a target state and
// no successor set is already known.
storm::expressions::Expression successorExpression;
if (targetCombinations.find(labelSet) == targetCombinations.end() && hasKnownSuccessor.find(labelSet) == hasKnownSuccessor.end()) {
successorExpression = variableInformation.manager->boolean(false);
auto const& followingLabelSets = followingLabels.at(labelSet);
for (auto const& followingSet : followingLabelSets) {
boost::container::flat_set<uint_fast64_t> tmpSet;
// Check which labels of the current following set are not known. This set must be non-empty, because
// otherwise a successor combination would already be known and control cannot reach this point.
std::set_difference(followingSet.begin(), followingSet.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(tmpSet, tmpSet.end()));
// Construct an expression that enables all unknown labels of the current following set.
storm::expressions::Expression conj = variableInformation.manager->boolean(true);
for (auto label : tmpSet) {
conj = conj && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label));
}
successorExpression = successorExpression || conj;
}
} else {
successorExpression = variableInformation.manager->boolean(true);
}
// Constructed following cuts at this point.
// Only build a constraint if the combination is no initial combination and no
// predecessor set is already known.
storm::expressions::Expression predecessorExpression;
if (initialCombinations.find(labelSet) == initialCombinations.end() && hasKnownPredecessor.find(labelSet) == hasKnownPredecessor.end()) {
predecessorExpression = variableInformation.manager->boolean(false);
// std::cout << "labelSet" << std::endl;
// for (auto const& e : labelSet) {
// std::cout << e << ", ";
// }
// std::cout << std::endl;
auto const& preceedingLabelSets = backwardImplications.at(labelSet);
for (auto const& preceedingSet : preceedingLabelSets) {
boost::container::flat_set<uint_fast64_t> tmpSet;
// Check which labels of the current following set are not known. This set must be non-empty, because
// otherwise a predecessor combination would already be known and control cannot reach this point.
std::set_difference(preceedingSet.begin(), preceedingSet.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(tmpSet, tmpSet.end()));
// Construct an expression that enables all unknown labels of the current following set.
storm::expressions::Expression conj = variableInformation.manager->boolean(true);
for (auto label : tmpSet) {
conj = conj && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label));
}
predecessorExpression = predecessorExpression || conj;
}
} else {
predecessorExpression = variableInformation.manager->boolean(true);
}
labelSetFormula = labelSetFormula || (successorExpression && predecessorExpression);
labelSetToFormula[labelSet] = labelSetFormula;
}
for (auto const& labelSetFormula : labelSetToFormula) {
solver.add(labelSetFormula.second || getOtherSynchronizationEnabledFormula(labelSetFormula.first, synchronizingLabels, labelSetToFormula, variableInformation, relevancyInformation));
}
STORM_LOG_DEBUG("Asserting synchronization cuts.");
// Finally, assert that if we take one of the synchronizing labels, we also take one of the combinations
// the label appears in.
for (auto const& labelSynchronizingSetsPair : synchronizingLabels) {
std::vector<storm::expressions::Expression> formulae;
if (relevancyInformation.knownLabels.find(labelSynchronizingSetsPair.first) == relevancyInformation.knownLabels.end()) {
formulae.push_back(!variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(labelSynchronizingSetsPair.first)));
}
// We need to be careful, because there may be one synchronisation set out of which all labels are
// known, which means we must not assert anything.
bool allImplicantsKnownForOneSet = false;
for (auto const& synchronizingSet : labelSynchronizingSetsPair.second) {
storm::expressions::Expression currentCombination = variableInformation.manager->boolean(true);
bool allImplicantsKnownForCurrentSet = true;
for (auto label : synchronizingSet) {
if (relevancyInformation.knownLabels.find(label) == relevancyInformation.knownLabels.end() && label != labelSynchronizingSetsPair.first) {
currentCombination = currentCombination && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label));
}
}
formulae.push_back(currentCombination);
// If all implicants of the current set are known, we do not need to further build the constraint.
if (allImplicantsKnownForCurrentSet) {
allImplicantsKnownForOneSet = true;
break;
}
}
if (!allImplicantsKnownForOneSet) {
assertDisjunction(solver, formulae, *variableInformation.manager);
}
}
}
/*!
* Asserts constraints necessary to encode the reachability of at least one target state from the initial states.
*/
static void assertReachabilityCuts(storm::models::sparse::Model<T> const& model, std::vector<boost::container::flat_set<uint_fast64_t>> const& labelSets, storm::storage::BitVector const& psiStates, VariableInformation const& variableInformation, RelevancyInformation const& relevancyInformation, storm::solver::SmtSolver& solver) {
if (!variableInformation.hasReachabilityVariables) {
throw storm::exceptions::InvalidStateException() << "Impossible to assert reachability cuts without the necessary variables.";
}
// Get some data from the model for convenient access.
storm::storage::SparseMatrix<T> const& transitionMatrix = model.getTransitionMatrix();
storm::storage::SparseMatrix<T> backwardTransitions = model.getBackwardTransitions();
// First, we add the formulas that encode
// (1) if an incoming transition is chosen, an outgoing one is chosen as well (for non-initial states)
// (2) an outgoing transition out of the initial states is taken.
storm::expressions::Expression initialStateExpression = variableInformation.manager->boolean(false);
for (auto relevantState : relevancyInformation.relevantStates) {
if (!model.getInitialStates().get(relevantState)) {
// Assert the constraints (1).
boost::container::flat_set<uint_fast64_t> relevantPredecessors;
for (auto const& predecessorEntry : backwardTransitions.getRow(relevantState)) {
if (relevantState != predecessorEntry.getColumn() && relevancyInformation.relevantStates.get(predecessorEntry.getColumn())) {
relevantPredecessors.insert(predecessorEntry.getColumn());
}
}
boost::container::flat_set<uint_fast64_t> relevantSuccessors;
for (auto const& relevantChoice : relevancyInformation.relevantChoicesForRelevantStates.at(relevantState)) {
for (auto const& successorEntry : transitionMatrix.getRow(relevantChoice)) {
if (relevantState != successorEntry.getColumn() && (relevancyInformation.relevantStates.get(successorEntry.getColumn()) || psiStates.get(successorEntry.getColumn()))) {
relevantSuccessors.insert(successorEntry.getColumn());
}
}
}
storm::expressions::Expression expression = variableInformation.manager->boolean(true);
for (auto predecessor : relevantPredecessors) {
expression = expression && !variableInformation.statePairVariables.at(variableInformation.statePairToIndexMap.at(std::make_pair(predecessor, relevantState)));
}
for (auto successor : relevantSuccessors) {
expression = expression || variableInformation.statePairVariables.at(variableInformation.statePairToIndexMap.at(std::make_pair(relevantState, successor)));
}
solver.add(expression);
} else {
// Assert the constraints (2).
boost::container::flat_set<uint_fast64_t> relevantSuccessors;
for (auto const& relevantChoice : relevancyInformation.relevantChoicesForRelevantStates.at(relevantState)) {
for (auto const& successorEntry : transitionMatrix.getRow(relevantChoice)) {
if (relevantState != successorEntry.getColumn() && (relevancyInformation.relevantStates.get(successorEntry.getColumn()) || psiStates.get(successorEntry.getColumn()))) {
relevantSuccessors.insert(successorEntry.getColumn());
}
}
}
for (auto successor : relevantSuccessors) {
initialStateExpression = initialStateExpression || variableInformation.statePairVariables.at(variableInformation.statePairToIndexMap.at(std::make_pair(relevantState, successor)));
}
}
}
solver.add(initialStateExpression);
// Finally, add constraints that
// (1) if a transition is selected, a valid labeling is selected as well.
// (2) enforce that if a transition from s to s' is selected, the ordering variables become strictly larger.
for (auto const& statePairIndexPair : variableInformation.statePairToIndexMap) {
uint_fast64_t sourceState = statePairIndexPair.first.first;
uint_fast64_t targetState = statePairIndexPair.first.second;
// Assert constraint for (1).
boost::container::flat_set<uint_fast64_t> choicesForStatePair;
for (auto const& relevantChoice : relevancyInformation.relevantChoicesForRelevantStates.at(sourceState)) {
for (auto const& successorEntry : transitionMatrix.getRow(relevantChoice)) {
if (successorEntry.getColumn() == targetState) {
choicesForStatePair.insert(relevantChoice);
}
}
}
storm::expressions::Expression labelExpression = !variableInformation.statePairVariables.at(statePairIndexPair.second);
for (auto choice : choicesForStatePair) {
storm::expressions::Expression choiceExpression = variableInformation.manager->boolean(true);
for (auto element : labelSets.at(choice)) {
if (relevancyInformation.knownLabels.find(element) == relevancyInformation.knownLabels.end()) {
choiceExpression = choiceExpression && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(element));
}
}
labelExpression = labelExpression || choiceExpression;
}
solver.add(labelExpression);
// Assert constraint for (2).
storm::expressions::Expression orderExpression = !variableInformation.statePairVariables.at(statePairIndexPair.second) || variableInformation.stateOrderVariables.at(variableInformation.relevantStatesToOrderVariableIndexMap.at(sourceState)).getExpression() < variableInformation.stateOrderVariables.at(variableInformation.relevantStatesToOrderVariableIndexMap.at(targetState)).getExpression();
solver.add(orderExpression);
}
}
/*!
* Asserts that the disjunction of the given formulae holds. If the content of the disjunction is empty,
* this corresponds to asserting false.
*
* @param solver The solver to use for the satisfiability evaluation.
* @param formulaVector A vector of expressions that shall form the disjunction.
* @param manager The expression manager to use.
*/
static void assertDisjunction(storm::solver::SmtSolver& solver, std::vector<storm::expressions::Expression> const& formulaVector, storm::expressions::ExpressionManager const& manager) {
storm::expressions::Expression disjunction = manager.boolean(false);
for (auto expr : formulaVector) {
disjunction = disjunction || expr;
}
solver.add(disjunction);
}
/*!
* Creates a full-adder for the two inputs and returns the resulting bit as well as the carry bit.
*
* @param in1 The first input to the adder.
* @param in2 The second input to the adder.
* @param carryIn The carry bit input to the adder.
* @return A pair whose first component represents the carry bit and whose second component represents the
* result bit.
*/
static std::pair<storm::expressions::Expression, storm::expressions::Expression> createFullAdder(storm::expressions::Expression in1, storm::expressions::Expression in2, storm::expressions::Expression carryIn) {
storm::expressions::Expression resultBit;
storm::expressions::Expression carryBit;
if (carryIn.isFalse()) {
resultBit = (in1 && !in2) || (!in1 && in2);
carryBit = in1 && in2;
} else {
resultBit = (in1 && !in2 && !carryIn) || (!in1 && in2 && !carryIn) || (!in1 && !in2 && carryIn) || (in1 && in2 && carryIn);
carryBit = in1 && in2 || in1 && carryIn || in2 && carryIn;
}
return std::make_pair(carryBit, resultBit);
}
/*!
* Creates an adder for the two inputs of equal size. The resulting vector represents the different bits of
* the sum (and is thus one bit longer than the two inputs).
*
* @param variableInformation The variable information structure.
* @param in1 The first input to the adder.
* @param in2 The second input to the adder.
* @return A vector representing the bits of the sum of the two inputs.
*/
static std::vector<storm::expressions::Expression> createAdder(VariableInformation const& variableInformation, std::vector<storm::expressions::Expression> const& in1, std::vector<storm::expressions::Expression> const& in2) {
// Sanity check for sizes of input.
if (in1.size() != in2.size() || in1.size() == 0) {
STORM_LOG_ERROR("Illegal input to adder (" << in1.size() << ", " << in2.size() << ").");
throw storm::exceptions::InvalidArgumentException() << "Illegal input to adder.";
}
// Prepare result.
std::vector<storm::expressions::Expression> result;
result.reserve(in1.size() + 1);
// Add all bits individually and pass on carry bit appropriately.
storm::expressions::Expression carryBit = variableInformation.manager->boolean(false);
for (uint_fast64_t currentBit = 0; currentBit < in1.size(); ++currentBit) {
std::pair<storm::expressions::Expression, storm::expressions::Expression> localResult = createFullAdder(in1[currentBit], in2[currentBit], carryBit);
result.push_back(localResult.second);
carryBit = localResult.first;
}
result.push_back(carryBit);
return result;
}
/*!
* Given a number of input numbers, creates a number of output numbers that corresponds to the sum of two
* consecutive numbers of the input. If the number if input numbers is odd, the last number is simply added
* to the output.
*
* @param variableInformation The variable information structure.
* @param in A vector or binary encoded numbers.
* @return A vector of numbers that each correspond to the sum of two consecutive elements of the input.
*/
static std::vector<std::vector<storm::expressions::Expression>> createAdderPairs(VariableInformation const& variableInformation, std::vector<std::vector<storm::expressions::Expression>> const& in) {
std::vector<std::vector<storm::expressions::Expression>> result;
result.reserve(in.size() / 2 + in.size() % 2);
for (uint_fast64_t index = 0; index < in.size() / 2; ++index) {
result.push_back(createAdder(variableInformation, in[2 * index], in[2 * index + 1]));
}
if (in.size() % 2 != 0) {
result.push_back(in.back());
result.back().push_back(variableInformation.manager->boolean(false));
}
return result;
}
/*!
* Creates a counter circuit that returns the number of literals out of the given vector that are set to true.
*
* @param variableInformation The variable information structure.
* @param literals The literals for which to create the adder circuit.
* @return A bit vector representing the number of literals that are set to true.
*/
static std::vector<storm::expressions::Expression> createCounterCircuit(VariableInformation const& variableInformation, std::vector<storm::expressions::Variable> const& literals) {
if (literals.empty()) {
return std::vector<storm::expressions::Expression>();
}
// Create the auxiliary vector.
std::vector<std::vector<storm::expressions::Expression>> aux;
for (uint_fast64_t index = 0; index < literals.size(); ++index) {
aux.emplace_back();
aux.back().push_back(literals[index]);
}
while (aux.size() > 1) {
aux = createAdderPairs(variableInformation, aux);
}
STORM_LOG_DEBUG("Created counter circuit for " << literals.size() << " literals.");
return aux.front();
}
/*!
* Determines whether the bit at the given index is set in the given value.
*
* @param value The value to test.
* @param index The index of the bit to test.
* @return True iff the bit at the given index is set in the given value.
*/
static bool bitIsSet(uint64_t value, uint64_t index) {
uint64_t mask = 1 << (index & 63);
return (value & mask) != 0;
}
/*!
* Asserts a constraint in the given solver that expresses that the value encoded by the given input variables
* may at most represent the number k. The constraint is associated with a relaxation variable, that is
* returned by this function and may be used to deactivate the constraint.
*
* @param solver The solver to use for the satisfiability evaluation.
* @param variableInformation The struct that holds the variable information.
* @param k The bound for the binary-encoded value.
* @return The relaxation variable associated with the constraint.
*/
static storm::expressions::Variable assertLessOrEqualKRelaxed(storm::solver::SmtSolver& solver, VariableInformation const& variableInformation, uint64_t k) {
STORM_LOG_DEBUG("Asserting solution has size less or equal " << k << ".");
std::vector<storm::expressions::Variable> const& input = variableInformation.adderVariables;
// If there are no input variables, the value is always 0 <= k, so there is nothing to assert.
if (input.empty()) {
std::stringstream variableName;
variableName << "relaxed" << k;
return variableInformation.manager->declareBooleanVariable(variableName.str());
}
storm::expressions::Expression result;
if (bitIsSet(k, 0)) {
result = variableInformation.manager->boolean(true);
} else {
result = !input.at(0);
}
for (uint_fast64_t index = 1; index < input.size(); ++index) {
storm::expressions::Expression i1;
storm::expressions::Expression i2;
if (bitIsSet(k, index)) {
i1 = !input.at(index);
i2 = result;
} else {
i1 = variableInformation.manager->boolean(false);
i2 = variableInformation.manager->boolean(false);
}
result = i1 || i2 || (!input.at(index) && result);
}
std::stringstream variableName;
variableName << "relaxed" << k;
storm::expressions::Variable relaxingVariable = variableInformation.manager->declareBooleanVariable(variableName.str());
result = result || relaxingVariable;
solver.add(result);
return relaxingVariable;
}
/*!
* Determines the set of labels that was chosen by the given model.
*
* @param model The model from which to extract the information.
* @param variableInformation A structure with information about the variables of the solver.
*/
static boost::container::flat_set<uint_fast64_t> getUsedLabelSet(storm::solver::SmtSolver::ModelReference const& model, VariableInformation const& variableInformation) {
boost::container::flat_set<uint_fast64_t> result;
for (auto const& labelIndexPair : variableInformation.labelToIndexMap) {
bool commandIncluded = model.getBooleanValue(variableInformation.labelVariables.at(labelIndexPair.second));
if (commandIncluded) {
result.insert(labelIndexPair.first);
}
}
return result;
}
/*!
* Asserts an adder structure in the given solver that counts the number of variables that are set to true
* out of the given variables.
*
* @param solver The solver for which to add the adder.
* @param variableInformation A structure with information about the variables of the solver.
*/
static std::vector<storm::expressions::Variable> assertAdder(storm::solver::SmtSolver& solver, VariableInformation const& variableInformation) {
auto start = std::chrono::high_resolution_clock::now();
std::stringstream variableName;
std::vector<storm::expressions::Variable> result;
std::vector<storm::expressions::Expression> adderVariables = createCounterCircuit(variableInformation, variableInformation.minimalityLabelVariables);
for (uint_fast64_t i = 0; i < adderVariables.size(); ++i) {
variableName.str("");
variableName.clear();
variableName << "adder" << i;
result.push_back(variableInformation.manager->declareBooleanVariable(variableName.str()));
solver.add(storm::expressions::implies(adderVariables[i], result.back()));
STORM_LOG_TRACE("Added bit " << i << " of adder.");
}
auto end = std::chrono::high_resolution_clock::now();
uint64_t duration = std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count();
STORM_LOG_DEBUG("Asserted adder in " << duration << "ms.");
return result;
}
/*!
* Finds the smallest set of labels such that the constraint system of the solver is still satisfiable.
*
* @param solver The solver to use for the satisfiability evaluation.
* @param variableInformation A structure with information about the variables of the solver.
* @param currentBound The currently known lower bound for the number of labels that need to be enabled
* in order to satisfy the constraint system.
* @return The smallest set of labels such that the constraint system of the solver is satisfiable.
*/
static boost::optional<boost::container::flat_set<uint_fast64_t>> findSmallestCommandSet(storm::solver::SmtSolver& solver, VariableInformation& variableInformation, uint_fast64_t& currentBound) {
// Check if we can find a solution with the current bound.
storm::expressions::Expression assumption = !variableInformation.auxiliaryVariables.back();
// As long as the constraints are unsatisfiable, we need to relax the last at-most-k constraint and
// try with an increased bound.
while (solver.checkWithAssumptions({assumption}) == storm::solver::SmtSolver::CheckResult::Unsat) {
STORM_LOG_DEBUG("Constraint system is unsatisfiable with at most " << currentBound << " taken commands; increasing bound.");
#ifndef NDEBUG
STORM_LOG_DEBUG("Sanity check to see whether constraint system is still satisfiable.");
STORM_LOG_ASSERT(solver.check() == storm::solver::SmtSolver::CheckResult::Sat, "Constraint system is not satisfiable anymore.");
#endif
solver.add(variableInformation.auxiliaryVariables.back());
variableInformation.auxiliaryVariables.push_back(assertLessOrEqualKRelaxed(solver, variableInformation, ++currentBound));
assumption = !variableInformation.auxiliaryVariables.back();
if (currentBound > variableInformation.minimalityLabelVariables.size()) {
STORM_LOG_DEBUG("Constraint system fully explored: Bound exceeds maximum of " << variableInformation.minimalityLabelVariables.size());
return boost::none;
}
}
// At this point we know that the constraint system was satisfiable, so compute the induced label
// set and return it.
return getUsedLabelSet(*solver.getModel(), variableInformation);
}
static void ruleOutSingleSolution(storm::solver::SmtSolver& solver, boost::container::flat_set<uint_fast64_t> const& labelSet, VariableInformation& variableInformation, RelevancyInformation const& relevancyInformation) {
std::vector<storm::expressions::Expression> formulae;
boost::container::flat_set<uint_fast64_t> unknownLabels;
std::set_intersection(labelSet.begin(), labelSet.end(), relevancyInformation.minimalityLabels.begin(), relevancyInformation.minimalityLabels.end(), std::inserter(unknownLabels, unknownLabels.end()));
//std::set_difference(labelSet.begin(), labelSet.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(unknownLabels, unknownLabels.end()));
for (auto const& label : unknownLabels) {
formulae.emplace_back(!variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label)));
}
boost::container::flat_set<uint_fast64_t> remainingLabels;
//std::set_difference(relevancyInformation.relevantLabels.begin(), relevancyInformation.relevantLabels.end(), labelSet.begin(), labelSet.end(), std::inserter(remainingLabels, remainingLabels.end()));
std::set_difference(relevancyInformation.minimalityLabels.begin(), relevancyInformation.minimalityLabels.end(), labelSet.begin(), labelSet.end(), std::inserter(remainingLabels, remainingLabels.end()));
for (auto const& label : remainingLabels) {
formulae.emplace_back(variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label)));
}
STORM_LOG_DEBUG("Ruling out single solution.");
assertDisjunction(solver, formulae, *variableInformation.manager);
}
static void ruleOutBiggerSolutions(storm::solver::SmtSolver& solver, boost::container::flat_set<uint_fast64_t> const& labelSet, VariableInformation& variableInformation, RelevancyInformation const& relevancyInformation) {
std::vector<storm::expressions::Expression> formulae;
boost::container::flat_set<uint_fast64_t> unknownLabels;
std::set_intersection(labelSet.begin(), labelSet.end(), relevancyInformation.minimalityLabels.begin(), relevancyInformation.minimalityLabels.end(), std::inserter(unknownLabels, unknownLabels.end()));
//std::set_difference(labelSet.begin(), labelSet.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(unknownLabels, unknownLabels.end()));
for (auto const& label : unknownLabels) {
formulae.emplace_back(!variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label)));
}
STORM_LOG_DEBUG("Ruling out set of solutions.");
assertDisjunction(solver, formulae, *variableInformation.manager);
}
/*!
* Analyzes the given sub-model that has a maximal reachability of zero (i.e. no psi states are reachable) and tries to construct assertions that aim to make at least one psi state reachable.
*
* @param solver The solver to use for the satisfiability evaluation.
* @param subModel The sub-model resulting from restricting the original model to the given command set.
* @param originalModel The original model.
* @param phiStates A bit vector characterizing all phi states in the model.
* @param psiState A bit vector characterizing all psi states in the model.
* @param commandSet The currently chosen set of commands.
* @param variableInformation A structure with information about the variables of the solver.
*/
static void analyzeZeroProbabilitySolution(storm::solver::SmtSolver& solver, storm::models::sparse::Model<T> const& subModel, std::vector<boost::container::flat_set<uint_fast64_t>> const& subLabelSets, storm::models::sparse::Model<T> const& originalModel, std::vector<boost::container::flat_set<uint_fast64_t>> const& originalLabelSets, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, boost::container::flat_set<uint_fast64_t> const& commandSet, VariableInformation& variableInformation, RelevancyInformation const& relevancyInformation) {
storm::storage::BitVector reachableStates(subModel.getNumberOfStates());
STORM_LOG_DEBUG("Analyzing solution with zero probability.");
// Initialize the stack for the DFS.
bool targetStateIsReachable = false;
std::vector<uint_fast64_t> stack;
stack.reserve(subModel.getNumberOfStates());
for (auto initialState : subModel.getInitialStates()) {
stack.push_back(initialState);
reachableStates.set(initialState, true);
}
storm::storage::SparseMatrix<T> const& transitionMatrix = subModel.getTransitionMatrix();
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
// Now determine which states and labels are actually reachable.
boost::container::flat_set<uint_fast64_t> reachableLabels;
while (!stack.empty()) {
uint_fast64_t currentState = stack.back();
stack.pop_back();
for (uint_fast64_t currentChoice = nondeterministicChoiceIndices[currentState]; currentChoice < nondeterministicChoiceIndices[currentState + 1]; ++currentChoice) {
bool choiceTargetsRelevantState = false;
for (auto const& successorEntry : transitionMatrix.getRow(currentChoice)) {
if (relevancyInformation.relevantStates.get(successorEntry.getColumn()) && currentState != successorEntry.getColumn()) {
choiceTargetsRelevantState = true;
if (!reachableStates.get(successorEntry.getColumn())) {
reachableStates.set(successorEntry.getColumn());
stack.push_back(successorEntry.getColumn());
}
} else if (psiStates.get(successorEntry.getColumn())) {
targetStateIsReachable = true;
}
}
if (choiceTargetsRelevantState) {
for (auto label : subLabelSets[currentChoice]) {
reachableLabels.insert(label);
}
}
}
}
STORM_LOG_DEBUG("Successfully performed reachability analysis.");
if (targetStateIsReachable) {
STORM_LOG_ERROR("Target must be unreachable for this analysis.");
throw storm::exceptions::InvalidStateException() << "Target must be unreachable for this analysis.";
}
storm::storage::BitVector unreachableRelevantStates = ~reachableStates & relevancyInformation.relevantStates;
storm::storage::BitVector statesThatCanReachTargetStates = storm::utility::graph::performProbGreater0E(subModel.getBackwardTransitions(), phiStates, psiStates);
boost::container::flat_set<uint_fast64_t> locallyRelevantLabels;
std::set_difference(relevancyInformation.relevantLabels.begin(), relevancyInformation.relevantLabels.end(), commandSet.begin(), commandSet.end(), std::inserter(locallyRelevantLabels, locallyRelevantLabels.begin()));
std::vector<boost::container::flat_set<uint_fast64_t>> guaranteedLabelSets = storm::utility::counterexamples::getGuaranteedLabelSets(originalModel, originalLabelSets, statesThatCanReachTargetStates, locallyRelevantLabels);
STORM_LOG_DEBUG("Found " << reachableLabels.size() << " reachable labels and " << reachableStates.getNumberOfSetBits() << " reachable states.");
// Search for states on the border of the reachable state space, i.e. states that are still reachable
// and possess a (disabled) option to leave the reachable part of the state space.
std::set<boost::container::flat_set<uint_fast64_t>> cutLabels;
for (auto state : reachableStates) {
for (auto currentChoice : relevancyInformation.relevantChoicesForRelevantStates.at(state)) {
if (!std::includes(commandSet.begin(), commandSet.end(), originalLabelSets[currentChoice].begin(), originalLabelSets[currentChoice].end())) {
bool isBorderChoice = false;
// Determine whether the state has the option to leave the reachable state space and go to the unreachable relevant states.
for (auto const& successorEntry : originalModel.getTransitionMatrix().getRow(currentChoice)) {
if (unreachableRelevantStates.get(successorEntry.getColumn())) {
isBorderChoice = true;
}
}
if (isBorderChoice) {
boost::container::flat_set<uint_fast64_t> currentLabelSet;
std::set_difference(originalLabelSets[currentChoice].begin(), originalLabelSets[currentChoice].end(), commandSet.begin(), commandSet.end(), std::inserter(currentLabelSet, currentLabelSet.begin()));
std::set_difference(guaranteedLabelSets[state].begin(), guaranteedLabelSets[state].end(), commandSet.begin(), commandSet.end(), std::inserter(currentLabelSet, currentLabelSet.end()));
cutLabels.insert(currentLabelSet);
}
}
}
}
// Given the results of the previous analysis, we construct the implications.
std::vector<storm::expressions::Expression> formulae;
boost::container::flat_set<uint_fast64_t> unknownReachableLabels;
std::set_difference(reachableLabels.begin(), reachableLabels.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(unknownReachableLabels, unknownReachableLabels.end()));
boost::container::flat_set<uint64_t> unknownReachableMinimalityLabels;
std::set_intersection(unknownReachableLabels.begin(), unknownReachableLabels.end(), relevancyInformation.minimalityLabels.begin(), relevancyInformation.minimalityLabels.end(), std::inserter(unknownReachableMinimalityLabels, unknownReachableMinimalityLabels.end()));
for (auto label : unknownReachableMinimalityLabels) {
formulae.push_back(!variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label)));
}
for (auto const& cutLabelSet : cutLabels) {
storm::expressions::Expression cube = variableInformation.manager->boolean(true);
for (auto cutLabel : cutLabelSet) {
cube = cube && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(cutLabel));
}
formulae.push_back(cube);
}
STORM_LOG_DEBUG("Asserting reachability implications.");
assertDisjunction(solver, formulae, *variableInformation.manager);
}
/*!
* Analyzes the given sub-model that has a non-zero maximal reachability and tries to construct assertions that aim to guide the solver to solutions
* with an improved probability value.
*
* @param solver The solver to use for the satisfiability evaluation.
* @param subModel The sub-model resulting from restricting the original model to the given command set.
* @param originalModel The original model.
* @param phiStates A bit vector characterizing all phi states in the model.
* @param psiState A bit vector characterizing all psi states in the model.
* @param commandSet The currently chosen set of commands.
* @param variableInformation A structure with information about the variables of the solver.
*/
static void analyzeInsufficientProbabilitySolution(storm::solver::SmtSolver& solver, storm::models::sparse::Model<T> const& subModel, std::vector<boost::container::flat_set<uint_fast64_t>> const& subLabelSets, storm::models::sparse::Model<T> const& originalModel, std::vector<boost::container::flat_set<uint_fast64_t>> const& originalLabelSets, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, boost::container::flat_set<uint_fast64_t> const& commandSet, VariableInformation& variableInformation, RelevancyInformation const& relevancyInformation) {
STORM_LOG_DEBUG("Analyzing solution with insufficient probability.");
storm::storage::BitVector reachableStates(subModel.getNumberOfStates());
// Initialize the stack for the DFS.
std::vector<uint_fast64_t> stack;
stack.reserve(subModel.getNumberOfStates());
for (auto initialState : subModel.getInitialStates()) {
stack.push_back(initialState);
reachableStates.set(initialState, true);
}
storm::storage::SparseMatrix<T> const& transitionMatrix = subModel.getTransitionMatrix();
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
// Now determine which states and labels are actually reachable.
boost::container::flat_set<uint_fast64_t> reachableLabels;
while (!stack.empty()) {
uint_fast64_t currentState = stack.back();
stack.pop_back();
for (uint_fast64_t currentChoice = nondeterministicChoiceIndices[currentState]; currentChoice < nondeterministicChoiceIndices[currentState + 1]; ++currentChoice) {
bool choiceTargetsRelevantState = false;
for (auto const& successorEntry : transitionMatrix.getRow(currentChoice)) {
if (relevancyInformation.relevantStates.get(successorEntry.getColumn()) && currentState != successorEntry.getColumn()) {
choiceTargetsRelevantState = true;
if (!reachableStates.get(successorEntry.getColumn())) {
reachableStates.set(successorEntry.getColumn(), true);
stack.push_back(successorEntry.getColumn());
}
} //else if (psiStates.get(successorEntry.getColumn())) {
//targetStateIsReachable = true;
//}
}
if (choiceTargetsRelevantState) {
for (auto label : subLabelSets[currentChoice]) {
reachableLabels.insert(label);
}
}
}
}
STORM_LOG_DEBUG("Successfully determined reachable state space.");
storm::storage::BitVector unreachableRelevantStates = ~reachableStates & relevancyInformation.relevantStates;
storm::storage::BitVector statesThatCanReachTargetStates = storm::utility::graph::performProbGreater0E(subModel.getBackwardTransitions(), phiStates, psiStates);
boost::container::flat_set<uint_fast64_t> locallyRelevantLabels;
std::set_difference(relevancyInformation.relevantLabels.begin(), relevancyInformation.relevantLabels.end(), commandSet.begin(), commandSet.end(), std::inserter(locallyRelevantLabels, locallyRelevantLabels.begin()));
std::vector<boost::container::flat_set<uint_fast64_t>> guaranteedLabelSets = storm::utility::counterexamples::getGuaranteedLabelSets(originalModel, originalLabelSets, statesThatCanReachTargetStates, locallyRelevantLabels);
// Search for states for which we could enable another option and possibly improve the reachability probability.
std::set<boost::container::flat_set<uint_fast64_t>> cutLabels;
for (auto state : reachableStates) {
for (auto currentChoice : relevancyInformation.relevantChoicesForRelevantStates.at(state)) {
if (!std::includes(commandSet.begin(), commandSet.end(), originalLabelSets[currentChoice].begin(), originalLabelSets[currentChoice].end())) {
boost::container::flat_set<uint_fast64_t> currentLabelSet;
std::set_difference(originalLabelSets[currentChoice].begin(), originalLabelSets[currentChoice].end(), commandSet.begin(), commandSet.end(), std::inserter(currentLabelSet, currentLabelSet.begin()));
std::set_difference(guaranteedLabelSets[state].begin(), guaranteedLabelSets[state].end(), commandSet.begin(), commandSet.end(), std::inserter(currentLabelSet, currentLabelSet.end()));
cutLabels.insert(currentLabelSet);
}
}
}
// Given the results of the previous analysis, we construct the implications
std::vector<storm::expressions::Expression> formulae;
boost::container::flat_set<uint_fast64_t> unknownReachableLabels;
std::set_difference(reachableLabels.begin(), reachableLabels.end(), relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end(), std::inserter(unknownReachableLabels, unknownReachableLabels.end()));
boost::container::flat_set<uint64_t> unknownReachableMinimalityLabels;
std::set_intersection(unknownReachableLabels.begin(), unknownReachableLabels.end(), relevancyInformation.minimalityLabels.begin(), relevancyInformation.minimalityLabels.end(), std::inserter(unknownReachableMinimalityLabels, unknownReachableMinimalityLabels.end()));
for (auto label : unknownReachableMinimalityLabels) {
formulae.push_back(!variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(label)));
}
for (auto const& cutLabelSet : cutLabels) {
storm::expressions::Expression cube = variableInformation.manager->boolean(true);
for (auto cutLabel : cutLabelSet) {
cube = cube && variableInformation.labelVariables.at(variableInformation.labelToIndexMap.at(cutLabel));
}
formulae.push_back(cube);
}
STORM_LOG_DEBUG("Asserting reachability implications.");
assertDisjunction(solver, formulae, *variableInformation.manager);
}
#endif
/*!
* Returns the sub-model obtained from removing all choices that do not originate from the specified filterLabelSet.
* Also returns the Labelsets of the sub-model.
*/
static std::pair<std::shared_ptr<storm::models::sparse::Model<T>>, std::vector<boost::container::flat_set<uint_fast64_t>>> restrictModelToLabelSet(storm::models::sparse::Model<T> const& model, boost::container::flat_set<uint_fast64_t> const& filterLabelSet, boost::optional<std::string> const& rewardName = boost::none, boost::optional<uint64_t> absorbState = boost::none) {
bool customRowGrouping = model.isOfType(storm::models::ModelType::Mdp);
std::vector<boost::container::flat_set<uint_fast64_t>> resultLabelSet;
storm::storage::SparseMatrixBuilder<T> transitionMatrixBuilder(0, model.getTransitionMatrix().getColumnCount(), 0, true, customRowGrouping, model.getTransitionMatrix().getRowGroupCount());
// Check for each choice of each state, whether the choice commands are fully contained in the given command set.
uint_fast64_t currentRow = 0;
for(uint_fast64_t state = 0; state < model.getNumberOfStates(); ++state) {
bool stateHasValidChoice = false;
for (uint_fast64_t choice = model.getTransitionMatrix().getRowGroupIndices()[state]; choice < model.getTransitionMatrix().getRowGroupIndices()[state + 1]; ++choice) {
auto const& choiceLabelSet = model.getChoiceOrigins()->isPrismChoiceOrigins() ? model.getChoiceOrigins()->asPrismChoiceOrigins().getCommandSet(choice) : model.getChoiceOrigins()->asJaniChoiceOrigins().getEdgeIndexSet(choice);
bool choiceValid = std::includes(filterLabelSet.begin(), filterLabelSet.end(), choiceLabelSet.begin(), choiceLabelSet.end());
// If the choice is valid, copy over all its elements.
if (choiceValid) {
if (!stateHasValidChoice && customRowGrouping) {
transitionMatrixBuilder.newRowGroup(currentRow);
}
stateHasValidChoice = true;
for (auto const& entry : model.getTransitionMatrix().getRow(choice)) {
transitionMatrixBuilder.addNextValue(currentRow, entry.getColumn(), entry.getValue());
}
resultLabelSet.push_back(choiceLabelSet);
++currentRow;
}
}
// If no choice of the current state may be taken, we insert a self-loop to the state instead.
if (!stateHasValidChoice) {
if (customRowGrouping) {
transitionMatrixBuilder.newRowGroup(currentRow);
}
uint64_t targetState = absorbState == boost::none ? state : absorbState.get();
transitionMatrixBuilder.addNextValue(currentRow, targetState, storm::utility::one<T>());
// Insert an empty label set for this choice
resultLabelSet.emplace_back();
++currentRow;
}
}
std::shared_ptr<storm::models::sparse::Model<T>> resultModel;
if (model.isOfType(storm::models::ModelType::Dtmc)) {
resultModel = std::make_shared<storm::models::sparse::Dtmc<T>>(transitionMatrixBuilder.build(), storm::models::sparse::StateLabeling(model.getStateLabeling()), model.getRewardModels());
} else {
resultModel = std::make_shared<storm::models::sparse::Mdp<T>>(transitionMatrixBuilder.build(), storm::models::sparse::StateLabeling(model.getStateLabeling()), model.getRewardModels());
}
return std::make_pair(resultModel, std::move(resultLabelSet));
}
static T computeMaximalReachabilityProbability(Environment const& env, storm::models::sparse::Model<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, boost::optional<std::string> const& rewardName) {
T result = storm::utility::zero<T>();
std::vector<T> allStatesResult;
STORM_LOG_DEBUG("Invoking model checker.");
if (model.isOfType(storm::models::ModelType::Dtmc)) {
if (rewardName == boost::none) {
allStatesResult = storm::modelchecker::helper::SparseDtmcPrctlHelper<T>::computeUntilProbabilities(env, false, model.getTransitionMatrix(), model.getBackwardTransitions(), phiStates, psiStates, false);
} else {
allStatesResult = storm::modelchecker::helper::SparseDtmcPrctlHelper<T>::computeReachabilityRewards(env, false, model.getTransitionMatrix(), model.getBackwardTransitions(), model.getRewardModel(rewardName.get()), psiStates, false);
}
} else {
if (rewardName == boost::none) {
storm::modelchecker::helper::SparseMdpPrctlHelper<T> modelCheckerHelper;
allStatesResult = std::move(modelCheckerHelper.computeUntilProbabilities(env, false, model.getTransitionMatrix(),model.getBackwardTransitions(), phiStates,psiStates, false, false).values);
} else {
STORM_LOG_THROW(rewardName != boost::none, storm::exceptions::NotSupportedException, "Reward property counterexample generation is currently only supported for DTMCs.");
}
}
for (auto state : model.getInitialStates()) {
result = std::max(result, allStatesResult[state]);
}
return result;
}
public:
struct Options {
Options(bool checkThresholdFeasible = false) : checkThresholdFeasible(checkThresholdFeasible) {
auto const& settings = storm::settings::getModule<storm::settings::modules::CounterexampleGeneratorSettings>();
encodeReachability = settings.isEncodeReachabilitySet();
useDynamicConstraints = settings.isUseDynamicConstraintsSet();
}
bool checkThresholdFeasible;
bool encodeReachability;
bool useDynamicConstraints;
bool silent = false;
uint64_t continueAfterFirstCounterexampleUntil = 0;
uint64_t maximumCounterexamples = 1;
uint64_t multipleCounterexampleSizeCap = 100000000;
};
struct GeneratorStats {
std::chrono::milliseconds setupTime;
std::chrono::milliseconds solverTime;
std::chrono::milliseconds modelCheckingTime;
std::chrono::milliseconds analysisTime;
};
/*!
* Computes the minimal command set that is needed in the given model to exceed the given probability threshold for satisfying phi until psi.
*
* @param symbolicModel The symbolic model description that was used to build the model.
* @param model The sparse model in which to find the minimal command set.
* @param phiStates A bit vector characterizing all phi states in the model.
* @param psiStates A bit vector characterizing all psi states in the model.
* @param propertyThreshold The threshold that is to be achieved or exceeded.
* @param rewardName The name of the reward structure to use, or boost::none if probabilities are considerd.
* @param strictBound Indicates whether the threshold needs to be achieved (true) or exceeded (false).
* @param options A set of options for customization.
*/
static std::vector<boost::container::flat_set<uint_fast64_t>> getMinimalLabelSet(Environment const& env, GeneratorStats& stats, storm::storage::SymbolicModelDescription const& symbolicModel, storm::models::sparse::Model<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, double propertyThreshold, boost::optional<std::string> const& rewardName, bool strictBound, boost::container::flat_set<uint_fast64_t> const& dontCareLabels = boost::container::flat_set<uint_fast64_t>(), Options const& options = Options()) {
#ifdef STORM_HAVE_Z3
std::vector<boost::container::flat_set<uint_fast64_t>> result;
// Set up all clocks used for time measurement.
auto totalClock = std::chrono::high_resolution_clock::now();
auto timeOfLastMessage = std::chrono::high_resolution_clock::now();
decltype(std::chrono::high_resolution_clock::now() - totalClock) totalTime(0);
auto setupTimeClock = std::chrono::high_resolution_clock::now();
decltype(std::chrono::high_resolution_clock::now() - setupTimeClock) totalSetupTime(0);
auto solverClock = std::chrono::high_resolution_clock::now();
decltype(std::chrono::high_resolution_clock::now() - solverClock) totalSolverTime(0);
auto modelCheckingClock = std::chrono::high_resolution_clock::now();
decltype(std::chrono::high_resolution_clock::now() - modelCheckingClock) totalModelCheckingTime(0);
auto analysisClock = std::chrono::high_resolution_clock::now();
decltype(std::chrono::high_resolution_clock::now() - analysisClock) totalAnalysisTime(0);
// (0) Obtain the label sets for each choice.
// The label set of a choice corresponds to the set of prism commands that induce the choice.
STORM_LOG_THROW(model.hasChoiceOrigins(), storm::exceptions::InvalidArgumentException, "Restriction to minimal command set is impossible for model without choice origins.");
STORM_LOG_THROW(model.getChoiceOrigins()->isPrismChoiceOrigins() || model.getChoiceOrigins()->isJaniChoiceOrigins(), storm::exceptions::InvalidArgumentException, "Restriction to label set is impossible for model without PRISM or JANI choice origins.");
std::vector<boost::container::flat_set<uint_fast64_t>> labelSets(model.getNumberOfChoices());
if (model.getChoiceOrigins()->isPrismChoiceOrigins()) {
storm::storage::sparse::PrismChoiceOrigins const& choiceOrigins = model.getChoiceOrigins()->asPrismChoiceOrigins();
for (uint_fast64_t choice = 0; choice < model.getNumberOfChoices(); ++choice) {
labelSets[choice] = choiceOrigins.getCommandSet(choice);
}
} else {
storm::storage::sparse::JaniChoiceOrigins const& choiceOrigins = model.getChoiceOrigins()->asJaniChoiceOrigins();
for (uint_fast64_t choice = 0; choice < model.getNumberOfChoices(); ++choice) {
labelSets[choice] = choiceOrigins.getEdgeIndexSet(choice);
}
}
assert(labelSets.size() == model.getNumberOfChoices());
// (1) Check whether its possible to exceed the threshold if checkThresholdFeasible is set.
double maximalReachabilityProbability = 0;
if (options.checkThresholdFeasible) {
maximalReachabilityProbability = computeMaximalReachabilityProbability(env, model, phiStates, psiStates, rewardName);
STORM_LOG_THROW((strictBound && maximalReachabilityProbability >= propertyThreshold) || (!strictBound && maximalReachabilityProbability > propertyThreshold), storm::exceptions::InvalidArgumentException, "Given probability threshold " << propertyThreshold << " can not be " << (strictBound ? "achieved" : "exceeded") << " in model with maximal reachability probability of " << maximalReachabilityProbability << ".");
std::cout << std::endl << "Maximal property value in model is " << maximalReachabilityProbability << "." << std::endl << std::endl;
}
// (2) Identify all states and commands that are relevant, because only these need to be considered later.
RelevancyInformation relevancyInformation = determineRelevantStatesAndLabels(model, labelSets, phiStates, psiStates, dontCareLabels);
// (3) Create a solver.
std::shared_ptr<storm::expressions::ExpressionManager> manager = std::make_shared<storm::expressions::ExpressionManager>();
std::unique_ptr<storm::solver::SmtSolver> solver = std::make_unique<storm::solver::Z3SmtSolver>(*manager);
// (4) Create the variables for the relevant commands.
VariableInformation variableInformation = createVariables(manager, model, psiStates, relevancyInformation, options.encodeReachability);
STORM_LOG_DEBUG("Created variables.");
// (5) Now assert an adder whose result variables can later be used to constrain the nummber of label
// variables that were set to true. Initially, we are looking for a solution that has no label enabled
// and subsequently relax that.
variableInformation.adderVariables = assertAdder(*solver, variableInformation);
variableInformation.auxiliaryVariables.push_back(assertLessOrEqualKRelaxed(*solver, variableInformation, 0));
// (6) Add constraints that cut off a lot of suboptimal solutions.
STORM_LOG_DEBUG("Asserting cuts.");
assertCuts(symbolicModel, model, labelSets, psiStates, variableInformation, relevancyInformation, *solver);
STORM_LOG_DEBUG("Asserted cuts.");
if (options.encodeReachability) {
assertReachabilityCuts(model, labelSets, psiStates, variableInformation, relevancyInformation, *solver);
STORM_LOG_DEBUG("Asserted reachability cuts.");
}
// As we are done with the setup at this point, stop the clock for the setup time.
totalSetupTime = std::chrono::high_resolution_clock::now() - setupTimeClock;
// (7) Find the smallest set of commands that satisfies all constraints. If the probability of
// satisfying phi until psi exceeds the given threshold, the set of labels is minimal and can be returned.
// Otherwise, the current solution has to be ruled out and the next smallest solution is retrieved from
// the solver.
boost::container::flat_set<uint_fast64_t> commandSet(relevancyInformation.knownLabels);
// If there are no relevant labels, return directly.
if (relevancyInformation.relevantLabels.empty()) {
return {commandSet};
} else if (relevancyInformation.minimalityLabels.empty()) {
commandSet.insert(relevancyInformation.relevantLabels.begin(), relevancyInformation.relevantLabels.end());
return {commandSet};
}
// Set up some variables for the iterations.
bool done = false;
uint_fast64_t lastSize = 0;
uint_fast64_t iterations = 0;
uint_fast64_t currentBound = 0;
double maximalPropertyValue = 0;
uint_fast64_t zeroProbabilityCount = 0;
uint64_t smallestCounterexampleSize = model.getNumberOfChoices(); // Definitive u
uint64_t progressDelay = storm::settings::getModule<storm::settings::modules::GeneralSettings>().getShowProgressDelay();
do {
STORM_LOG_DEBUG("Computing minimal command set.");
solverClock = std::chrono::high_resolution_clock::now();
boost::optional<boost::container::flat_set<uint_fast64_t>> smallest = findSmallestCommandSet(*solver, variableInformation, currentBound);
totalSolverTime += std::chrono::high_resolution_clock::now() - solverClock;
if(smallest == boost::none) {
STORM_LOG_DEBUG("No further counterexamples.");
break;
} else {
commandSet = smallest.get();
}
STORM_LOG_DEBUG("Computed minimal command with bound " << currentBound << " and set of size " << commandSet.size() + relevancyInformation.knownLabels.size() << " (" << commandSet.size() << " + " << relevancyInformation.knownLabels.size() << ") ");
// Restrict the given model to the current set of labels and compute the reachability probability.
modelCheckingClock = std::chrono::high_resolution_clock::now();
commandSet.insert(relevancyInformation.knownLabels.begin(), relevancyInformation.knownLabels.end());
commandSet.insert(relevancyInformation.dontCareLabels.begin(), relevancyInformation.dontCareLabels.end());
if (commandSet.size() > smallestCounterexampleSize + options.continueAfterFirstCounterexampleUntil || (result.size() > 1 && commandSet.size() > options.multipleCounterexampleSizeCap) ) {
STORM_LOG_DEBUG("No further counterexamples of similar size.");
break;
}
auto subChoiceOrigins = restrictModelToLabelSet(model, commandSet, rewardName, psiStates.getNextSetIndex(0));
std::shared_ptr<storm::models::sparse::Model<T>> const& subModel = subChoiceOrigins.first;
std::vector<boost::container::flat_set<uint_fast64_t>> const& subLabelSets = subChoiceOrigins.second;
// Now determine the maximal reachability probability in the sub-model.
maximalPropertyValue = computeMaximalReachabilityProbability(env, *subModel, phiStates, psiStates, rewardName);
totalModelCheckingTime += std::chrono::high_resolution_clock::now() - modelCheckingClock;
// Depending on whether the threshold was successfully achieved or not, we proceed by either analyzing the bad solution or stopping the iteration process.
analysisClock = std::chrono::high_resolution_clock::now();
if ((strictBound && maximalPropertyValue < propertyThreshold) || (!strictBound && maximalPropertyValue <= propertyThreshold)) {
if (maximalPropertyValue == storm::utility::zero<T>()) {
++zeroProbabilityCount;
}
if (options.useDynamicConstraints) {
// Determine which of the two analysis techniques to call by performing a reachability analysis.
storm::storage::BitVector reachableStates = storm::utility::graph::getReachableStates(subModel->getTransitionMatrix(), subModel->getInitialStates(), phiStates, psiStates);
if (reachableStates.isDisjointFrom(psiStates)) {
// If there was no target state reachable, analyze the solution and guide the solver into the right direction.
analyzeZeroProbabilitySolution(*solver, *subModel, subLabelSets, model, labelSets, phiStates, psiStates, commandSet, variableInformation, relevancyInformation);
} else {
// If the reachability probability was greater than zero (i.e. there is a reachable target state), but the probability was insufficient to exceed
// the given threshold, we analyze the solution and try to guide the solver into the right direction.
analyzeInsufficientProbabilitySolution(*solver, *subModel, subLabelSets, model, labelSets, phiStates, psiStates, commandSet, variableInformation, relevancyInformation);
}
if (relevancyInformation.dontCareLabels.size() > 0) {
ruleOutSingleSolution(*solver, commandSet, variableInformation, relevancyInformation);
}
} else {
// Do not guide solver, just rule out current solution.
ruleOutSingleSolution(*solver, commandSet, variableInformation, relevancyInformation);
}
} else {
STORM_LOG_DEBUG("Found a counterexample.");
result.push_back(commandSet);
if (options.maximumCounterexamples > result.size()) {
STORM_LOG_DEBUG("Exclude counterexample for future.");
ruleOutBiggerSolutions(*solver, commandSet, variableInformation, relevancyInformation);
} else {
STORM_LOG_DEBUG("Stop searching for further counterexamples.");
done = true;
}
}
totalAnalysisTime += (std::chrono::high_resolution_clock::now() - analysisClock);
++iterations;
auto now = std::chrono::high_resolution_clock::now();
auto durationSinceLastMessage = std::chrono::duration_cast<std::chrono::seconds>(now - timeOfLastMessage).count();
if (static_cast<uint64_t>(durationSinceLastMessage) >= progressDelay || lastSize < commandSet.size()) {
auto milliseconds = std::chrono::duration_cast<std::chrono::milliseconds>(now - totalClock).count();
if (lastSize < commandSet.size()) {
std::cout << "Improved lower bound to " << currentBound << " after " << milliseconds << "ms." << std::endl;
lastSize = commandSet.size();
} else {
std::cout << "Lower bound on label set size is " << currentBound << " after " << milliseconds << "ms (checked " << iterations << " models, " << zeroProbabilityCount << " could not reach the target set)." << std::endl;
timeOfLastMessage = std::chrono::high_resolution_clock::now();
}
}
} while (!done);
// Compute and emit the time measurements if the corresponding flag was set.
totalTime = std::chrono::high_resolution_clock::now() - totalClock;
stats.analysisTime = std::chrono::duration_cast<std::chrono::milliseconds>(totalAnalysisTime);
stats.setupTime = std::chrono::duration_cast<std::chrono::milliseconds>(totalSetupTime);
stats.modelCheckingTime = std::chrono::duration_cast<std::chrono::milliseconds>(totalModelCheckingTime);
stats.solverTime = std::chrono::duration_cast<std::chrono::milliseconds>(totalSolverTime);
if (storm::settings::getModule<storm::settings::modules::CoreSettings>().isShowStatisticsSet()) {
boost::container::flat_set<uint64_t> allLabels;
for (auto const& e : labelSets) {
allLabels.insert(e.begin(), e.end());
}
std::cout << "Metrics:" << std::endl;
std::cout << " * all labels: " << allLabels.size() << std::endl;
std::cout << " * known labels: " << relevancyInformation.knownLabels.size() << std::endl;
std::cout << " * relevant labels: " << (relevancyInformation.knownLabels.size() + relevancyInformation.relevantLabels.size()) << std::endl;
std::cout << std::endl;
std::cout << "Time breakdown:" << std::endl;
std::cout << " * time for setup: " << std::chrono::duration_cast<std::chrono::milliseconds>(totalSetupTime).count() << "ms" << std::endl;
std::cout << " * time for solving: " << std::chrono::duration_cast<std::chrono::milliseconds>(totalSolverTime).count() << "ms" << std::endl;
std::cout << " * time for checking: " << std::chrono::duration_cast<std::chrono::milliseconds>(totalModelCheckingTime).count() << "ms" << std::endl;
std::cout << " * time for analysis: " << std::chrono::duration_cast<std::chrono::milliseconds>(totalAnalysisTime).count() << "ms" << std::endl;
std::cout << "------------------------------------------" << std::endl;
std::cout << " * total time: " << std::chrono::duration_cast<std::chrono::milliseconds>(totalTime).count() << "ms" << std::endl;
std::cout << std::endl;
std::cout << "Other:" << std::endl;
std::cout << " * number of models checked: " << iterations << std::endl;
std::cout << " * number of models that could not reach a target state: " << zeroProbabilityCount << " (" << 100 * static_cast<double>(zeroProbabilityCount)/iterations << "%)" << std::endl << std::endl;
}
return result;
#else
throw storm::exceptions::NotImplementedException() << "This functionality is unavailable since storm has been compiled without support for Z3.";
#endif
}
static void extendLabelSetLowerBound(storm::models::sparse::Model<T> const& model, boost::container::flat_set<uint_fast64_t>& commandSet, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool silent = false) {
auto startTime = std::chrono::high_resolution_clock::now();
// Create sub-model that only contains the choices allowed by the given command set.
std::shared_ptr<storm::models::sparse::Model<T>> subModel = restrictModelToLabelSet(model, commandSet).first;
// Then determine all prob0E(psi) states that are reachable in the sub-model.
storm::storage::BitVector reachableProb0EStates = storm::utility::graph::getReachableStates(subModel->getTransitionMatrix(), subModel->getInitialStates(), phiStates, psiStates);
// Create a queue of reachable prob0E(psi) states so we can check which commands need to be added
// to give them a strategy that avoids psi states.
std::queue<uint_fast64_t> prob0EWorklist;
for (auto const& e : reachableProb0EStates) {
prob0EWorklist.push(e);
}
// As long as there are reachable prob0E(psi) states, we add commands so they can stay within
// prob0E(states).
while (!prob0EWorklist.empty()) {
uint_fast64_t state = prob0EWorklist.front();
prob0EWorklist.pop();
// Now iterate over the original choices of the prob0E(psi) state and add at least one.
bool hasLabeledChoice = false;
uint64_t smallestCommandSetSize = 0;
uint64_t smallestCommandChoice = model.getTransitionMatrix().getRowGroupIndices()[state];
// Determine the choice with the least amount of commands (bad heuristic).
for (uint64_t choice = smallestCommandChoice; choice < model.getTransitionMatrix().getRowGroupIndices()[state + 1]; ++choice) {
bool onlyProb0ESuccessors = true;
for (auto const& successorEntry : model.getTransitionMatrix().getRow(choice)) {
if (!psiStates.get(successorEntry.getColumn())) {
onlyProb0ESuccessors = false;
break;
}
}
if (onlyProb0ESuccessors) {
uint64_t labelSetSize = 0;
if (model.getChoiceOrigins()->isPrismChoiceOrigins()) {
labelSetSize = model.getChoiceOrigins()->asPrismChoiceOrigins().getCommandSet(choice).size();
} else {
assert(model.getChoiceOrigins()->isJaniChoiceOrigins());
labelSetSize = model.getChoiceOrigins()->asJaniChoiceOrigins().getEdgeIndexSet(choice).size();
}
hasLabeledChoice |= (labelSetSize != 0);
if (smallestCommandChoice == 0 || labelSetSize < smallestCommandSetSize) {
smallestCommandSetSize = labelSetSize;
smallestCommandChoice = choice;
}
}
}
if (hasLabeledChoice) {
// Take all labels of the selected choice.
if (model.getChoiceOrigins()->isPrismChoiceOrigins()) {
auto const& labelSet = model.getChoiceOrigins()->asPrismChoiceOrigins().getCommandSet(smallestCommandChoice);
commandSet.insert(labelSet.begin(), labelSet.end());
} else {
assert(model.getChoiceOrigins()->isJaniChoiceOrigins());
auto const& labelSet = model.getChoiceOrigins()->asJaniChoiceOrigins().getEdgeIndexSet(smallestCommandChoice);
commandSet.insert(labelSet.begin(), labelSet.end());
}
// Check for which successor states choices need to be added
for (auto const& successorEntry : model.getTransitionMatrix().getRow(smallestCommandChoice)) {
if (!storm::utility::isZero(successorEntry.getValue())) {
if (!reachableProb0EStates.get(successorEntry.getColumn())) {
reachableProb0EStates.set(successorEntry.getColumn());
prob0EWorklist.push(successorEntry.getColumn());
}
}
}
}
}
auto endTime = std::chrono::high_resolution_clock::now();
if (!silent) {
std::cout << std::endl << "Extended command for lower bounded property to size " << commandSet.size() << " in " << std::chrono::duration_cast<std::chrono::milliseconds>(endTime - startTime).count() << "ms." << std::endl;
}
}
static std::vector<boost::container::flat_set<uint_fast64_t>> computeCounterexampleLabelSet(Environment const& env, GeneratorStats& stats, storm::storage::SymbolicModelDescription const& symbolicModel, storm::models::sparse::Model<T> const& model, std::shared_ptr<storm::logic::Formula const> const& formula, boost::container::flat_set<uint_fast64_t> const& dontCareLabels = boost::container::flat_set<uint_fast64_t>(), Options const& options = Options(true)) {
STORM_LOG_THROW(model.isOfType(storm::models::ModelType::Dtmc) || model.isOfType(storm::models::ModelType::Mdp), storm::exceptions::NotSupportedException, "MaxSAT-based counterexample generation is supported only for discrete-time models.");
if (!options.silent) {
std::cout << std::endl << "Generating minimal label counterexample for formula " << *formula << std::endl;
}
storm::logic::ComparisonType comparisonType;
double threshold;
boost::optional<std::string> rewardName = boost::none;
STORM_LOG_THROW(formula->isProbabilityOperatorFormula() || formula->isRewardOperatorFormula(), storm::exceptions::InvalidPropertyException, "Counterexample generation does not support this kind of formula. Expecting a probability operator as the outermost formula element.");
if (formula->isProbabilityOperatorFormula()) {
storm::logic::ProbabilityOperatorFormula const& probabilityOperator = formula->asProbabilityOperatorFormula();
STORM_LOG_THROW(probabilityOperator.hasBound(), storm::exceptions::InvalidPropertyException, "Counterexample generation only supports bounded formulas.");
STORM_LOG_THROW(probabilityOperator.getSubformula().isUntilFormula() || probabilityOperator.getSubformula().isEventuallyFormula(), storm::exceptions::InvalidPropertyException, "Path formula is required to be of the form 'phi U psi' for counterexample generation.");
comparisonType = probabilityOperator.getComparisonType();
threshold = probabilityOperator.getThresholdAs<T>();
} else {
assert(formula->isRewardOperatorFormula());
storm::logic::RewardOperatorFormula const& rewardOperator = formula->asRewardOperatorFormula();
STORM_LOG_THROW(rewardOperator.hasBound(), storm::exceptions::InvalidPropertyException, "Counterexample generation only supports bounded formulas.");
STORM_LOG_THROW( rewardOperator.getSubformula().isEventuallyFormula(), storm::exceptions::InvalidPropertyException, "Path formula is required to be of the form 'F phi' for counterexample generation.");
comparisonType = rewardOperator.getComparisonType();
threshold = rewardOperator.getThresholdAs<T>();
rewardName = rewardOperator.getRewardModelName();
STORM_LOG_THROW(!storm::logic::isLowerBound(comparisonType), storm::exceptions::NotSupportedException, "Lower bounds in counterexamples are only supported for probability formulas.");
STORM_LOG_THROW(model.hasRewardModel(rewardName.get()), storm::exceptions::InvalidPropertyException, "Property refers to reward " << rewardName.get() << " but model does not contain such a reward model.");
STORM_LOG_THROW(model.getRewardModel(rewardName.get()).hasOnlyStateRewards(), storm::exceptions::NotSupportedException, "We only support state-based rewards at the moment.");
}
bool strictBound = comparisonType == storm::logic::ComparisonType::Less;
storm::logic::Formula const& subformula = formula->asOperatorFormula().getSubformula();
storm::storage::BitVector phiStates;
storm::storage::BitVector psiStates;
storm::modelchecker::SparsePropositionalModelChecker<storm::models::sparse::Model<T>> modelchecker(model);
if (subformula.isUntilFormula()) {
STORM_LOG_THROW(!storm::logic::isLowerBound(comparisonType), storm::exceptions::NotSupportedException, "Lower bounds in counterexamples are only supported for eventually formulas.");
storm::logic::UntilFormula const& untilFormula = subformula.asUntilFormula();
std::unique_ptr<storm::modelchecker::CheckResult> leftResult = modelchecker.check(env, untilFormula.getLeftSubformula());
std::unique_ptr<storm::modelchecker::CheckResult> rightResult = modelchecker.check(env, untilFormula.getRightSubformula());
storm::modelchecker::ExplicitQualitativeCheckResult const& leftQualitativeResult = leftResult->asExplicitQualitativeCheckResult();
storm::modelchecker::ExplicitQualitativeCheckResult const& rightQualitativeResult = rightResult->asExplicitQualitativeCheckResult();
phiStates = leftQualitativeResult.getTruthValuesVector();
psiStates = rightQualitativeResult.getTruthValuesVector();
} else if (subformula.isEventuallyFormula()) {
storm::logic::EventuallyFormula const& eventuallyFormula = subformula.asEventuallyFormula();
std::unique_ptr<storm::modelchecker::CheckResult> subResult = modelchecker.check(env, eventuallyFormula.getSubformula());
storm::modelchecker::ExplicitQualitativeCheckResult const& subQualitativeResult = subResult->asExplicitQualitativeCheckResult();
phiStates = storm::storage::BitVector(model.getNumberOfStates(), true);
psiStates = subQualitativeResult.getTruthValuesVector();
}
bool lowerBoundedFormula = false;
if (storm::logic::isLowerBound(comparisonType)) {
// If the formula specifies a lower bound, we need to modify the phi and psi states.
// More concretely, we convert P(min)>lambda(F psi) to P(max)<(1-lambda)(G !psi) = P(max)<(1-lambda)(!psi U prob0E(psi))
// where prob0E(psi) is the set of states for which there exists a strategy \sigma_0 that avoids
// reaching psi states completely.
// This means that from all states in prob0E(psi) we need to include labels such that \sigma_0
// is actually included in the resulting model. This prevents us from guaranteeing the minimality of
// the returned counterexample, so we warn about that.
if (!options.silent) {
STORM_LOG_WARN("Generating counterexample for lower-bounded property. The resulting command set need not be minimal.");
}
// Modify bound appropriately.
comparisonType = storm::logic::invertPreserveStrictness(comparisonType);
threshold = storm::utility::one<T>() - threshold;
// Modify the phi and psi states appropriately.
storm::storage::BitVector statesWithProbability0E = storm::utility::graph::performProb0E(model.getTransitionMatrix(), model.getTransitionMatrix().getRowGroupIndices(), model.getBackwardTransitions(), phiStates, psiStates);
phiStates = ~psiStates;
psiStates = std::move(statesWithProbability0E);
// Remember our transformation so we can add commands to guarantee that the prob0E(a) states actually
// have a strategy that voids a states.
lowerBoundedFormula = true;
}
// Delegate the actual computation work to the function of equal name.
auto startTime = std::chrono::high_resolution_clock::now();
auto labelSets = getMinimalLabelSet(env, stats, symbolicModel, model, phiStates, psiStates, threshold, rewardName, strictBound, dontCareLabels, options);
auto endTime = std::chrono::high_resolution_clock::now();
if (!options.silent) {
for (auto const& labelSet : labelSets) {
std::cout << std::endl << "Computed minimal label set of size " << labelSet.size();
}
std::cout << std::endl << " in " << std::chrono::duration_cast<std::chrono::milliseconds>(endTime - startTime).count() << "ms." << std::endl;
}
// Extend the command set properly.
for (auto& labelSet : labelSets) {
if (lowerBoundedFormula) {
extendLabelSetLowerBound(model, labelSet, phiStates, psiStates, options.silent);
}
}
return labelSets;
}
static std::shared_ptr<HighLevelCounterexample> computeCounterexample(Environment const& env, storm::storage::SymbolicModelDescription const& symbolicModel, storm::models::sparse::Model<T> const& model, std::shared_ptr<storm::logic::Formula const> const& formula) {
#ifdef STORM_HAVE_Z3
GeneratorStats stats;
auto labelSets = computeCounterexampleLabelSet(env, stats, symbolicModel, model, formula);
if (symbolicModel.isPrismProgram()) {
return std::make_shared<HighLevelCounterexample>(symbolicModel.asPrismProgram().restrictCommands(labelSets[0]));
} else {
STORM_LOG_ASSERT(symbolicModel.isJaniModel(), "Unknown symbolic model description type.");
return std::make_shared<HighLevelCounterexample>(symbolicModel.asJaniModel().restrictEdges(labelSets[0]));
}
#else
throw storm::exceptions::NotImplementedException() << "This functionality is unavailable since storm has been compiled without support for Z3.";
return nullptr;
#endif
}
};
} // namespace counterexamples
} // namespace storm