#include "src/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.h"
#include "src/modelchecker/prctl/helper/SparseMdpPrctlHelper.h"
#include "src/models/sparse/StandardRewardModel.h"
#include "src/storage/StronglyConnectedComponentDecomposition.h"
#include "src/storage/MaximalEndComponentDecomposition.h"
#include "src/settings/SettingsManager.h"
#include "src/settings/modules/GeneralSettings.h"
#include "src/utility/macros.h"
#include "src/utility/vector.h"
#include "src/utility/graph.h"
#include "src/storage/expressions/Variable.h"
#include "src/storage/expressions/Expression.h"
#include "src/utility/numerical.h"
#include "src/solver/MinMaxLinearEquationSolver.h"
#include "src/solver/LpSolver.h"
#include "src/exceptions/InvalidStateException.h"
#include "src/exceptions/InvalidPropertyException.h"
namespace storm {
namespace modelchecker {
namespace helper {
template<typename ValueType>
void SparseMarkovAutomatonCslHelper<ValueType>::computeBoundedReachabilityProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRates, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& goalStates, storm::storage::BitVector const& markovianNonGoalStates, storm::storage::BitVector const& probabilisticNonGoalStates, std::vector<ValueType>& markovianNonGoalValues, std::vector<ValueType>& probabilisticNonGoalValues, ValueType delta, uint_fast64_t numberOfSteps, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Start by computing four sparse matrices:
// * a matrix aMarkovian with all (discretized) transitions from Markovian non-goal states to all Markovian non-goal states.
// * a matrix aMarkovianToProbabilistic with all (discretized) transitions from Markovian non-goal states to all probabilistic non-goal states.
// * a matrix aProbabilistic with all (non-discretized) transitions from probabilistic non-goal states to other probabilistic non-goal states.
// * a matrix aProbabilisticToMarkovian with all (non-discretized) transitions from probabilistic non-goal states to all Markovian non-goal states.
typename storm::storage::SparseMatrix<ValueType> aMarkovian = transitionMatrix.getSubmatrix(true, markovianNonGoalStates, markovianNonGoalStates, true);
typename storm::storage::SparseMatrix<ValueType> aMarkovianToProbabilistic = transitionMatrix.getSubmatrix(true, markovianNonGoalStates, probabilisticNonGoalStates);
typename storm::storage::SparseMatrix<ValueType> aProbabilistic = transitionMatrix.getSubmatrix(true, probabilisticNonGoalStates, probabilisticNonGoalStates);
typename storm::storage::SparseMatrix<ValueType> aProbabilisticToMarkovian = transitionMatrix.getSubmatrix(true, probabilisticNonGoalStates, markovianNonGoalStates);
// The matrices with transitions from Markovian states need to be digitized.
// Digitize aMarkovian. Based on whether the transition is a self-loop or not, we apply the two digitization rules.
uint_fast64_t rowIndex = 0;
for (auto state : markovianNonGoalStates) {
for (auto& element : aMarkovian.getRow(rowIndex)) {
ValueType eTerm = std::exp(-exitRates[state] * delta);
if (element.getColumn() == rowIndex) {
element.setValue((storm::utility::one<ValueType>() - eTerm) * element.getValue() + eTerm);
} else {
element.setValue((storm::utility::one<ValueType>() - eTerm) * element.getValue());
}
}
++rowIndex;
}
// Digitize aMarkovianToProbabilistic. As there are no self-loops in this case, we only need to apply the digitization formula for regular successors.
rowIndex = 0;
for (auto state : markovianNonGoalStates) {
for (auto& element : aMarkovianToProbabilistic.getRow(rowIndex)) {
element.setValue((1 - std::exp(-exitRates[state] * delta)) * element.getValue());
}
++rowIndex;
}
// Initialize the two vectors that hold the variable one-step probabilities to all target states for probabilistic and Markovian (non-goal) states.
std::vector<ValueType> bProbabilistic(aProbabilistic.getRowCount());
std::vector<ValueType> bMarkovian(markovianNonGoalStates.getNumberOfSetBits());
// Compute the two fixed right-hand side vectors, one for Markovian states and one for the probabilistic ones.
std::vector<ValueType> bProbabilisticFixed = transitionMatrix.getConstrainedRowSumVector(probabilisticNonGoalStates, goalStates);
std::vector<ValueType> bMarkovianFixed;
bMarkovianFixed.reserve(markovianNonGoalStates.getNumberOfSetBits());
for (auto state : markovianNonGoalStates) {
bMarkovianFixed.push_back(storm::utility::zero<ValueType>());
for (auto& element : transitionMatrix.getRowGroup(state)) {
if (goalStates.get(element.getColumn())) {
bMarkovianFixed.back() += (1 - std::exp(-exitRates[state] * delta)) * element.getValue();
}
}
}
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(aProbabilistic);
// Perform the actual value iteration
// * loop until the step bound has been reached
// * in the loop:
// * perform value iteration using A_PSwG, v_PS and the vector b where b = (A * 1_G)|PS + A_PStoMS * v_MS
// and 1_G being the characteristic vector for all goal states.
// * perform one timed-step using v_MS := A_MSwG * v_MS + A_MStoPS * v_PS + (A * 1_G)|MS
std::vector<ValueType> markovianNonGoalValuesSwap(markovianNonGoalValues);
std::vector<ValueType> multiplicationResultScratchMemory(aProbabilistic.getRowCount());
std::vector<ValueType> aProbabilisticScratchMemory(probabilisticNonGoalValues.size());
for (uint_fast64_t currentStep = 0; currentStep < numberOfSteps; ++currentStep) {
// Start by (re-)computing bProbabilistic = bProbabilisticFixed + aProbabilisticToMarkovian * vMarkovian.
aProbabilisticToMarkovian.multiplyWithVector(markovianNonGoalValues, bProbabilistic);
storm::utility::vector::addVectors(bProbabilistic, bProbabilisticFixed, bProbabilistic);
// Now perform the inner value iteration for probabilistic states.
solver->solveEquationSystem(dir, probabilisticNonGoalValues, bProbabilistic, &multiplicationResultScratchMemory, &aProbabilisticScratchMemory);
// (Re-)compute bMarkovian = bMarkovianFixed + aMarkovianToProbabilistic * vProbabilistic.
aMarkovianToProbabilistic.multiplyWithVector(probabilisticNonGoalValues, bMarkovian);
storm::utility::vector::addVectors(bMarkovian, bMarkovianFixed, bMarkovian);
aMarkovian.multiplyWithVector(markovianNonGoalValues, markovianNonGoalValuesSwap);
std::swap(markovianNonGoalValues, markovianNonGoalValuesSwap);
storm::utility::vector::addVectors(markovianNonGoalValues, bMarkovian, markovianNonGoalValues);
}
// After the loop, perform one more step of the value iteration for PS states.
aProbabilisticToMarkovian.multiplyWithVector(markovianNonGoalValues, bProbabilistic);
storm::utility::vector::addVectors(bProbabilistic, bProbabilisticFixed, bProbabilistic);
solver->solveEquationSystem(dir, probabilisticNonGoalValues, bProbabilistic, &multiplicationResultScratchMemory, &aProbabilisticScratchMemory);
}
template<typename ValueType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper<ValueType>::computeBoundedUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, double lowerBound, double upperBound, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
uint_fast64_t numberOfStates = transitionMatrix.getRowGroupCount();
// (1) Compute the accuracy we need to achieve the required error bound.
ValueType maxExitRate = 0;
for (auto value : exitRateVector) {
maxExitRate = std::max(maxExitRate, value);
}
ValueType delta = (2 * storm::settings::generalSettings().getPrecision()) / (upperBound * maxExitRate * maxExitRate);
// (2) Compute the number of steps we need to make for the interval.
uint_fast64_t numberOfSteps = static_cast<uint_fast64_t>(std::ceil((upperBound - lowerBound) / delta));
STORM_LOG_INFO("Performing " << numberOfSteps << " iterations (delta=" << delta << ") for interval [" << lowerBound << ", " << upperBound << "]." << std::endl);
// (3) Compute the non-goal states and initialize two vectors
// * vProbabilistic holds the probability values of probabilistic non-goal states.
// * vMarkovian holds the probability values of Markovian non-goal states.
storm::storage::BitVector const& markovianNonGoalStates = markovianStates & ~psiStates;
storm::storage::BitVector const& probabilisticNonGoalStates = ~markovianStates & ~psiStates;
std::vector<ValueType> vProbabilistic(probabilisticNonGoalStates.getNumberOfSetBits());
std::vector<ValueType> vMarkovian(markovianNonGoalStates.getNumberOfSetBits());
computeBoundedReachabilityProbabilities(dir, transitionMatrix, exitRateVector, markovianStates, psiStates, markovianNonGoalStates, probabilisticNonGoalStates, vMarkovian, vProbabilistic, delta, numberOfSteps, minMaxLinearEquationSolverFactory);
// (4) If the lower bound of interval was non-zero, we need to take the current values as the starting values for a subsequent value iteration.
if (lowerBound != storm::utility::zero<ValueType>()) {
std::vector<ValueType> vAllProbabilistic((~markovianStates).getNumberOfSetBits());
std::vector<ValueType> vAllMarkovian(markovianStates.getNumberOfSetBits());
// Create the starting value vectors for the next value iteration based on the results of the previous one.
storm::utility::vector::setVectorValues<ValueType>(vAllProbabilistic, psiStates % ~markovianStates, storm::utility::one<ValueType>());
storm::utility::vector::setVectorValues<ValueType>(vAllProbabilistic, ~psiStates % ~markovianStates, vProbabilistic);
storm::utility::vector::setVectorValues<ValueType>(vAllMarkovian, psiStates % markovianStates, storm::utility::one<ValueType>());
storm::utility::vector::setVectorValues<ValueType>(vAllMarkovian, ~psiStates % markovianStates, vMarkovian);
// Compute the number of steps to reach the target interval.
numberOfSteps = static_cast<uint_fast64_t>(std::ceil(lowerBound / delta));
STORM_LOG_INFO("Performing " << numberOfSteps << " iterations (delta=" << delta << ") for interval [0, " << lowerBound << "]." << std::endl);
// Compute the bounded reachability for interval [0, b-a].
computeBoundedReachabilityProbabilities(dir, transitionMatrix, exitRateVector, markovianStates, storm::storage::BitVector(numberOfStates), markovianStates, ~markovianStates, vAllMarkovian, vAllProbabilistic, delta, numberOfSteps, minMaxLinearEquationSolverFactory);
// Create the result vector out of vAllProbabilistic and vAllMarkovian and return it.
std::vector<ValueType> result(numberOfStates, storm::utility::zero<ValueType>());
storm::utility::vector::setVectorValues(result, ~markovianStates, vAllProbabilistic);
storm::utility::vector::setVectorValues(result, markovianStates, vAllMarkovian);
return result;
} else {
// Create the result vector out of 1_G, vProbabilistic and vMarkovian and return it.
std::vector<ValueType> result(numberOfStates);
storm::utility::vector::setVectorValues<ValueType>(result, psiStates, storm::utility::one<ValueType>());
storm::utility::vector::setVectorValues(result, probabilisticNonGoalStates, vProbabilistic);
storm::utility::vector::setVectorValues(result, markovianNonGoalStates, vMarkovian);
return result;
}
}
template<typename ValueType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper<ValueType>::computeUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
return std::move(storm::modelchecker::helper::SparseMdpPrctlHelper<ValueType>::computeUntilProbabilities(dir, transitionMatrix, backwardTransitions, phiStates, psiStates, qualitative, false, minMaxLinearEquationSolverFactory).values);
}
template <typename ValueType>
template <typename RewardModelType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper<ValueType>::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::BitVector const& psiStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
std::vector<ValueType> totalRewardVector = rewardModel.getTotalRewardVector(transitionMatrix.getRowCount(), transitionMatrix, storm::storage::BitVector(transitionMatrix.getRowGroupCount(), true));
return computeExpectedRewards(dir, transitionMatrix, backwardTransitions, exitRateVector, markovianStates, psiStates, totalRewardVector, minMaxLinearEquationSolverFactory);
}
template<typename ValueType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper<ValueType>::computeLongRunAverageProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
uint_fast64_t numberOfStates = transitionMatrix.getRowGroupCount();
// If there are no goal states, we avoid the computation and directly return zero.
if (psiStates.empty()) {
return std::vector<ValueType>(numberOfStates, storm::utility::zero<ValueType>());
}
// Likewise, if all bits are set, we can avoid the computation and set.
if ((~psiStates).empty()) {
return std::vector<ValueType>(numberOfStates, storm::utility::one<ValueType>());
}
// Start by decomposing the Markov automaton into its MECs.
storm::storage::MaximalEndComponentDecomposition<double> mecDecomposition(transitionMatrix, backwardTransitions);
// Get some data members for convenience.
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
// Now start with compute the long-run average for all end components in isolation.
std::vector<ValueType> lraValuesForEndComponents;
// While doing so, we already gather some information for the following steps.
std::vector<uint_fast64_t> stateToMecIndexMap(numberOfStates);
storm::storage::BitVector statesInMecs(numberOfStates);
for (uint_fast64_t currentMecIndex = 0; currentMecIndex < mecDecomposition.size(); ++currentMecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[currentMecIndex];
// Gather information for later use.
for (auto const& stateChoicesPair : mec) {
uint_fast64_t state = stateChoicesPair.first;
statesInMecs.set(state);
stateToMecIndexMap[state] = currentMecIndex;
}
// Compute the LRA value for the current MEC.
lraValuesForEndComponents.push_back(computeLraForMaximalEndComponent(dir, transitionMatrix, exitRateVector, markovianStates, psiStates, mec));
}
// For fast transition rewriting, we build some auxiliary data structures.
storm::storage::BitVector statesNotContainedInAnyMec = ~statesInMecs;
uint_fast64_t firstAuxiliaryStateIndex = statesNotContainedInAnyMec.getNumberOfSetBits();
uint_fast64_t lastStateNotInMecs = 0;
uint_fast64_t numberOfStatesNotInMecs = 0;
std::vector<uint_fast64_t> statesNotInMecsBeforeIndex;
statesNotInMecsBeforeIndex.reserve(numberOfStates);
for (auto state : statesNotContainedInAnyMec) {
while (lastStateNotInMecs <= state) {
statesNotInMecsBeforeIndex.push_back(numberOfStatesNotInMecs);
++lastStateNotInMecs;
}
++numberOfStatesNotInMecs;
}
// Finally, we are ready to create the SSP matrix and right-hand side of the SSP.
std::vector<ValueType> b;
typename storm::storage::SparseMatrixBuilder<ValueType> sspMatrixBuilder(0, 0, 0, false, true, numberOfStatesNotInMecs + mecDecomposition.size());
// If the source state is not contained in any MEC, we copy its choices (and perform the necessary modifications).
uint_fast64_t currentChoice = 0;
for (auto state : statesNotContainedInAnyMec) {
sspMatrixBuilder.newRowGroup(currentChoice);
for (uint_fast64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice, ++currentChoice) {
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
b.push_back(storm::utility::zero<ValueType>());
for (auto element : transitionMatrix.getRow(choice)) {
if (statesNotContainedInAnyMec.get(element.getColumn())) {
// If the target state is not contained in an MEC, we can copy over the entry.
sspMatrixBuilder.addNextValue(currentChoice, statesNotInMecsBeforeIndex[element.getColumn()], element.getValue());
} else {
// If the target state is contained in MEC i, we need to add the probability to the corresponding field in the vector
// so that we are able to write the cumulative probability to the MEC into the matrix.
auxiliaryStateToProbabilityMap[stateToMecIndexMap[element.getColumn()]] += element.getValue();
}
}
// Now insert all (cumulative) probability values that target an MEC.
for (uint_fast64_t mecIndex = 0; mecIndex < auxiliaryStateToProbabilityMap.size(); ++mecIndex) {
if (auxiliaryStateToProbabilityMap[mecIndex] != 0) {
sspMatrixBuilder.addNextValue(currentChoice, firstAuxiliaryStateIndex + mecIndex, auxiliaryStateToProbabilityMap[mecIndex]);
}
}
}
}
// Now we are ready to construct the choices for the auxiliary states.
for (uint_fast64_t mecIndex = 0; mecIndex < mecDecomposition.size(); ++mecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[mecIndex];
sspMatrixBuilder.newRowGroup(currentChoice);
for (auto const& stateChoicesPair : mec) {
uint_fast64_t state = stateChoicesPair.first;
boost::container::flat_set<uint_fast64_t> const& choicesInMec = stateChoicesPair.second;
for (uint_fast64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice) {
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
// If the choice is not contained in the MEC itself, we have to add a similar distribution to the auxiliary state.
if (choicesInMec.find(choice) == choicesInMec.end()) {
b.push_back(storm::utility::zero<ValueType>());
for (auto element : transitionMatrix.getRow(choice)) {
if (statesNotContainedInAnyMec.get(element.getColumn())) {
// If the target state is not contained in an MEC, we can copy over the entry.
sspMatrixBuilder.addNextValue(currentChoice, statesNotInMecsBeforeIndex[element.getColumn()], element.getValue());
} else {
// If the target state is contained in MEC i, we need to add the probability to the corresponding field in the vector
// so that we are able to write the cumulative probability to the MEC into the matrix.
auxiliaryStateToProbabilityMap[stateToMecIndexMap[element.getColumn()]] += element.getValue();
}
}
// Now insert all (cumulative) probability values that target an MEC.
for (uint_fast64_t targetMecIndex = 0; targetMecIndex < auxiliaryStateToProbabilityMap.size(); ++targetMecIndex) {
if (auxiliaryStateToProbabilityMap[targetMecIndex] != 0) {
sspMatrixBuilder.addNextValue(currentChoice, firstAuxiliaryStateIndex + targetMecIndex, auxiliaryStateToProbabilityMap[targetMecIndex]);
}
}
++currentChoice;
}
}
}
// For each auxiliary state, there is the option to achieve the reward value of the LRA associated with the MEC.
++currentChoice;
b.push_back(lraValuesForEndComponents[mecIndex]);
}
// Finalize the matrix and solve the corresponding system of equations.
storm::storage::SparseMatrix<ValueType> sspMatrix = sspMatrixBuilder.build(currentChoice);
std::vector<ValueType> x(numberOfStatesNotInMecs + mecDecomposition.size());
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(sspMatrix);
solver->solveEquationSystem(dir, x, b);
// Prepare result vector.
std::vector<ValueType> result(numberOfStates);
// Set the values for states not contained in MECs.
storm::utility::vector::setVectorValues(result, statesNotContainedInAnyMec, x);
// Set the values for all states in MECs.
for (auto state : statesInMecs) {
result[state] = x[firstAuxiliaryStateIndex + stateToMecIndexMap[state]];
}
return result;
}
template <typename ValueType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper<ValueType>::computeTimes(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
uint_fast64_t numberOfStates = transitionMatrix.getRowGroupCount();
std::vector<ValueType> rewardValues(numberOfStates, storm::utility::zero<ValueType>());
storm::utility::vector::setVectorValues(rewardValues, markovianStates, storm::utility::one<ValueType>());
return computeExpectedRewards(dir, transitionMatrix, backwardTransitions, exitRateVector, markovianStates, psiStates, rewardValues, minMaxLinearEquationSolverFactory);
}
template <typename ValueType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper<ValueType>::computeExpectedRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& goalStates, std::vector<ValueType> const& stateRewards, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
uint_fast64_t numberOfStates = transitionMatrix.getRowGroupCount();
// First, we need to check which states have infinite expected time (by definition).
storm::storage::BitVector infinityStates;
if (dir ==OptimizationDirection::Minimize) {
// If we need to compute the minimum expected times, we have to set the values of those states to infinity that, under all schedulers,
// reach a bottom SCC without a goal state.
// So we start by computing all bottom SCCs without goal states.
storm::storage::StronglyConnectedComponentDecomposition<double> sccDecomposition(transitionMatrix, ~goalStates, true, true);
// Now form the union of all these SCCs.
storm::storage::BitVector unionOfNonGoalBSccs(numberOfStates);
for (auto const& scc : sccDecomposition) {
for (auto state : scc) {
unionOfNonGoalBSccs.set(state);
}
}
// Finally, if this union is non-empty, compute the states such that all schedulers reach some state of the union.
if (!unionOfNonGoalBSccs.empty()) {
infinityStates = storm::utility::graph::performProbGreater0A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, storm::storage::BitVector(numberOfStates, true), unionOfNonGoalBSccs);
} else {
// Otherwise, we have no infinity states.
infinityStates = storm::storage::BitVector(numberOfStates);
}
} else {
// If we maximize the property, the expected time of a state is infinite, if an end-component without any goal state is reachable.
// So we start by computing all MECs that have no goal state.
storm::storage::MaximalEndComponentDecomposition<double> mecDecomposition(transitionMatrix, backwardTransitions, ~goalStates);
// Now we form the union of all states in these end components.
storm::storage::BitVector unionOfNonGoalMaximalEndComponents(numberOfStates);
for (auto const& mec : mecDecomposition) {
for (auto const& stateActionPair : mec) {
unionOfNonGoalMaximalEndComponents.set(stateActionPair.first);
}
}
if (!unionOfNonGoalMaximalEndComponents.empty()) {
// Now we need to check for which states there exists a scheduler that reaches one of the previously computed states.
infinityStates = storm::utility::graph::performProbGreater0E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, storm::storage::BitVector(numberOfStates, true), unionOfNonGoalMaximalEndComponents);
} else {
// Otherwise, we have no infinity states.
infinityStates = storm::storage::BitVector(numberOfStates);
}
}
// Now we identify the states for which values need to be computed.
storm::storage::BitVector maybeStates = ~(goalStates | infinityStates);
// Create resulting vector.
std::vector<ValueType> result(numberOfStates);
if (!maybeStates.empty()) {
// Then, we can eliminate the rows and columns for all states whose values are already known.
std::vector<ValueType> x(maybeStates.getNumberOfSetBits());
storm::storage::SparseMatrix<ValueType> submatrix = transitionMatrix.getSubmatrix(true, maybeStates, maybeStates);
// Now prepare the expected reward values for all states so they can be used as the right-hand side of the equation system.
std::vector<ValueType> rewardValues(stateRewards);
for (auto state : markovianStates) {
rewardValues[state] = rewardValues[state] / exitRateVector[state];
}
// Finally, prepare the actual right-hand side.
std::vector<ValueType> b(submatrix.getRowCount());
storm::utility::vector::selectVectorValuesRepeatedly(b, maybeStates, transitionMatrix.getRowGroupIndices(), rewardValues);
// Solve the corresponding system of equations.
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(submatrix);
solver->solveEquationSystem(dir, x, b);
// Set values of resulting vector according to previous result and return the result.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, x);
}
storm::utility::vector::setVectorValues(result, goalStates, storm::utility::zero<ValueType>());
storm::utility::vector::setVectorValues(result, infinityStates, storm::utility::infinity<ValueType>());
return result;
}
template<typename ValueType>
ValueType SparseMarkovAutomatonCslHelper<ValueType>::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& goalStates, storm::storage::MaximalEndComponent const& mec) {
std::unique_ptr<storm::utility::solver::LpSolverFactory> lpSolverFactory(new storm::utility::solver::LpSolverFactory());
std::unique_ptr<storm::solver::LpSolver> solver = lpSolverFactory->create("LRA for MEC");
solver->setOptimizationDirection(invert(dir));
// First, we need to create the variables for the problem.
std::map<uint_fast64_t, storm::expressions::Variable> stateToVariableMap;
for (auto const& stateChoicesPair : mec) {
std::string variableName = "x" + std::to_string(stateChoicesPair.first);
stateToVariableMap[stateChoicesPair.first] = solver->addUnboundedContinuousVariable(variableName);
}
storm::expressions::Variable k = solver->addUnboundedContinuousVariable("k", 1);
solver->update();
// Now we encode the problem as constraints.
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
for (auto const& stateChoicesPair : mec) {
uint_fast64_t state = stateChoicesPair.first;
// Now, based on the type of the state, create a suitable constraint.
if (markovianStates.get(state)) {
storm::expressions::Expression constraint = stateToVariableMap.at(state);
for (auto element : transitionMatrix.getRow(nondeterministicChoiceIndices[state])) {
constraint = constraint - stateToVariableMap.at(element.getColumn()) * solver->getConstant(element.getValue());
}
constraint = constraint + solver->getConstant(storm::utility::one<ValueType>() / exitRateVector[state]) * k;
storm::expressions::Expression rightHandSide = goalStates.get(state) ? solver->getConstant(storm::utility::one<ValueType>() / exitRateVector[state]) : solver->getConstant(0);
if (dir == OptimizationDirection::Minimize) {
constraint = constraint <= rightHandSide;
} else {
constraint = constraint >= rightHandSide;
}
solver->addConstraint("state" + std::to_string(state), constraint);
} else {
// For probabilistic states, we want to add the constraint x_s <= sum P(s, a, s') * x_s' where a is the current action
// and the sum ranges over all states s'.
for (auto choice : stateChoicesPair.second) {
storm::expressions::Expression constraint = stateToVariableMap.at(state);
for (auto element : transitionMatrix.getRow(choice)) {
constraint = constraint - stateToVariableMap.at(element.getColumn()) * solver->getConstant(element.getValue());
}
storm::expressions::Expression rightHandSide = solver->getConstant(storm::utility::zero<ValueType>());
if (dir == OptimizationDirection::Minimize) {
constraint = constraint <= rightHandSide;
} else {
constraint = constraint >= rightHandSide;
}
solver->addConstraint("state" + std::to_string(state), constraint);
}
}
}
solver->optimize();
return solver->getContinuousValue(k);
}
template class SparseMarkovAutomatonCslHelper<double>;
template std::vector<double> SparseMarkovAutomatonCslHelper<double>::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::BitVector const& psiStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
}
}
}