1034 lines
70 KiB
1034 lines
70 KiB
#ifndef STORM_COUNTEREXAMPLES_MILPMINIMALLABELSETGENERATOR_MDP_H_
|
|
#define STORM_COUNTEREXAMPLES_MILPMINIMALLABELSETGENERATOR_MDP_H_
|
|
|
|
#include <chrono>
|
|
|
|
#include "src/models/sparse/Mdp.h"
|
|
#include "src/logic/Formulas.h"
|
|
#include "src/storage/prism/Program.h"
|
|
#include "src/modelchecker/prctl/helper/SparseMdpPrctlHelper.h"
|
|
#include "src/modelchecker/results/ExplicitQualitativeCheckResult.h"
|
|
#include "src/modelchecker/results/ExplicitQuantitativeCheckResult.h"
|
|
#include "src/exceptions/NotImplementedException.h"
|
|
#include "src/exceptions/InvalidPropertyException.h"
|
|
#include "src/exceptions/InvalidArgumentException.h"
|
|
#include "src/exceptions/InvalidStateException.h"
|
|
|
|
#include "src/utility/graph.h"
|
|
#include "src/utility/counterexamples.h"
|
|
#include "src/utility/solver.h"
|
|
#include "src/solver/LpSolver.h"
|
|
|
|
#include "src/settings/SettingsManager.h"
|
|
#include "src/settings/modules/GeneralSettings.h"
|
|
#include "src/settings/modules/CounterexampleGeneratorSettings.h"
|
|
|
|
namespace storm {
|
|
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 MILPMinimalLabelSetGenerator {
|
|
private:
|
|
/*!
|
|
* A helper class that provides the functionality to compute a hash value for pairs of state indices.
|
|
*/
|
|
class PairHash {
|
|
public:
|
|
std::size_t operator()(std::pair<uint_fast64_t, uint_fast64_t> const& pair) const {
|
|
size_t seed = 0;
|
|
boost::hash_combine(seed, pair.first);
|
|
boost::hash_combine(seed, pair.second);
|
|
return seed;
|
|
}
|
|
};
|
|
|
|
/*!
|
|
* A helper struct storing which states are relevant or problematic.
|
|
*/
|
|
struct StateInformation {
|
|
storm::storage::BitVector relevantStates;
|
|
storm::storage::BitVector problematicStates;
|
|
};
|
|
|
|
/*!
|
|
* A helper struct capturing information about relevant and problematic choices of states and which labels
|
|
* are relevant.
|
|
*/
|
|
struct ChoiceInformation {
|
|
std::unordered_map<uint_fast64_t, std::list<uint_fast64_t>> relevantChoicesForRelevantStates;
|
|
std::unordered_map<uint_fast64_t, std::list<uint_fast64_t>> problematicChoicesForProblematicStates;
|
|
boost::container::flat_set<uint_fast64_t> allRelevantLabels;
|
|
boost::container::flat_set<uint_fast64_t> knownLabels;
|
|
};
|
|
|
|
/*!
|
|
* A helper struct capturing information about the variables of the MILP formulation.
|
|
*/
|
|
struct VariableInformation {
|
|
std::unordered_map<uint_fast64_t, storm::expressions::Variable> labelToVariableMap;
|
|
std::unordered_map<uint_fast64_t, std::list<storm::expressions::Variable>> stateToChoiceVariablesMap;
|
|
std::unordered_map<uint_fast64_t, storm::expressions::Variable> initialStateToChoiceVariableMap;
|
|
std::unordered_map<uint_fast64_t, storm::expressions::Variable> stateToProbabilityVariableMap;
|
|
storm::expressions::Variable virtualInitialStateVariable;
|
|
std::unordered_map<uint_fast64_t, storm::expressions::Variable> problematicStateToVariableMap;
|
|
std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, storm::expressions::Variable, PairHash> problematicTransitionToVariableMap;
|
|
uint_fast64_t numberOfVariables;
|
|
|
|
VariableInformation() : numberOfVariables(0) {}
|
|
};
|
|
|
|
/*!
|
|
* Determines the relevant and the problematic states of the given MDP with respect to the given phi and psi
|
|
* state sets. The relevant states are those for which there exists at least one scheduler that attains a
|
|
* non-zero probability of satisfying phi until psi. Problematic states are relevant states that have at
|
|
* least one scheduler such that the probability of satisfying phi until psi is zero.
|
|
*
|
|
* @param labeledMdp The MDP whose states to search.
|
|
* @param phiStates A bit vector characterizing all states satisfying phi.
|
|
* @param psiStates A bit vector characterizing all states satisfying psi.
|
|
* @return A structure that stores the relevant and problematic states.
|
|
*/
|
|
static struct StateInformation determineRelevantAndProblematicStates(storm::models::sparse::Mdp<T> const& labeledMdp, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
|
|
StateInformation result;
|
|
result.relevantStates = storm::utility::graph::performProbGreater0E(labeledMdp.getTransitionMatrix(), labeledMdp.getNondeterministicChoiceIndices(), labeledMdp.getBackwardTransitions(), phiStates, psiStates);
|
|
result.relevantStates &= ~psiStates;
|
|
result.problematicStates = storm::utility::graph::performProb0E(labeledMdp.getTransitionMatrix(), labeledMdp.getNondeterministicChoiceIndices(), labeledMdp.getBackwardTransitions(), phiStates, psiStates);
|
|
result.problematicStates &= result.relevantStates;
|
|
LOG4CPLUS_DEBUG(logger, "Found " << phiStates.getNumberOfSetBits() << " filter states.");
|
|
LOG4CPLUS_DEBUG(logger, "Found " << psiStates.getNumberOfSetBits() << " target states.");
|
|
LOG4CPLUS_DEBUG(logger, "Found " << result.relevantStates.getNumberOfSetBits() << " relevant states.");
|
|
LOG4CPLUS_DEBUG(logger, "Found " << result.problematicStates.getNumberOfSetBits() << " problematic states.");
|
|
return result;
|
|
}
|
|
|
|
/*!
|
|
* Determines the relevant and problematic choices of the given MDP with respect to the given parameters.
|
|
*
|
|
* @param labeledMdp The MDP whose choices to search.
|
|
* @param stateInformation The relevant and problematic states of the model.
|
|
* @param psiStates A bit vector characterizing the psi states in the model.
|
|
* @return A structure that stores the relevant and problematic choices in the model as well as the set
|
|
* of relevant labels.
|
|
*/
|
|
static struct ChoiceInformation determineRelevantAndProblematicChoices(storm::models::sparse::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, storm::storage::BitVector const& psiStates) {
|
|
// Create result and shortcuts to needed data for convenience.
|
|
ChoiceInformation result;
|
|
storm::storage::SparseMatrix<T> const& transitionMatrix = labeledMdp.getTransitionMatrix();
|
|
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = labeledMdp.getNondeterministicChoiceIndices();
|
|
std::vector<boost::container::flat_set<uint_fast64_t>> const& choiceLabeling = labeledMdp.getChoiceLabeling();
|
|
|
|
// Now traverse all choices of all relevant states and check whether there is a relevant target state.
|
|
// If so, the associated labels become relevant. Also, if a choice of relevant state has at least one
|
|
// relevant successor, the choice is considered to be relevant.
|
|
for (auto state : stateInformation.relevantStates) {
|
|
result.relevantChoicesForRelevantStates.emplace(state, std::list<uint_fast64_t>());
|
|
if (stateInformation.problematicStates.get(state)) {
|
|
result.problematicChoicesForProblematicStates.emplace(state, std::list<uint_fast64_t>());
|
|
}
|
|
for (uint_fast64_t row = nondeterministicChoiceIndices[state]; row < nondeterministicChoiceIndices[state + 1]; ++row) {
|
|
bool currentChoiceRelevant = false;
|
|
bool allSuccessorsProblematic = true;
|
|
for (auto const& successorEntry : transitionMatrix.getRow(row)) {
|
|
// If there is a relevant successor, we need to add the labels of the current choice.
|
|
if (stateInformation.relevantStates.get(successorEntry.getColumn()) || psiStates.get(successorEntry.getColumn())) {
|
|
for (auto const& label : choiceLabeling[row]) {
|
|
result.allRelevantLabels.insert(label);
|
|
}
|
|
if (!currentChoiceRelevant) {
|
|
currentChoiceRelevant = true;
|
|
result.relevantChoicesForRelevantStates[state].push_back(row);
|
|
}
|
|
}
|
|
if (!stateInformation.problematicStates.get(successorEntry.getColumn())) {
|
|
allSuccessorsProblematic = false;
|
|
}
|
|
}
|
|
|
|
// If all successors of a problematic state are problematic themselves, we record this choice
|
|
// as being problematic.
|
|
if (stateInformation.problematicStates.get(state) && allSuccessorsProblematic) {
|
|
result.problematicChoicesForProblematicStates[state].push_back(row);
|
|
}
|
|
}
|
|
}
|
|
|
|
// Finally, determine the set of labels that are known to be taken.
|
|
result.knownLabels = storm::utility::counterexamples::getGuaranteedLabelSet(labeledMdp, psiStates, result.allRelevantLabels);
|
|
LOG4CPLUS_DEBUG(logger, "Found " << result.allRelevantLabels.size() << " relevant labels and " << result.knownLabels.size() << " known labels.");
|
|
|
|
return result;
|
|
}
|
|
|
|
/*!
|
|
* Creates the variables for the labels of the model.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param relevantLabels The set of relevant labels of the model.
|
|
* @return A mapping from labels to variable indices.
|
|
*/
|
|
static std::pair<std::unordered_map<uint_fast64_t, storm::expressions::Variable>, uint_fast64_t> createLabelVariables(storm::solver::LpSolver& solver, boost::container::flat_set<uint_fast64_t> const& relevantLabels) {
|
|
std::stringstream variableNameBuffer;
|
|
std::unordered_map<uint_fast64_t, storm::expressions::Variable> resultingMap;
|
|
for (auto const& label : relevantLabels) {
|
|
variableNameBuffer.str("");
|
|
variableNameBuffer.clear();
|
|
variableNameBuffer << "label" << label;
|
|
resultingMap[label] = solver.addBinaryVariable(variableNameBuffer.str(), 1);
|
|
}
|
|
return std::make_pair(resultingMap, relevantLabels.size());
|
|
}
|
|
|
|
/*!
|
|
* Creates the variables for the relevant choices in the model.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param stateInformation The information about the states of the model.
|
|
* @param choiceInformation The information about the choices of the model.
|
|
* @return A mapping from states to a list of choice variable indices.
|
|
*/
|
|
static std::pair<std::unordered_map<uint_fast64_t, std::list<storm::expressions::Variable>>, uint_fast64_t> createSchedulerVariables(storm::solver::LpSolver& solver, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation) {
|
|
std::stringstream variableNameBuffer;
|
|
uint_fast64_t numberOfVariablesCreated = 0;
|
|
std::unordered_map<uint_fast64_t, std::list<storm::expressions::Variable>> resultingMap;
|
|
|
|
for (auto state : stateInformation.relevantStates) {
|
|
resultingMap.emplace(state, std::list<storm::expressions::Variable>());
|
|
std::list<uint_fast64_t> const& relevantChoicesForState = choiceInformation.relevantChoicesForRelevantStates.at(state);
|
|
for (uint_fast64_t row : relevantChoicesForState) {
|
|
variableNameBuffer.str("");
|
|
variableNameBuffer.clear();
|
|
variableNameBuffer << "choice" << row << "in" << state;
|
|
resultingMap[state].push_back(solver.addBinaryVariable(variableNameBuffer.str()));
|
|
++numberOfVariablesCreated;
|
|
}
|
|
}
|
|
return std::make_pair(resultingMap, numberOfVariablesCreated);
|
|
}
|
|
|
|
/*!
|
|
* Creates the variables needed for encoding the nondeterministic selection of one of the initial states
|
|
* in the model.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param stateInformation The information about the states of the model.
|
|
* @return A mapping from initial states to choice variable indices.
|
|
*/
|
|
static std::pair<std::unordered_map<uint_fast64_t, storm::expressions::Variable>, uint_fast64_t> createInitialChoiceVariables(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, StateInformation const& stateInformation) {
|
|
std::stringstream variableNameBuffer;
|
|
uint_fast64_t numberOfVariablesCreated = 0;
|
|
std::unordered_map<uint_fast64_t, storm::expressions::Variable> resultingMap;
|
|
|
|
for (auto initialState : labeledMdp.getStates("init")) {
|
|
// Only consider this initial state if it is relevant.
|
|
if (stateInformation.relevantStates.get(initialState)) {
|
|
variableNameBuffer.str("");
|
|
variableNameBuffer.clear();
|
|
variableNameBuffer << "init" << initialState;
|
|
resultingMap[initialState] = solver.addBinaryVariable(variableNameBuffer.str());
|
|
++numberOfVariablesCreated;
|
|
}
|
|
}
|
|
return std::make_pair(resultingMap, numberOfVariablesCreated);
|
|
}
|
|
|
|
/*!
|
|
* Creates the variables for the probabilities in the model.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @return A mapping from states to the index of the corresponding probability variables.
|
|
*/
|
|
static std::pair<std::unordered_map<uint_fast64_t, storm::expressions::Variable>, uint_fast64_t> createProbabilityVariables(storm::solver::LpSolver& solver, StateInformation const& stateInformation) {
|
|
std::stringstream variableNameBuffer;
|
|
uint_fast64_t numberOfVariablesCreated = 0;
|
|
std::unordered_map<uint_fast64_t, storm::expressions::Variable> resultingMap;
|
|
|
|
for (auto state : stateInformation.relevantStates) {
|
|
variableNameBuffer.str("");
|
|
variableNameBuffer.clear();
|
|
variableNameBuffer << "p" << state;
|
|
resultingMap[state] = solver.addBoundedContinuousVariable(variableNameBuffer.str(), 0, 1);
|
|
++numberOfVariablesCreated;
|
|
}
|
|
return std::make_pair(resultingMap, numberOfVariablesCreated);
|
|
}
|
|
|
|
/*!
|
|
* Creates the variable for the probability of the virtual initial state.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param maximizeProbability If set to true, the objective function is constructed in a way that a
|
|
* label-minimal subsystem of maximal probability is computed.
|
|
* @return The index of the variable for the probability of the virtual initial state.
|
|
*/
|
|
static std::pair<storm::expressions::Variable, uint_fast64_t> createVirtualInitialStateVariable(storm::solver::LpSolver& solver, bool maximizeProbability = false) {
|
|
std::stringstream variableNameBuffer;
|
|
variableNameBuffer << "pinit";
|
|
storm::expressions::Variable variable = solver.addBoundedContinuousVariable(variableNameBuffer.str(), 0, 1);
|
|
return std::make_pair(variable, 1);
|
|
}
|
|
|
|
/*!
|
|
* Creates the variables for the problematic states in the model.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @return A mapping from problematic states to the index of the corresponding variables.
|
|
*/
|
|
static std::pair<std::unordered_map<uint_fast64_t, storm::expressions::Variable>, uint_fast64_t> createProblematicStateVariables(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation) {
|
|
std::stringstream variableNameBuffer;
|
|
uint_fast64_t numberOfVariablesCreated = 0;
|
|
std::unordered_map<uint_fast64_t, storm::expressions::Variable> resultingMap;
|
|
|
|
for (auto state : stateInformation.problematicStates) {
|
|
// First check whether there is not already a variable for this state and advance to the next state
|
|
// in this case.
|
|
if (resultingMap.find(state) == resultingMap.end()) {
|
|
variableNameBuffer.str("");
|
|
variableNameBuffer.clear();
|
|
variableNameBuffer << "r" << state;
|
|
resultingMap[state] = solver.addBoundedContinuousVariable(variableNameBuffer.str(), 0, 1);
|
|
++numberOfVariablesCreated;
|
|
}
|
|
|
|
std::list<uint_fast64_t> const& relevantChoicesForState = choiceInformation.relevantChoicesForRelevantStates.at(state);
|
|
for (uint_fast64_t row : relevantChoicesForState) {
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(row)) {
|
|
if (stateInformation.relevantStates.get(successorEntry.getColumn())) {
|
|
if (resultingMap.find(successorEntry.getColumn()) == resultingMap.end()) {
|
|
variableNameBuffer.str("");
|
|
variableNameBuffer.clear();
|
|
variableNameBuffer << "r" << successorEntry.getColumn();
|
|
resultingMap[successorEntry.getColumn()] = solver.addBoundedContinuousVariable(variableNameBuffer.str(), 0, 1);
|
|
++numberOfVariablesCreated;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return std::make_pair(resultingMap, numberOfVariablesCreated);
|
|
}
|
|
|
|
/*!
|
|
* Creates the variables for the problematic choices in the model.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @return A mapping from problematic choices to the index of the corresponding variables.
|
|
*/
|
|
static std::pair<std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, storm::expressions::Variable, PairHash>, uint_fast64_t> createProblematicChoiceVariables(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation) {
|
|
std::stringstream variableNameBuffer;
|
|
uint_fast64_t numberOfVariablesCreated = 0;
|
|
std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, storm::expressions::Variable, PairHash> resultingMap;
|
|
|
|
for (auto state : stateInformation.problematicStates) {
|
|
std::list<uint_fast64_t> const& relevantChoicesForState = choiceInformation.relevantChoicesForRelevantStates.at(state);
|
|
for (uint_fast64_t row : relevantChoicesForState) {
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(row)) {
|
|
if (stateInformation.relevantStates.get(successorEntry.getColumn())) {
|
|
variableNameBuffer.str("");
|
|
variableNameBuffer.clear();
|
|
variableNameBuffer << "t" << state << "to" << successorEntry.getColumn();
|
|
resultingMap[std::make_pair(state, successorEntry.getColumn())] = solver.addBinaryVariable(variableNameBuffer.str());
|
|
++numberOfVariablesCreated;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return std::make_pair(resultingMap, numberOfVariablesCreated);
|
|
}
|
|
|
|
/*!
|
|
* Creates all variables needed to encode the problem as an MILP problem and returns a struct containing
|
|
* information about the variables that were created. This implicitly establishes the objective function
|
|
* passed to the solver.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
*/
|
|
static VariableInformation createVariables(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation) {
|
|
// Create a struct that stores all information about variables.
|
|
VariableInformation result;
|
|
|
|
// Create variables for involved labels.
|
|
std::pair<std::unordered_map<uint_fast64_t, storm::expressions::Variable>, uint_fast64_t> labelVariableResult = createLabelVariables(solver, choiceInformation.allRelevantLabels);
|
|
result.labelToVariableMap = std::move(labelVariableResult.first);
|
|
result.numberOfVariables += labelVariableResult.second;
|
|
LOG4CPLUS_DEBUG(logger, "Created variables for labels.");
|
|
|
|
// Create scheduler variables for relevant states and their actions.
|
|
std::pair<std::unordered_map<uint_fast64_t, std::list<storm::expressions::Variable>>, uint_fast64_t> schedulerVariableResult = createSchedulerVariables(solver, stateInformation, choiceInformation);
|
|
result.stateToChoiceVariablesMap = std::move(schedulerVariableResult.first);
|
|
result.numberOfVariables += schedulerVariableResult.second;
|
|
LOG4CPLUS_DEBUG(logger, "Created variables for nondeterministic choices.");
|
|
|
|
// Create scheduler variables for nondeterministically choosing an initial state.
|
|
std::pair<std::unordered_map<uint_fast64_t, storm::expressions::Variable>, uint_fast64_t> initialChoiceVariableResult = createInitialChoiceVariables(solver, labeledMdp, stateInformation);
|
|
result.initialStateToChoiceVariableMap = std::move(initialChoiceVariableResult.first);
|
|
result.numberOfVariables += initialChoiceVariableResult.second;
|
|
LOG4CPLUS_DEBUG(logger, "Created variables for the nondeterministic choice of the initial state.");
|
|
|
|
// Create variables for probabilities for all relevant states.
|
|
std::pair<std::unordered_map<uint_fast64_t, storm::expressions::Variable>, uint_fast64_t> probabilityVariableResult = createProbabilityVariables(solver, stateInformation);
|
|
result.stateToProbabilityVariableMap = std::move(probabilityVariableResult.first);
|
|
result.numberOfVariables += probabilityVariableResult.second;
|
|
LOG4CPLUS_DEBUG(logger, "Created variables for the reachability probabilities.");
|
|
|
|
// Create a probability variable for a virtual initial state that nondeterministically chooses one of the system's real initial states as its target state.
|
|
std::pair<storm::expressions::Variable, uint_fast64_t> virtualInitialStateVariableResult = createVirtualInitialStateVariable(solver);
|
|
result.virtualInitialStateVariable = virtualInitialStateVariableResult.first;
|
|
result.numberOfVariables += virtualInitialStateVariableResult.second;
|
|
LOG4CPLUS_DEBUG(logger, "Created variables for the virtual initial state.");
|
|
|
|
// Create variables for problematic states.
|
|
std::pair<std::unordered_map<uint_fast64_t, storm::expressions::Variable>, uint_fast64_t> problematicStateVariableResult = createProblematicStateVariables(solver, labeledMdp, stateInformation, choiceInformation);
|
|
result.problematicStateToVariableMap = std::move(problematicStateVariableResult.first);
|
|
result.numberOfVariables += problematicStateVariableResult.second;
|
|
LOG4CPLUS_DEBUG(logger, "Created variables for the problematic states.");
|
|
|
|
// Create variables for problematic choices.
|
|
std::pair<std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, storm::expressions::Variable, PairHash>, uint_fast64_t> problematicTransitionVariableResult = createProblematicChoiceVariables(solver, labeledMdp, stateInformation, choiceInformation);
|
|
result.problematicTransitionToVariableMap = problematicTransitionVariableResult.first;
|
|
result.numberOfVariables += problematicTransitionVariableResult.second;
|
|
LOG4CPLUS_DEBUG(logger, "Created variables for the problematic choices.");
|
|
|
|
// Finally, we need to update the model to make the new variables usable.
|
|
solver.update();
|
|
LOG4CPLUS_INFO(logger, "Successfully created " << result.numberOfVariables << " MILP variables.");
|
|
|
|
// Finally, return variable information struct.
|
|
return result;
|
|
}
|
|
|
|
/*!
|
|
* Asserts a constraint in the MILP problem that makes sure the reachability probability in the subsystem
|
|
* exceeds the given threshold.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @param probabilityThreshold The probability that the subsystem must exceed.
|
|
* @param strictBound A flag indicating whether the threshold must be exceeded or only matched.
|
|
* @return The total number of constraints that were created.
|
|
*/
|
|
static uint_fast64_t assertProbabilityGreaterThanThreshold(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, VariableInformation const& variableInformation, double probabilityThreshold, bool strictBound) {
|
|
storm::expressions::Expression constraint;
|
|
if (strictBound) {
|
|
constraint = variableInformation.virtualInitialStateVariable > solver.getConstant(probabilityThreshold);
|
|
} else {
|
|
constraint = variableInformation.virtualInitialStateVariable >= solver.getConstant(probabilityThreshold);
|
|
}
|
|
solver.addConstraint("ProbGreaterThreshold", constraint);
|
|
return 1;
|
|
}
|
|
|
|
/*!
|
|
* Asserts constraints that make sure the selected policy is valid, i.e. chooses at most one action in each state.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @return The total number of constraints that were created.
|
|
*/
|
|
static uint_fast64_t assertValidPolicy(storm::solver::LpSolver& solver, StateInformation const& stateInformation, VariableInformation const& variableInformation) {
|
|
// Assert that the policy chooses at most one action in each state of the system.
|
|
uint_fast64_t numberOfConstraintsCreated = 0;
|
|
for (auto state : stateInformation.relevantStates) {
|
|
std::list<storm::expressions::Variable> const& choiceVariableIndices = variableInformation.stateToChoiceVariablesMap.at(state);
|
|
storm::expressions::Expression constraint = solver.getConstant(0);
|
|
|
|
for (auto const& choiceVariable : choiceVariableIndices) {
|
|
constraint = constraint + choiceVariable;
|
|
}
|
|
|
|
constraint = constraint <= solver.getConstant(1);
|
|
|
|
solver.addConstraint("ValidPolicy" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
|
|
// Now assert that the virtual initial state picks exactly one initial state from the system as its
|
|
// successor state.
|
|
storm::expressions::Expression constraint = solver.getConstant(0);
|
|
for (auto const& initialStateVariablePair : variableInformation.initialStateToChoiceVariableMap) {
|
|
constraint = constraint + initialStateVariablePair.second;
|
|
}
|
|
constraint = constraint == solver.getConstant(1);
|
|
|
|
solver.addConstraint("VirtualInitialStateChoosesOneInitialState", constraint);
|
|
++numberOfConstraintsCreated;
|
|
|
|
return numberOfConstraintsCreated;
|
|
}
|
|
|
|
/*!
|
|
* Asserts constraints that make sure the labels are included in the solution set if the policy selects a
|
|
* choice that is labeled with the label in question.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @return The total number of constraints that were created.
|
|
*/
|
|
static uint_fast64_t assertChoicesImplyLabels(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
|
|
uint_fast64_t numberOfConstraintsCreated = 0;
|
|
|
|
std::vector<boost::container::flat_set<uint_fast64_t>> const& choiceLabeling = labeledMdp.getChoiceLabeling();
|
|
for (auto state : stateInformation.relevantStates) {
|
|
std::list<storm::expressions::Variable>::const_iterator choiceVariableIterator = variableInformation.stateToChoiceVariablesMap.at(state).begin();
|
|
for (auto choice : choiceInformation.relevantChoicesForRelevantStates.at(state)) {
|
|
for (auto label : choiceLabeling[choice]) {
|
|
storm::expressions::Expression constraint = variableInformation.labelToVariableMap.at(label) - *choiceVariableIterator >= solver.getConstant(0);
|
|
solver.addConstraint("ChoicesImplyLabels" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
++choiceVariableIterator;
|
|
}
|
|
}
|
|
return numberOfConstraintsCreated;
|
|
}
|
|
|
|
/*!
|
|
* Asserts constraints that make sure the reachability probability is zero for states in which the policy
|
|
* does not pick any outgoing action.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @return The total number of constraints that were created.
|
|
*/
|
|
static uint_fast64_t assertZeroProbabilityWithoutChoice(storm::solver::LpSolver& solver, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
|
|
uint_fast64_t numberOfConstraintsCreated = 0;
|
|
for (auto state : stateInformation.relevantStates) {
|
|
storm::expressions::Expression constraint = variableInformation.stateToProbabilityVariableMap.at(state);
|
|
for (auto const& choiceVariable : variableInformation.stateToChoiceVariablesMap.at(state)) {
|
|
constraint = constraint - choiceVariable;
|
|
}
|
|
constraint = constraint <= solver.getConstant(0);
|
|
solver.addConstraint("ProbabilityIsZeroIfNoAction" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
return numberOfConstraintsCreated;
|
|
}
|
|
|
|
/*!
|
|
* Asserts constraints that encode the correct reachability probabilities for all states.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param psiStates A bit vector characterizing the psi states in the model.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @return The total number of constraints that were created.
|
|
*/
|
|
static uint_fast64_t assertReachabilityProbabilities(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, storm::storage::BitVector const& psiStates, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
|
|
uint_fast64_t numberOfConstraintsCreated = 0;
|
|
for (auto state : stateInformation.relevantStates) {
|
|
std::list<storm::expressions::Variable>::const_iterator choiceVariableIterator = variableInformation.stateToChoiceVariablesMap.at(state).begin();
|
|
for (auto choice : choiceInformation.relevantChoicesForRelevantStates.at(state)) {
|
|
storm::expressions::Expression constraint = variableInformation.stateToProbabilityVariableMap.at(state);
|
|
|
|
double rightHandSide = 1;
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(choice)) {
|
|
if (stateInformation.relevantStates.get(successorEntry.getColumn())) {
|
|
constraint = constraint - solver.getConstant(successorEntry.getValue()) * variableInformation.stateToProbabilityVariableMap.at(successorEntry.getColumn());
|
|
} else if (psiStates.get(successorEntry.getColumn())) {
|
|
rightHandSide += successorEntry.getValue();
|
|
}
|
|
}
|
|
|
|
constraint = constraint + *choiceVariableIterator <= solver.getConstant(rightHandSide);
|
|
solver.addConstraint("ReachabilityProbabilities" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
|
|
++numberOfConstraintsCreated;
|
|
++choiceVariableIterator;
|
|
}
|
|
}
|
|
|
|
// Make sure that the virtual initial state is being assigned the probability from the initial state
|
|
// that it selected as a successor state.
|
|
for (auto const& initialStateVariablePair : variableInformation.initialStateToChoiceVariableMap) {
|
|
storm::expressions::Expression constraint = variableInformation.virtualInitialStateVariable - variableInformation.stateToProbabilityVariableMap.at(initialStateVariablePair.first) + initialStateVariablePair.second <= solver.getConstant(1);
|
|
solver.addConstraint("VirtualInitialStateHasCorrectProbability" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
|
|
return numberOfConstraintsCreated;
|
|
}
|
|
|
|
/*!
|
|
* Asserts constraints that make sure an unproblematic state is reachable from each problematic state.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @return The total number of constraints that were created.
|
|
*/
|
|
static uint_fast64_t assertUnproblematicStateReachable(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
|
|
uint_fast64_t numberOfConstraintsCreated = 0;
|
|
|
|
for (auto stateListPair : choiceInformation.problematicChoicesForProblematicStates) {
|
|
for (auto problematicChoice : stateListPair.second) {
|
|
std::list<storm::expressions::Variable>::const_iterator choiceVariableIterator = variableInformation.stateToChoiceVariablesMap.at(stateListPair.first).begin();
|
|
for (auto relevantChoice : choiceInformation.relevantChoicesForRelevantStates.at(stateListPair.first)) {
|
|
if (relevantChoice == problematicChoice) {
|
|
break;
|
|
}
|
|
++choiceVariableIterator;
|
|
}
|
|
|
|
storm::expressions::Expression constraint = *choiceVariableIterator;
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(problematicChoice)) {
|
|
constraint = constraint - variableInformation.problematicTransitionToVariableMap.at(std::make_pair(stateListPair.first, successorEntry.getColumn()));
|
|
}
|
|
constraint = constraint <= solver.getConstant(0);
|
|
|
|
solver.addConstraint("UnproblematicStateReachable" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
}
|
|
|
|
for (auto state : stateInformation.problematicStates) {
|
|
for (auto problematicChoice : choiceInformation.problematicChoicesForProblematicStates.at(state)) {
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(problematicChoice)) {
|
|
storm::expressions::Expression constraint = variableInformation.problematicStateToVariableMap.at(state);
|
|
constraint = constraint - variableInformation.problematicStateToVariableMap.at(successorEntry.getColumn());
|
|
constraint = constraint + variableInformation.problematicTransitionToVariableMap.at(std::make_pair(state, successorEntry.getColumn()));
|
|
constraint = constraint < solver.getConstant(1);
|
|
|
|
solver.addConstraint("UnproblematicStateReachable" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
}
|
|
}
|
|
return numberOfConstraintsCreated;
|
|
}
|
|
|
|
/*
|
|
* Asserts that labels that are on all paths from initial to target states are definitely taken.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param psiStates A bit vector characterizing the psi states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @return The total number of constraints that were created.
|
|
*/
|
|
static uint_fast64_t assertKnownLabels(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, storm::storage::BitVector const& psiStates, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
|
|
uint_fast64_t numberOfConstraintsCreated = 0;
|
|
|
|
for (auto label : choiceInformation.knownLabels) {
|
|
storm::expressions::Expression constraint = variableInformation.labelToVariableMap.at(label) == solver.getConstant(1);
|
|
solver.addConstraint("KnownLabels" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
|
|
return numberOfConstraintsCreated;
|
|
}
|
|
|
|
/*!
|
|
* Asserts constraints that rule out many suboptimal policies.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param psiStates A bit vector characterizing the psi states in the model.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @return The total number of constraints that were created.
|
|
*/
|
|
static uint_fast64_t assertSchedulerCuts(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, storm::storage::BitVector const& psiStates, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
|
|
storm::storage::SparseMatrix<T> backwardTransitions = labeledMdp.getBackwardTransitions();
|
|
uint_fast64_t numberOfConstraintsCreated = 0;
|
|
|
|
for (auto state : stateInformation.relevantStates) {
|
|
// Assert that all states, that select an action, this action either has a non-zero probability to
|
|
// go to a psi state directly, or in the successor states, at least one action is selected as well.
|
|
std::list<storm::expressions::Variable>::const_iterator choiceVariableIterator = variableInformation.stateToChoiceVariablesMap.at(state).begin();
|
|
for (auto choice : choiceInformation.relevantChoicesForRelevantStates.at(state)) {
|
|
bool psiStateReachableInOneStep = false;
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(choice)) {
|
|
if (psiStates.get(successorEntry.getColumn())) {
|
|
psiStateReachableInOneStep = true;
|
|
}
|
|
}
|
|
|
|
if (!psiStateReachableInOneStep) {
|
|
storm::expressions::Expression constraint = *choiceVariableIterator;
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(choice)) {
|
|
if (state != successorEntry.getColumn() && stateInformation.relevantStates.get(successorEntry.getColumn())) {
|
|
std::list<storm::expressions::Variable> const& successorChoiceVariableIndices = variableInformation.stateToChoiceVariablesMap.at(successorEntry.getColumn());
|
|
|
|
for (auto const& choiceVariable : successorChoiceVariableIndices) {
|
|
constraint = constraint - choiceVariable;
|
|
}
|
|
}
|
|
}
|
|
constraint = constraint <= solver.getConstant(1);
|
|
|
|
solver.addConstraint("SchedulerCuts" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
|
|
++choiceVariableIterator;
|
|
}
|
|
|
|
// For all states assert that there is either a selected incoming transition in the subsystem or the
|
|
// state is the chosen initial state if there is one selected action in the current state.
|
|
storm::expressions::Expression constraint = solver.getConstant(0);
|
|
|
|
for (auto const& choiceVariable : variableInformation.stateToChoiceVariablesMap.at(state)) {
|
|
constraint = constraint + choiceVariable;
|
|
}
|
|
|
|
// Compute the set of predecessors.
|
|
std::unordered_set<uint_fast64_t> predecessors;
|
|
for (auto const& predecessorEntry : backwardTransitions.getRow(state)) {
|
|
if (state != predecessorEntry.getColumn()) {
|
|
predecessors.insert(predecessorEntry.getColumn());
|
|
}
|
|
}
|
|
|
|
for (auto predecessor : predecessors) {
|
|
// If the predecessor is not a relevant state, we need to skip it.
|
|
if (!stateInformation.relevantStates.get(predecessor)) {
|
|
continue;
|
|
}
|
|
|
|
std::list<storm::expressions::Variable>::const_iterator choiceVariableIterator = variableInformation.stateToChoiceVariablesMap.at(predecessor).begin();
|
|
for (auto relevantChoice : choiceInformation.relevantChoicesForRelevantStates.at(predecessor)) {
|
|
bool choiceTargetsCurrentState = false;
|
|
|
|
// Check if the current choice targets the current state.
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(relevantChoice)) {
|
|
if (state == successorEntry.getColumn()) {
|
|
choiceTargetsCurrentState = true;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// If it does, we can add the choice to the sum.
|
|
if (choiceTargetsCurrentState) {
|
|
constraint = constraint - *choiceVariableIterator;
|
|
}
|
|
++choiceVariableIterator;
|
|
}
|
|
}
|
|
|
|
// If the current state is an initial state and is selected as a successor state by the virtual
|
|
// initial state, then this also justifies making a choice in the current state.
|
|
if (labeledMdp.getStates("init").get(state)) {
|
|
constraint = constraint - variableInformation.initialStateToChoiceVariableMap.at(state);
|
|
}
|
|
constraint = constraint <= solver.getConstant(0);
|
|
|
|
solver.addConstraint("SchedulerCuts" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
}
|
|
|
|
// Assert that at least one initial state selects at least one action.
|
|
storm::expressions::Expression constraint = solver.getConstant(0);
|
|
for (auto initialState : labeledMdp.getStates("init")) {
|
|
for (auto const& choiceVariable : variableInformation.stateToChoiceVariablesMap.at(initialState)) {
|
|
constraint = constraint + choiceVariable;
|
|
}
|
|
}
|
|
constraint = constraint >= solver.getConstant(1);
|
|
solver.addConstraint("SchedulerCuts" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
|
|
// Add constraints that ensure at least one choice is selected that targets a psi state.
|
|
constraint = solver.getConstant(0);
|
|
std::unordered_set<uint_fast64_t> predecessors;
|
|
for (auto psiState : psiStates) {
|
|
// Compute the set of predecessors.
|
|
for (auto const& predecessorEntry : backwardTransitions.getRow(psiState)) {
|
|
if (psiState != predecessorEntry.getColumn()) {
|
|
predecessors.insert(predecessorEntry.getColumn());
|
|
}
|
|
}
|
|
}
|
|
|
|
for (auto predecessor : predecessors) {
|
|
// If the predecessor is not a relevant state, we need to skip it.
|
|
if (!stateInformation.relevantStates.get(predecessor)) {
|
|
continue;
|
|
}
|
|
|
|
std::list<storm::expressions::Variable>::const_iterator choiceVariableIterator = variableInformation.stateToChoiceVariablesMap.at(predecessor).begin();
|
|
for (auto relevantChoice : choiceInformation.relevantChoicesForRelevantStates.at(predecessor)) {
|
|
bool choiceTargetsPsiState = false;
|
|
|
|
// Check if the current choice targets the current state.
|
|
for (auto const& successorEntry : labeledMdp.getTransitionMatrix().getRow(relevantChoice)) {
|
|
if (psiStates.get(successorEntry.getColumn())) {
|
|
choiceTargetsPsiState = true;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// If it does, we can add the choice to the sum.
|
|
if (choiceTargetsPsiState) {
|
|
constraint = constraint + *choiceVariableIterator;
|
|
}
|
|
++choiceVariableIterator;
|
|
}
|
|
}
|
|
constraint = constraint >= solver.getConstant(1);
|
|
|
|
solver.addConstraint("SchedulerCuts" + std::to_string(numberOfConstraintsCreated), constraint);
|
|
++numberOfConstraintsCreated;
|
|
|
|
return numberOfConstraintsCreated;
|
|
}
|
|
|
|
/*!
|
|
* Builds a system of constraints that express that the reachability probability in the subsystem exceeeds
|
|
* the given threshold.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param psiStates A bit vector characterizing all psi states in the model.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
* @param probabilityThreshold The probability threshold the subsystem is required to exceed.
|
|
* @param strictBound A flag indicating whether the threshold must be exceeded or only matched.
|
|
* @param includeSchedulerCuts If set to true, additional constraints are asserted that reduce the set of
|
|
* possible choices.
|
|
*/
|
|
static void buildConstraintSystem(storm::solver::LpSolver& solver, storm::models::sparse::Mdp<T> const& labeledMdp, storm::storage::BitVector const& psiStates, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation, double probabilityThreshold, bool strictBound, bool includeSchedulerCuts = false) {
|
|
// Assert that the reachability probability in the subsystem exceeds the given threshold.
|
|
uint_fast64_t numberOfConstraints = assertProbabilityGreaterThanThreshold(solver, labeledMdp, variableInformation, probabilityThreshold, strictBound);
|
|
LOG4CPLUS_DEBUG(logger, "Asserted that reachability probability exceeds threshold.");
|
|
|
|
// Add constraints that assert the policy takes at most one action in each state.
|
|
numberOfConstraints += assertValidPolicy(solver, stateInformation, variableInformation);
|
|
LOG4CPLUS_DEBUG(logger, "Asserted that policy is valid.");
|
|
|
|
// Add constraints that assert the labels that belong to some taken choices are taken as well.
|
|
numberOfConstraints += assertChoicesImplyLabels(solver, labeledMdp, stateInformation, choiceInformation, variableInformation);
|
|
LOG4CPLUS_DEBUG(logger, "Asserted that labels implied by choices are taken.");
|
|
|
|
// Add constraints that encode that the reachability probability from states which do not pick any action
|
|
// is zero.
|
|
numberOfConstraints += assertZeroProbabilityWithoutChoice(solver, stateInformation, choiceInformation, variableInformation);
|
|
LOG4CPLUS_DEBUG(logger, "Asserted that reachability probability is zero if no choice is taken.");
|
|
|
|
// Add constraints that encode the reachability probabilities for states.
|
|
numberOfConstraints += assertReachabilityProbabilities(solver, labeledMdp, psiStates, stateInformation, choiceInformation, variableInformation);
|
|
LOG4CPLUS_DEBUG(logger, "Asserted constraints for reachability probabilities.");
|
|
|
|
// Add constraints that ensure the reachability of an unproblematic state from each problematic state.
|
|
numberOfConstraints += assertUnproblematicStateReachable(solver, labeledMdp, stateInformation, choiceInformation, variableInformation);
|
|
LOG4CPLUS_DEBUG(logger, "Asserted that unproblematic state reachable from problematic states.");
|
|
|
|
// Add constraints that express that certain labels are already known to be taken.
|
|
numberOfConstraints += assertKnownLabels(solver, labeledMdp, psiStates, choiceInformation, variableInformation);
|
|
LOG4CPLUS_DEBUG(logger, "Asserted known labels are taken.");
|
|
|
|
// If required, assert additional constraints that reduce the number of possible policies.
|
|
if (includeSchedulerCuts) {
|
|
numberOfConstraints += assertSchedulerCuts(solver, labeledMdp, psiStates, stateInformation, choiceInformation, variableInformation);
|
|
LOG4CPLUS_DEBUG(logger, "Asserted scheduler cuts.");
|
|
}
|
|
|
|
// Finally, we can tell the solver to incorporate the latest changes.
|
|
solver.update();
|
|
|
|
LOG4CPLUS_INFO(logger, "Successfully created " << numberOfConstraints << " MILP constraints.");
|
|
}
|
|
|
|
/*!
|
|
* Computes the set of labels that was used in the given optimized model.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
*/
|
|
static boost::container::flat_set<uint_fast64_t> getUsedLabelsInSolution(storm::solver::LpSolver const& solver, VariableInformation const& variableInformation) {
|
|
boost::container::flat_set<uint_fast64_t> result;
|
|
|
|
for (auto const& labelVariablePair : variableInformation.labelToVariableMap) {
|
|
bool labelTaken = solver.getBinaryValue(labelVariablePair.second);
|
|
|
|
if (labelTaken) {
|
|
result.insert(labelVariablePair.first);
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/*!
|
|
* Computes a mapping from relevant states to choices such that a state is mapped to one of its choices if
|
|
* it is selected by the subsystem computed by the solver.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param stateInformation The information about the states in the model.
|
|
* @param choiceInformation The information about the choices in the model.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
*/
|
|
static std::map<uint_fast64_t, uint_fast64_t> getChoices(storm::solver::LpSolver const& solver, storm::models::sparse::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
|
|
std::map<uint_fast64_t, uint_fast64_t> result;
|
|
|
|
for (auto state : stateInformation.relevantStates) {
|
|
std::list<storm::expressions::Variable>::const_iterator choiceVariableIterator = variableInformation.stateToChoiceVariablesIndexMap.at(state).begin();
|
|
for (auto choice : choiceInformation.relevantChoicesForRelevantStates.at(state)) {
|
|
bool choiceTaken = solver.getBinaryValue(*choiceVariableIterator);
|
|
++choiceVariableIterator;
|
|
if (choiceTaken) {
|
|
result.emplace_hint(result.end(), state, choice);
|
|
}
|
|
}
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
/*!
|
|
* Computes the reachability probability and the selected initial state in the given optimized MILP model.
|
|
*
|
|
* @param solver The MILP solver.
|
|
* @param labeledMdp The labeled MDP.
|
|
* @param variableInformation A struct with information about the variables of the model.
|
|
*/
|
|
static std::pair<uint_fast64_t, double> getReachabilityProbability(storm::solver::LpSolver const& solver, storm::models::sparse::Mdp<T> const& labeledMdp, VariableInformation const& variableInformation) {
|
|
uint_fast64_t selectedInitialState = 0;
|
|
for (auto const& initialStateVariablePair : variableInformation.initialStateToChoiceVariableMap) {
|
|
bool initialStateChosen = solver.getBinaryValue(initialStateVariablePair.second);
|
|
if (initialStateChosen) {
|
|
selectedInitialState = initialStateVariablePair.first;
|
|
break;
|
|
}
|
|
}
|
|
|
|
double reachabilityProbability = solver.getContinuousValue(variableInformation.virtualInitialStateVariable);
|
|
return std::make_pair(selectedInitialState, reachabilityProbability);
|
|
}
|
|
|
|
public:
|
|
|
|
static boost::container::flat_set<uint_fast64_t> getMinimalLabelSet(storm::logic::Formula const& pathFormula, storm::models::sparse::Mdp<T> const& labeledMdp, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, double probabilityThreshold, bool strictBound, bool checkThresholdFeasible = false, bool includeSchedulerCuts = false) {
|
|
// (0) Check whether the MDP is indeed labeled.
|
|
if (!labeledMdp.hasChoiceLabeling()) {
|
|
throw storm::exceptions::InvalidArgumentException() << "Minimal label set generation is impossible for unlabeled model.";
|
|
}
|
|
|
|
// (1) Check whether its possible to exceed the threshold if checkThresholdFeasible is set.
|
|
double maximalReachabilityProbability = 0;
|
|
if (checkThresholdFeasible) {
|
|
storm::modelchecker::helper::SparseMdpPrctlHelper<T> modelcheckerHelper;
|
|
std::vector<T> result = std::move(modelcheckerHelper.computeUntilProbabilities(false, labeledMdp.getTransitionMatrix(), labeledMdp.getBackwardTransitions(), phiStates, psiStates, false, false, storm::utility::solver::MinMaxLinearEquationSolverFactory<T>()).result);
|
|
for (auto state : labeledMdp.getInitialStates()) {
|
|
maximalReachabilityProbability = std::max(maximalReachabilityProbability, result[state]);
|
|
}
|
|
STORM_LOG_THROW((strictBound && maximalReachabilityProbability >= probabilityThreshold) || (!strictBound && maximalReachabilityProbability > probabilityThreshold), storm::exceptions::InvalidArgumentException, "Given probability threshold " << probabilityThreshold << " can not be " << (strictBound ? "achieved" : "exceeded") << " in model with maximal reachability probability of " << maximalReachabilityProbability << ".");
|
|
std::cout << std::endl << "Maximal reachability in model is " << maximalReachabilityProbability << "." << std::endl << std::endl;
|
|
}
|
|
|
|
// (2) Identify relevant and problematic states.
|
|
StateInformation stateInformation = determineRelevantAndProblematicStates(labeledMdp, phiStates, psiStates);
|
|
|
|
// (3) Determine sets of relevant labels and problematic choices.
|
|
ChoiceInformation choiceInformation = determineRelevantAndProblematicChoices(labeledMdp, stateInformation, psiStates);
|
|
|
|
// (4) Encode resulting system as MILP problem.
|
|
std::shared_ptr<storm::solver::LpSolver> solver = storm::utility::solver::getLpSolver("MinimalCommandSetCounterexample");
|
|
|
|
// (4.1) Create variables.
|
|
VariableInformation variableInformation = createVariables(*solver, labeledMdp, stateInformation, choiceInformation);
|
|
|
|
// (4.2) Construct constraint system.
|
|
buildConstraintSystem(*solver, labeledMdp, psiStates, stateInformation, choiceInformation, variableInformation, probabilityThreshold, strictBound, includeSchedulerCuts);
|
|
|
|
// (4.3) Optimize the model.
|
|
solver->optimize();
|
|
|
|
// (4.4) Read off result from variables.
|
|
boost::container::flat_set<uint_fast64_t> usedLabelSet = getUsedLabelsInSolution(*solver, variableInformation);
|
|
usedLabelSet.insert(choiceInformation.knownLabels.begin(), choiceInformation.knownLabels.end());
|
|
|
|
// (5) Return result.
|
|
return usedLabelSet;
|
|
}
|
|
|
|
/*!
|
|
* Computes a (minimally labeled) counterexample for the given model and (safety) formula. If the model satisfies the property, an exception is thrown.
|
|
*
|
|
* @param labeledMdp A labeled MDP that is the model in which to generate the counterexample.
|
|
* @param formulaPtr A pointer to a safety formula. The outermost operator must be a probabilistic bound operator with a strict upper bound. The nested
|
|
* formula can be either an unbounded until formula or an eventually formula.
|
|
*/
|
|
static void computeCounterexample(storm::prism::Program const& program, storm::models::sparse::Mdp<T> const& labeledMdp, std::shared_ptr<const storm::logic::Formula> const& formula) {
|
|
std::cout << std::endl << "Generating minimal label counterexample for formula " << *formula << std::endl;
|
|
|
|
STORM_LOG_THROW(formula->isProbabilityOperatorFormula(), storm::exceptions::InvalidPropertyException, "Counterexample generation does not support this kind of formula. Expecting a probability operator as the outermost formula element.");
|
|
storm::logic::ProbabilityOperatorFormula const& probabilityOperator = formula->asProbabilityOperatorFormula();
|
|
STORM_LOG_THROW(probabilityOperator.hasBound(), storm::exceptions::InvalidPropertyException, "Counterexample generation only supports bounded formulas.");
|
|
storm::logic::ComparisonType comparisonType = probabilityOperator.getComparisonType();
|
|
STORM_LOG_THROW(comparisonType == storm::logic::ComparisonType::Less || comparisonType == storm::logic::ComparisonType::LessEqual, storm::exceptions::InvalidPropertyException, "Counterexample generation only supports formulas with an upper probability bound.");
|
|
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.");
|
|
|
|
bool strictBound = comparisonType == storm::logic::ComparisonType::Less;
|
|
double bound = probabilityOperator.getBound();
|
|
|
|
storm::storage::BitVector phiStates;
|
|
storm::storage::BitVector psiStates;
|
|
storm::modelchecker::SparsePropositionalModelChecker<storm::models::sparse::Mdp<T>> modelchecker(labeledMdp);
|
|
|
|
if (probabilityOperator.getSubformula().isUntilFormula()) {
|
|
storm::logic::UntilFormula const& untilFormula = probabilityOperator.getSubformula().asUntilFormula();
|
|
|
|
std::unique_ptr<storm::modelchecker::CheckResult> leftResult = modelchecker.check(untilFormula.getLeftSubformula());
|
|
std::unique_ptr<storm::modelchecker::CheckResult> rightResult = modelchecker.check(untilFormula.getRightSubformula());
|
|
|
|
storm::modelchecker::ExplicitQualitativeCheckResult const& leftQualitativeResult = leftResult->asExplicitQualitativeCheckResult();
|
|
storm::modelchecker::ExplicitQualitativeCheckResult const& rightQualitativeResult = rightResult->asExplicitQualitativeCheckResult();
|
|
|
|
phiStates = leftQualitativeResult.getTruthValuesVector();
|
|
psiStates = rightQualitativeResult.getTruthValuesVector();
|
|
} else if (probabilityOperator.getSubformula().isEventuallyFormula()) {
|
|
storm::logic::EventuallyFormula const& eventuallyFormula = probabilityOperator.getSubformula().asEventuallyFormula();
|
|
|
|
std::unique_ptr<storm::modelchecker::CheckResult> subResult = modelchecker.check(eventuallyFormula.getSubformula());
|
|
|
|
storm::modelchecker::ExplicitQualitativeCheckResult const& subQualitativeResult = subResult->asExplicitQualitativeCheckResult();
|
|
|
|
phiStates = storm::storage::BitVector(labeledMdp.getNumberOfStates(), true);
|
|
psiStates = subQualitativeResult.getTruthValuesVector();
|
|
}
|
|
|
|
// Delegate the actual computation work to the function of equal name.
|
|
auto startTime = std::chrono::high_resolution_clock::now();
|
|
boost::container::flat_set<uint_fast64_t> usedLabelSet = getMinimalLabelSet(probabilityOperator.getSubformula(), labeledMdp, phiStates, psiStates, bound, strictBound, true, storm::settings::counterexampleGeneratorSettings().isUseSchedulerCutsSet());
|
|
auto endTime = std::chrono::high_resolution_clock::now();
|
|
std::cout << std::endl << "Computed minimal label set of size " << usedLabelSet.size() << " in " << std::chrono::duration_cast<std::chrono::milliseconds>(endTime - startTime).count() << "ms." << std::endl;
|
|
|
|
std::cout << "Resulting program:" << std::endl;
|
|
storm::prism::Program restrictedProgram = program.restrictCommands(usedLabelSet);
|
|
std::cout << restrictedProgram << std::endl;
|
|
std::cout << std::endl << "-------------------------------------------" << std::endl;
|
|
}
|
|
|
|
};
|
|
|
|
} // namespace counterexamples
|
|
} // namespace storm
|
|
|
|
#endif /* STORM_COUNTEREXAMPLES_MILPMINIMALLABELSETGENERATOR_MDP_H_ */
|