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tempest/src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHel...

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#include "storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.h"
#include "storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.h"
#include "storm/models/sparse/StandardRewardModel.h"
#include "storm/storage/StronglyConnectedComponentDecomposition.h"
#include "storm/storage/MaximalEndComponentDecomposition.h"
#include "storm/settings/SettingsManager.h"
#include "storm/settings/modules/GeneralSettings.h"
#include "storm/settings/modules/MinMaxEquationSolverSettings.h"
#include "storm/settings/modules/MarkovAutomatonSettings.h"
#include "storm/environment/Environment.h"
#include "storm/utility/macros.h"
#include "storm/utility/vector.h"
#include "storm/utility/graph.h"
#include "storm/storage/expressions/Variable.h"
#include "storm/storage/expressions/Expression.h"
#include "storm/storage/expressions/ExpressionManager.h"
//#include "storm/utility/numerical.h"
#include "storm/solver/MinMaxLinearEquationSolver.h"
#include "storm/solver/LpSolver.h"
#include "storm/exceptions/InvalidStateException.h"
#include "storm/exceptions/InvalidPropertyException.h"
#include "storm/exceptions/InvalidOperationException.h"
#include "storm/exceptions/UncheckedRequirementException.h"
namespace storm {
namespace modelchecker {
namespace helper {
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
void SparseMarkovAutomatonCslHelper::computeBoundedReachabilityProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRates, 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, uint64_t numberOfSteps, storm::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);
bool existProbabilisticStates = !probabilisticNonGoalStates.empty();
typename storm::storage::SparseMatrix<ValueType> aMarkovianToProbabilistic;
typename storm::storage::SparseMatrix<ValueType> aProbabilistic;
typename storm::storage::SparseMatrix<ValueType> aProbabilisticToMarkovian;
if (existProbabilisticStates) {
aMarkovianToProbabilistic = transitionMatrix.getSubmatrix(true, markovianNonGoalStates, probabilisticNonGoalStates);
aProbabilistic = transitionMatrix.getSubmatrix(true, probabilisticNonGoalStates, probabilisticNonGoalStates);
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.
uint64_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.
if (existProbabilisticStates) {
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(existProbabilisticStates ? aProbabilistic.getRowCount() : 0);
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;
if (existProbabilisticStates) {
bProbabilisticFixed = transitionMatrix.getConstrainedRowGroupSumVector(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();
}
}
}
// Check for requirements of the solver.
// The solution is unique as we assume non-zeno MAs.
storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(env, true, dir, true);
requirements.clearBounds();
STORM_LOG_THROW(requirements.empty(), storm::exceptions::UncheckedRequirementException, "Cannot establish requirements for solver.");
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(env, aProbabilistic);
solver->setHasUniqueSolution();
solver->setBounds(storm::utility::zero<ValueType>(), storm::utility::one<ValueType>());
solver->setRequirementsChecked();
solver->setCachingEnabled(true);
// 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);
for (uint64_t currentStep = 0; currentStep < numberOfSteps; ++currentStep) {
if (existProbabilisticStates) {
// 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->solveEquations(env, dir, probabilisticNonGoalValues, bProbabilistic);
// (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);
if (existProbabilisticStates) {
storm::utility::vector::addVectors(markovianNonGoalValues, bMarkovian, markovianNonGoalValues);
} else {
storm::utility::vector::addVectors(markovianNonGoalValues, bMarkovianFixed, markovianNonGoalValues);
}
}
if (existProbabilisticStates) {
// 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->solveEquations(env, dir, probabilisticNonGoalValues, bProbabilistic);
}
}
template <typename ValueType, typename std::enable_if<!storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
void SparseMarkovAutomatonCslHelper::computeBoundedReachabilityProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRates, 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, uint64_t numberOfSteps, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
STORM_LOG_THROW(false, storm::exceptions::InvalidOperationException, "Computing bounded reachability probabilities is unsupported for this value type.");
}
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
void SparseMarkovAutomatonCslHelper::calculateVu(Environment const& env, std::vector<std::vector<ValueType>> const& relativeReachability, OptimizationDirection dir,
uint64_t k, uint64_t node, uint64_t const kind, ValueType lambda, uint64_t probSize,
std::vector<std::vector<std::vector<ValueType>>>& unifVectors, storm::storage::SparseMatrix<ValueType> const& fullTransitionMatrix,
storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates,
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> const& solver,
storm::utility::numerical::FoxGlynnResult<ValueType> const & poisson, bool cycleFree){
if (unifVectors[1][k][node]!=-1){return;} //dynamic programming. avoiding multiple calculation.
uint64_t N = unifVectors[1].size()-1;
auto const& rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
ValueType res =0;
for (uint64_t i = k ; i < N ; i++ ){
if (unifVectors[2][N-1-(i-k)][node]==-1){
calculateUnifPlusVector(env, N-1-(i-k),node,2,lambda,probSize,relativeReachability,dir,unifVectors,fullTransitionMatrix, markovianStates,psiStates,solver, poisson, cycleFree);
}
if (i>=poisson.left && i<=poisson.right){
res+=poisson.weights[i-poisson.left]*unifVectors[2][N-1-(i-k)][node];
}
}
unifVectors[1][k][node]=res;
}
template<typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
void SparseMarkovAutomatonCslHelper::calculateUnifPlusVector(Environment const& env, uint64_t k, uint64_t node, uint64_t const kind, ValueType lambda, uint64_t probSize,
std::vector<std::vector<ValueType>> const &relativeReachability,
OptimizationDirection dir,
std::vector<std::vector<std::vector<ValueType>>> &unifVectors,
storm::storage::SparseMatrix<ValueType> const &fullTransitionMatrix,
storm::storage::BitVector const &markovianStates,
storm::storage::BitVector const &psiStates,
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> const &solver,
storm::utility::numerical::FoxGlynnResult<ValueType> const & poisson, bool cycleFree) {
if (unifVectors[kind][k][node]!=-1){
return; //already calculated
}
auto numberOfStates=fullTransitionMatrix.getRowGroupCount();
auto numberOfProbStates = numberOfStates - markovianStates.getNumberOfSetBits();
uint64_t N = unifVectors[kind].size()-1;
auto const& rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
ValueType res;
// First Case, k==N, independent from kind of state
if (k==N){
unifVectors[kind][k][node]=0;
return;
}
//goal state, independent from kind of state
if (psiStates[node]){
if (kind==0){
// Vd
res = storm::utility::zero<ValueType>();
for (uint64_t i = k ; i<N ; i++){
if (i>=poisson.left && i<=poisson.right){
ValueType between = poisson.weights[i-poisson.left];
res+=between;
}
}
unifVectors[kind][k][node]=res;
} else {
// WU
unifVectors[kind][k][node]=1;
}
return;
}
//markovian non-goal State
if (markovianStates[node]){
res = 0;
auto line = fullTransitionMatrix.getRow(rowGroupIndices[node]);
for (auto &element : line){
uint64_t to = element.getColumn();
if (unifVectors[kind][k+1][to]==-1){
calculateUnifPlusVector(env, k+1,to,kind,lambda,probSize,relativeReachability,dir,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, poisson, cycleFree);
}
res+=element.getValue()*unifVectors[kind][k+1][to];
}
unifVectors[kind][k][node]=res;
return;
}
//probabilistic non-goal State
if (cycleFree) {
//cycle free -- slight ValueIteration
res = -1;
uint64_t rowStart = rowGroupIndices[node];
uint64_t rowEnd = rowGroupIndices[node + 1];
for (uint64_t i = rowStart; i < rowEnd; i++) {
auto line = fullTransitionMatrix.getRow(i);
ValueType between = 0;
for (auto &element: line) {
uint64_t to = element.getColumn();
if (to == node) {
continue;
}
if (unifVectors[kind][k][to] == -1) {
calculateUnifPlusVector(env, k, to, kind, lambda, probSize, relativeReachability, dir,
unifVectors, fullTransitionMatrix, markovianStates, psiStates,
solver, poisson, cycleFree);
}
between += element.getValue() * unifVectors[kind][k][to];
}
if (maximize(dir)) {
res = std::max(res, between);
} else {
if (res != -1) {
res = std::min(res, between);
} else {
res = between;
}
}
}
unifVectors[kind][k][node] = res;
return;
}
//not cycle free - use solver technique, calling SVI per default
//solving all sub-MDP's in one iteration
std::vector<ValueType> b(probSize, 0), x(numberOfProbStates,0);
//calculate b
uint64_t lineCounter=0;
for (int i =0; i<numberOfStates; i++) {
if (markovianStates[i]) {
continue;
}
auto rowStart = rowGroupIndices[i];
auto rowEnd = rowGroupIndices[i + 1];
for (auto j = rowStart; j < rowEnd; j++) {
uint64_t stateCount = 0;
res = 0;
for (auto &element:fullTransitionMatrix.getRow(j)) {
auto to = element.getColumn();
if (!markovianStates[to]) {
continue;
}
if (unifVectors[kind][k][to] == -1) {
calculateUnifPlusVector(env, k, to, kind, lambda, probSize, relativeReachability, dir,
unifVectors, fullTransitionMatrix, markovianStates,
psiStates, solver, poisson, cycleFree);
}
res = res + relativeReachability[j][stateCount] * unifVectors[kind][k][to];
stateCount++;
}
b[lineCounter] = res;
lineCounter++;
}
}
solver->solveEquations(env, dir, x, b);
for (uint64_t i =0 ; i<numberOfProbStates; i++){
auto trueI = transformIndice(~markovianStates,i);
unifVectors[kind][k][trueI]=x[i];
}
//end probabilistic states
}
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
void SparseMarkovAutomatonCslHelper::deleteProbDiagonals(storm::storage::SparseMatrix<ValueType>& transitionMatrix, storm::storage::BitVector const& markovianStates){
auto const& rowGroupIndices = transitionMatrix.getRowGroupIndices();
for (uint64_t i =0; i<transitionMatrix.getRowGroupCount(); i++) {
if (markovianStates[i]) {
continue;
}
auto from = rowGroupIndices[i];
auto to = rowGroupIndices[i + 1];
for (uint64_t j = from; j < to; j++) {
ValueType selfLoop = 0;
for (auto& element: transitionMatrix.getRow(j)){
if (element.getColumn()==i){
selfLoop = element.getValue();
}
}
if (selfLoop==0){
continue;
}
for (auto& element : transitionMatrix.getRow(j)){
if (element.getColumn()!=i ){
if (selfLoop!=1){
element.setValue(element.getValue()/(1-selfLoop));
}
} else {
element.setValue(0);
}
}
}
}
}
template<typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::unifPlus(Environment const& env, OptimizationDirection dir,
std::pair<double, double> const &boundsPair,
std::vector<ValueType> const &exitRateVector,
storm::storage::SparseMatrix<ValueType> const &transitionMatrix,
storm::storage::BitVector const &markovStates,
storm::storage::BitVector const &psiStates,
storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const &minMaxLinearEquationSolverFactory) {
STORM_LOG_TRACE("Using UnifPlus to compute bounded until probabilities.");
//bitvectors to identify different kind of states
storm::storage::BitVector markovianStates = markovStates;
storm::storage::BitVector allStates(markovianStates.size(), true);
storm::storage::BitVector probabilisticStates = ~markovianStates;
//searching for SCC on Underlying MDP to decide which algorhitm is applied
storm::storage::StronglyConnectedComponentDecomposition<double> sccList(transitionMatrix, probabilisticStates, true, false);
bool cycleFree = sccList.size() == 0;
//vectors to save calculation
std::vector<std::vector<std::vector<ValueType>>> unifVectors{};
//transitions from goalStates will be ignored. still: they are not allowed to be probabilistic!
// to make sure we apply our formula and NOT the MDP algorithm
for (uint64_t i = 0; i < psiStates.size(); i++) {
if (psiStates[i]) {
markovianStates.set(i, true);
probabilisticStates.set(i, false);
}
}
//transition matrix with extended with diagonal entries. Therefore, the values can be changed during uniformisation
// exitRateVector with changeable exit Rates
std::vector<ValueType> exitRate{exitRateVector};
typename storm::storage::SparseMatrix<ValueType> fullTransitionMatrix = transitionMatrix.getSubmatrix(
true, allStates, allStates, true);
// delete diagonals - needed for VI, not vor SVI
deleteProbDiagonals(fullTransitionMatrix, markovianStates);
typename storm::storage::SparseMatrix<ValueType> probMatrix{};
uint64_t probSize = 0;
if (probabilisticStates.getNumberOfSetBits() != 0) { //work around in case there are no prob states
probMatrix = fullTransitionMatrix.getSubmatrix(true, probabilisticStates, probabilisticStates,
true);
probSize = probMatrix.getRowCount();
}
// indices for transition martrix
auto &rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
//(1) define/declare horizon, epsilon, kappa , N, lambda, maxNorm
uint64_t numberOfStates = fullTransitionMatrix.getRowGroupCount();
double T = boundsPair.second;
ValueType kappa = storm::utility::one<ValueType>() / 10; // would be better as option-parameter
ValueType epsilon = storm::settings::getModule<storm::settings::modules::GeneralSettings>().getPrecision();
ValueType lambda = exitRate[0];
for (ValueType act: exitRate) {
lambda = std::max(act, lambda);
}
uint64_t N;
ValueType maxNorm = storm::utility::zero<ValueType>();
//calculate relative ReachabilityVectors and create solver - just needed for cycles
std::vector<ValueType> in{};
std::vector<std::vector<ValueType>> relReachability(transitionMatrix.getRowCount(), in);
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver;
if (!cycleFree) {
//calculate relative reachability
for (uint64_t i = 0; i < numberOfStates; i++) {
if (markovianStates[i]) {
continue;
}
auto from = rowGroupIndices[i];
auto to = rowGroupIndices[i + 1];
for (auto j = from; j < to; j++) {
for (auto &element: fullTransitionMatrix.getRow(j)) {
if (markovianStates[element.getColumn()]) {
relReachability[j].push_back(element.getValue());
}
}
}
}
//create equitation solver
storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(
env, true, dir);
requirements.clearBounds();
STORM_LOG_THROW(requirements.empty(), storm::exceptions::UncheckedRequirementException,
"Cannot establish requirements for solver.");
if (probSize != 0) {
solver = minMaxLinearEquationSolverFactory.create(env, probMatrix);
solver->setHasUniqueSolution();
solver->setBounds(storm::utility::zero<ValueType>(), storm::utility::one<ValueType>());
solver->setRequirementsChecked();
solver->setCachingEnabled(true);
}
}
// while not close enough to precision:
do {
maxNorm = storm::utility::zero<ValueType>();
// (2) update parameter
N = ceil(lambda * T * exp(2) - log(kappa * epsilon));
// (3) uniform - just applied to markovian states
for (uint64_t i = 0; i < fullTransitionMatrix.getRowGroupCount(); i++) {
if (!markovianStates[i] || psiStates[i]) {
continue;
}
uint64_t from = rowGroupIndices[i]; //markovian state -> no Nondeterminism -> only one row
if (exitRate[i] == lambda) {
continue; //already unified
}
auto line = fullTransitionMatrix.getRow(from);
ValueType exitOld = exitRate[i];
ValueType exitNew = lambda;
for (auto &v : line) {
if (v.getColumn() == i) { //diagonal element
ValueType newSelfLoop = exitNew - exitOld + v.getValue()*exitOld;
ValueType newRate = newSelfLoop / exitNew;
v.setValue(newRate);
} else { //modify probability
ValueType propOld = v.getValue();
ValueType propNew = propOld * exitOld / exitNew;
v.setValue(propNew);
}
}
exitRate[i] = exitNew;
}
// calculate poisson distribution
storm::utility::numerical::FoxGlynnResult<ValueType> foxGlynnResult = storm::utility::numerical::foxGlynn(lambda*T, epsilon*kappa/100);
// Scale the weights so they add up to one.
for (auto& element : foxGlynnResult.weights) {
element /= foxGlynnResult.totalWeight;
}
// (4) define vectors/matrices
std::vector<ValueType> init(numberOfStates, -1);
std::vector<std::vector<ValueType>> v = std::vector<std::vector<ValueType>>(N + 1, init);
unifVectors.clear();
unifVectors.push_back(v);
unifVectors.push_back(v);
unifVectors.push_back(v);
//define 0=vd 1=vu 2=wu
// (5) calculate vectors and maxNorm
for (uint64_t i = 0; i < numberOfStates; i++) {
for (uint64_t k = N; k <= N; k--) {
calculateUnifPlusVector(env, k, i, 0, lambda, probSize, relReachability, dir, unifVectors,
fullTransitionMatrix, markovianStates, psiStates, solver,
foxGlynnResult, cycleFree);
calculateUnifPlusVector(env, k, i, 2, lambda, probSize, relReachability, dir, unifVectors,
fullTransitionMatrix, markovianStates, psiStates, solver,
foxGlynnResult, cycleFree);
calculateVu(env, relReachability, dir, k, i, 1, lambda, probSize, unifVectors,
fullTransitionMatrix, markovianStates, psiStates, solver,
foxGlynnResult, cycleFree);
}
}
//only iterate over result vector, as the results can only get more precise
for (uint64_t i = 0; i < numberOfStates; i++){
ValueType diff = std::abs(unifVectors[0][0][i]-unifVectors[1][0][i]);
maxNorm = std::max(maxNorm, diff);
}
// (6) double lambda
lambda = 2 * lambda;
} while (maxNorm > epsilon*(1 - kappa));
return unifVectors[0][0];
}
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilitiesImca(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
STORM_LOG_TRACE("Using IMCA's technique to compute bounded until probabilities.");
uint64_t numberOfStates = transitionMatrix.getRowGroupCount();
// 'Unpack' the bounds to make them more easily accessible.
double lowerBound = boundsPair.first;
double upperBound = boundsPair.second;
// (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::getModule<storm::settings::modules::GeneralSettings>().getPrecision()) / (upperBound * maxExitRate * maxExitRate);
// (2) Compute the number of steps we need to make for the interval.
uint64_t numberOfSteps = static_cast<uint64_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(env, dir, transitionMatrix, exitRateVector, 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<uint64_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(env, dir, transitionMatrix, exitRateVector, 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, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
auto const& markovAutomatonSettings = storm::settings::getModule<storm::settings::modules::MarkovAutomatonSettings>();
if (markovAutomatonSettings.getTechnique() == storm::settings::modules::MarkovAutomatonSettings::BoundedReachabilityTechnique::Imca) {
return computeBoundedUntilProbabilitiesImca(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair, minMaxLinearEquationSolverFactory);
} else {
STORM_LOG_ASSERT(markovAutomatonSettings.getTechnique() == storm::settings::modules::MarkovAutomatonSettings::BoundedReachabilityTechnique::UnifPlus, "Unknown solution technique.");
return unifPlus(env, dir, boundsPair, exitRateVector, transitionMatrix, markovianStates, psiStates, minMaxLinearEquationSolverFactory);
}
}
template <typename ValueType, typename std::enable_if<!storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
STORM_LOG_THROW(false, storm::exceptions::InvalidOperationException, "Computing bounded until probabilities is unsupported for this value type.");
}
template<typename ValueType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeUntilProbabilities(Environment const& env, 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::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
return std::move(storm::modelchecker::helper::SparseMdpPrctlHelper<ValueType>::computeUntilProbabilities(env, dir, transitionMatrix, backwardTransitions, phiStates, psiStates, qualitative, false, minMaxLinearEquationSolverFactory).values);
}
template <typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(Environment const& env, 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, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Get a reward model where the state rewards are scaled accordingly
std::vector<ValueType> stateRewardWeights(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
for (auto const markovianState : markovianStates) {
stateRewardWeights[markovianState] = storm::utility::one<ValueType>() / exitRateVector[markovianState];
}
std::vector<ValueType> totalRewardVector = rewardModel.getTotalActionRewardVector(transitionMatrix, stateRewardWeights);
RewardModelType scaledRewardModel(boost::none, std::move(totalRewardVector));
return SparseMdpPrctlHelper<ValueType>::computeReachabilityRewards(env, dir, transitionMatrix, backwardTransitions, scaledRewardModel, psiStates, false, false, minMaxLinearEquationSolverFactory).values;
}
template<typename ValueType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeLongRunAverageProbabilities(Environment const& env, 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, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
uint64_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.full()) {
return std::vector<ValueType>(numberOfStates, storm::utility::one<ValueType>());
}
// Otherwise, reduce the long run average probabilities to long run average rewards.
// Every Markovian goal state gets reward one.
std::vector<ValueType> stateRewards(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
storm::utility::vector::setVectorValues(stateRewards, markovianStates & psiStates, storm::utility::one<ValueType>());
storm::models::sparse::StandardRewardModel<ValueType> rewardModel(std::move(stateRewards));
return computeLongRunAverageRewards(env, dir, transitionMatrix, backwardTransitions, exitRateVector, markovianStates, rewardModel, minMaxLinearEquationSolverFactory);
}
template<typename ValueType, typename RewardModelType>
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards(Environment const& env, 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::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
uint64_t numberOfStates = transitionMatrix.getRowGroupCount();
// Start by decomposing the Markov automaton into its MECs.
storm::storage::MaximalEndComponentDecomposition<ValueType> mecDecomposition(transitionMatrix, backwardTransitions);
// Get some data members for convenience.
std::vector<uint64_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<uint64_t> stateToMecIndexMap(numberOfStates);
storm::storage::BitVector statesInMecs(numberOfStates);
for (uint64_t currentMecIndex = 0; currentMecIndex < mecDecomposition.size(); ++currentMecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[currentMecIndex];
// Gather information for later use.
for (auto const& stateChoicesPair : mec) {
uint64_t state = stateChoicesPair.first;
statesInMecs.set(state);
stateToMecIndexMap[state] = currentMecIndex;
}
// Compute the LRA value for the current MEC.
lraValuesForEndComponents.push_back(computeLraForMaximalEndComponent(env, dir, transitionMatrix, exitRateVector, markovianStates, rewardModel, mec, minMaxLinearEquationSolverFactory));
}
// For fast transition rewriting, we build some auxiliary data structures.
storm::storage::BitVector statesNotContainedInAnyMec = ~statesInMecs;
uint64_t firstAuxiliaryStateIndex = statesNotContainedInAnyMec.getNumberOfSetBits();
uint64_t lastStateNotInMecs = 0;
uint64_t numberOfStatesNotInMecs = 0;
std::vector<uint64_t> statesNotInMecsBeforeIndex;
statesNotInMecsBeforeIndex.reserve(numberOfStates);
for (auto state : statesNotContainedInAnyMec) {
while (lastStateNotInMecs <= state) {
statesNotInMecsBeforeIndex.push_back(numberOfStatesNotInMecs);
++lastStateNotInMecs;
}
++numberOfStatesNotInMecs;
}
uint64_t numberOfSspStates = numberOfStatesNotInMecs + mecDecomposition.size();
// 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, numberOfSspStates , 0, false, true, numberOfSspStates);
// If the source state is not contained in any MEC, we copy its choices (and perform the necessary modifications).
uint64_t currentChoice = 0;
for (auto state : statesNotContainedInAnyMec) {
sspMatrixBuilder.newRowGroup(currentChoice);
for (uint64_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 (uint64_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 (uint64_t mecIndex = 0; mecIndex < mecDecomposition.size(); ++mecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[mecIndex];
sspMatrixBuilder.newRowGroup(currentChoice);
for (auto const& stateChoicesPair : mec) {
uint64_t state = stateChoicesPair.first;
boost::container::flat_set<uint64_t> const& choicesInMec = stateChoicesPair.second;
for (uint64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice) {
// 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()) {
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 (uint64_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, numberOfSspStates, numberOfSspStates);
std::vector<ValueType> x(numberOfSspStates);
// Check for requirements of the solver.
storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(env, true, dir, true);
requirements.clearBounds();
STORM_LOG_THROW(requirements.empty(), storm::exceptions::UncheckedRequirementException, "Cannot establish requirements for solver.");
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(env, sspMatrix);
solver->setHasUniqueSolution();
solver->setLowerBound(storm::utility::zero<ValueType>());
solver->setUpperBound(*std::max_element(lraValuesForEndComponents.begin(), lraValuesForEndComponents.end()));
solver->setRequirementsChecked();
solver->solveEquations(env, 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::computeReachabilityTimes(Environment const& env, 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, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Get a reward model representing expected sojourn times
std::vector<ValueType> rewardValues(transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
for (auto const markovianState : markovianStates) {
rewardValues[transitionMatrix.getRowGroupIndices()[markovianState]] = storm::utility::one<ValueType>() / exitRateVector[markovianState];
}
storm::models::sparse::StandardRewardModel<ValueType> rewardModel(boost::none, std::move(rewardValues));
return SparseMdpPrctlHelper<ValueType>::computeReachabilityRewards(env, dir, transitionMatrix, backwardTransitions, rewardModel, psiStates, false, false, minMaxLinearEquationSolverFactory).values;
}
template<typename ValueType, typename RewardModelType>
ValueType SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponent(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// If the mec only consists of a single state, we compute the LRA value directly
if (++mec.begin() == mec.end()) {
uint64_t state = mec.begin()->first;
STORM_LOG_THROW(markovianStates.get(state), storm::exceptions::InvalidOperationException, "Markov Automaton has Zeno behavior. Computation of Long Run Average values not supported.");
ValueType result = rewardModel.hasStateRewards() ? rewardModel.getStateReward(state) : storm::utility::zero<ValueType>();
if (rewardModel.hasStateActionRewards() || rewardModel.hasTransitionRewards()) {
STORM_LOG_ASSERT(mec.begin()->second.size() == 1, "Markovian state has nondeterministic behavior.");
uint64_t choice = *mec.begin()->second.begin();
result += exitRateVector[state] * rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, storm::utility::zero<ValueType>());
}
return result;
}
// Solve MEC with the method specified in the settings
storm::solver::LraMethod method = storm::settings::getModule<storm::settings::modules::MinMaxEquationSolverSettings>().getLraMethod();
if (method == storm::solver::LraMethod::LinearProgramming) {
return computeLraForMaximalEndComponentLP(env, dir, transitionMatrix, exitRateVector, markovianStates, rewardModel, mec);
} else if (method == storm::solver::LraMethod::ValueIteration) {
return computeLraForMaximalEndComponentVI(env, dir, transitionMatrix, exitRateVector, markovianStates, rewardModel, mec, minMaxLinearEquationSolverFactory);
} else {
STORM_LOG_THROW(false, storm::exceptions::InvalidSettingsException, "Unsupported technique.");
}
}
template<typename ValueType, typename RewardModelType>
ValueType SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentLP(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec) {
std::unique_ptr<storm::utility::solver::LpSolverFactory<ValueType>> lpSolverFactory(new storm::utility::solver::LpSolverFactory<ValueType>());
std::unique_ptr<storm::solver::LpSolver<ValueType>> solver = lpSolverFactory->create("LRA for MEC");
solver->setOptimizationDirection(invert(dir));
// First, we need to create the variables for the problem.
std::map<uint64_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", storm::utility::one<ValueType>());
solver->update();
// Now we encode the problem as constraints.
std::vector<uint64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
for (auto const& stateChoicesPair : mec) {
uint64_t state = stateChoicesPair.first;
// Now, based on the type of the state, create a suitable constraint.
if (markovianStates.get(state)) {
STORM_LOG_ASSERT(stateChoicesPair.second.size() == 1, "Markovian state " << state << " is not deterministic: It has " << stateChoicesPair.second.size() << " choices.");
uint64_t choice = *stateChoicesPair.second.begin();
storm::expressions::Expression constraint = stateToVariableMap.at(state);
for (auto element : transitionMatrix.getRow(nondeterministicChoiceIndices[state])) {
constraint = constraint - stateToVariableMap.at(element.getColumn()) * solver->getManager().rational((element.getValue()));
}
constraint = constraint + solver->getManager().rational(storm::utility::one<ValueType>() / exitRateVector[state]) * k;
storm::expressions::Expression rightHandSide = solver->getManager().rational(rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, (ValueType) (storm::utility::one<ValueType>() / exitRateVector[state])));
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->getManager().rational(element.getValue());
}
storm::expressions::Expression rightHandSide = solver->getManager().rational(rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, 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<typename ValueType, typename RewardModelType>
ValueType SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentVI(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Initialize data about the mec
storm::storage::BitVector mecStates(transitionMatrix.getRowGroupCount(), false);
storm::storage::BitVector mecChoices(transitionMatrix.getRowCount(), false);
for (auto const& stateChoicesPair : mec) {
mecStates.set(stateChoicesPair.first);
for (auto const& choice : stateChoicesPair.second) {
mecChoices.set(choice);
}
}
storm::storage::BitVector markovianMecStates = mecStates & markovianStates;
storm::storage::BitVector probabilisticMecStates = mecStates & ~markovianStates;
storm::storage::BitVector probabilisticMecChoices = transitionMatrix.getRowFilter(probabilisticMecStates) & mecChoices;
STORM_LOG_THROW(!markovianMecStates.empty(), storm::exceptions::InvalidOperationException, "Markov Automaton has Zeno behavior. Computation of Long Run Average values not supported.");
// Get the uniformization rate
ValueType uniformizationRate = storm::utility::vector::max_if(exitRateVector, markovianMecStates);
// To ensure that the model is aperiodic, we need to make sure that every Markovian state gets a self loop.
// Hence, we increase the uniformization rate a little.
uniformizationRate += storm::utility::one<ValueType>(); // Todo: try other values such as *=1.01
// Get the transitions of the submodel, that is
// * a matrix aMarkovian with all (uniformized) transitions from Markovian mec states to all Markovian mec states.
// * a matrix aMarkovianToProbabilistic with all (uniformized) transitions from Markovian mec states to all probabilistic mec states.
// * a matrix aProbabilistic with all transitions from probabilistic mec states to other probabilistic mec states.
// * a matrix aProbabilisticToMarkovian with all transitions from probabilistic mec states to all Markovian mec states.
typename storm::storage::SparseMatrix<ValueType> aMarkovian = transitionMatrix.getSubmatrix(true, markovianMecStates, markovianMecStates, true);
typename storm::storage::SparseMatrix<ValueType> aMarkovianToProbabilistic = transitionMatrix.getSubmatrix(true, markovianMecStates, probabilisticMecStates);
typename storm::storage::SparseMatrix<ValueType> aProbabilistic = transitionMatrix.getSubmatrix(false, probabilisticMecChoices, probabilisticMecStates);
typename storm::storage::SparseMatrix<ValueType> aProbabilisticToMarkovian = transitionMatrix.getSubmatrix(false, probabilisticMecChoices, markovianMecStates);
// The matrices with transitions from Markovian states need to be uniformized.
uint64_t subState = 0;
for (auto state : markovianMecStates) {
ValueType uniformizationFactor = exitRateVector[state] / uniformizationRate;
for (auto& entry : aMarkovianToProbabilistic.getRow(subState)) {
entry.setValue(entry.getValue() * uniformizationFactor);
}
for (auto& entry : aMarkovian.getRow(subState)) {
if (entry.getColumn() == subState) {
entry.setValue(storm::utility::one<ValueType>() - uniformizationFactor * (storm::utility::one<ValueType>() - entry.getValue()));
} else {
entry.setValue(entry.getValue() * uniformizationFactor);
}
}
++subState;
}
// Compute the rewards obtained in a single uniformization step
std::vector<ValueType> markovianChoiceRewards;
markovianChoiceRewards.reserve(aMarkovian.getRowCount());
for (auto const& state : markovianMecStates) {
ValueType stateRewardScalingFactor = storm::utility::one<ValueType>() / uniformizationRate;
ValueType actionRewardScalingFactor = exitRateVector[state] / uniformizationRate;
assert(transitionMatrix.getRowGroupSize(state) == 1);
uint64_t choice = transitionMatrix.getRowGroupIndices()[state];
markovianChoiceRewards.push_back(rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, stateRewardScalingFactor, actionRewardScalingFactor));
}
std::vector<ValueType> probabilisticChoiceRewards;
probabilisticChoiceRewards.reserve(aProbabilistic.getRowCount());
for (auto const& state : probabilisticMecStates) {
uint64_t groupStart = transitionMatrix.getRowGroupIndices()[state];
uint64_t groupEnd = transitionMatrix.getRowGroupIndices()[state + 1];
for (uint64_t choice = probabilisticMecChoices.getNextSetIndex(groupStart); choice < groupEnd; choice = probabilisticMecChoices.getNextSetIndex(choice + 1)) {
probabilisticChoiceRewards.push_back(rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, storm::utility::zero<ValueType>()));
}
}
// start the iterations
ValueType precision = storm::utility::convertNumber<ValueType>(storm::settings::getModule<storm::settings::modules::GeneralSettings>().getPrecision()) / uniformizationRate;
std::vector<ValueType> v(aMarkovian.getRowCount(), storm::utility::zero<ValueType>());
std::vector<ValueType> w = v;
std::vector<ValueType> x(aProbabilistic.getRowGroupCount(), storm::utility::zero<ValueType>());
std::vector<ValueType> b = probabilisticChoiceRewards;
// Check for requirements of the solver.
// The solution is unique as we assume non-zeno MAs.
storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(env, true, dir, true);
requirements.clearLowerBounds();
STORM_LOG_THROW(requirements.empty(), storm::exceptions::UncheckedRequirementException, "Cannot establish requirements for solver.");
auto solver = minMaxLinearEquationSolverFactory.create(env, std::move(aProbabilistic));
solver->setLowerBound(storm::utility::zero<ValueType>());
solver->setHasUniqueSolution(true);
solver->setRequirementsChecked(true);
solver->setCachingEnabled(true);
while (true) {
// Compute the expected total rewards for the probabilistic states
solver->solveEquations(env, dir, x, b);
// now compute the values for the markovian states. We also keep track of the maximal and minimal difference between two values (for convergence checking)
auto vIt = v.begin();
uint64_t row = 0;
ValueType newValue = markovianChoiceRewards[row] + aMarkovianToProbabilistic.multiplyRowWithVector(row, x) + aMarkovian.multiplyRowWithVector(row, w);
ValueType maxDiff = newValue - *vIt;
ValueType minDiff = maxDiff;
*vIt = newValue;
for (++vIt, ++row; row < aMarkovian.getRowCount(); ++vIt, ++row) {
newValue = markovianChoiceRewards[row] + aMarkovianToProbabilistic.multiplyRowWithVector(row, x) + aMarkovian.multiplyRowWithVector(row, w);
ValueType diff = newValue - *vIt;
maxDiff = std::max(maxDiff, diff);
minDiff = std::min(minDiff, diff);
*vIt = newValue;
}
// Check for convergence
if (maxDiff - minDiff < precision) {
break;
}
// update the rhs of the MinMax equation system
ValueType referenceValue = v.front();
storm::utility::vector::applyPointwise<ValueType, ValueType>(v, w, [&referenceValue] (ValueType const& v_i) -> ValueType { return v_i - referenceValue; });
aProbabilisticToMarkovian.multiplyWithVector(w, b);
storm::utility::vector::addVectors(b, probabilisticChoiceRewards, b);
}
return v.front() * uniformizationRate;
}
template std::vector<double> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template std::vector<double> SparseMarkovAutomatonCslHelper::computeUntilProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template std::vector<double> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(Environment const& env, 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, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template std::vector<double> SparseMarkovAutomatonCslHelper::computeLongRunAverageProbabilities(Environment const& env, 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::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template std::vector<double> SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards(Environment const& env, 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::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template std::vector<double> SparseMarkovAutomatonCslHelper::computeReachabilityTimes(Environment const& env, 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::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template void SparseMarkovAutomatonCslHelper::computeBoundedReachabilityProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRates, storm::storage::BitVector const& goalStates, storm::storage::BitVector const& markovianNonGoalStates, storm::storage::BitVector const& probabilisticNonGoalStates, std::vector<double>& markovianNonGoalValues, std::vector<double>& probabilisticNonGoalValues, double delta, uint64_t numberOfSteps, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template double SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponent(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template double SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentLP(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec);
template double SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentVI(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeUntilProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeLongRunAverageProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeReachabilityTimes(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template void SparseMarkovAutomatonCslHelper::computeBoundedReachabilityProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRates, storm::storage::BitVector const& goalStates, storm::storage::BitVector const& markovianNonGoalStates, storm::storage::BitVector const& probabilisticNonGoalStates, std::vector<storm::RationalNumber>& markovianNonGoalValues, std::vector<storm::RationalNumber>& probabilisticNonGoalValues, storm::RationalNumber delta, uint64_t numberOfSteps, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template storm::RationalNumber SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponent(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template storm::RationalNumber SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentLP(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec);
template storm::RationalNumber SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentVI(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
}
}
}