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451 lines
23 KiB
451 lines
23 KiB
/*
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* SparseDtmcPrctlModelChecker.h
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*
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* Created on: 22.10.2012
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* Author: Thomas Heinemann
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*/
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#ifndef STORM_MODELCHECKER_SPARSEDTMCPRCTLMODELCHECKER_H_
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#define STORM_MODELCHECKER_SPARSEDTMCPRCTLMODELCHECKER_H_
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#include "src/modelchecker/AbstractModelChecker.h"
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#include "src/models/Dtmc.h"
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#include "src/utility/Vector.h"
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#include "src/utility/graph.h"
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#include <vector>
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namespace storm {
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namespace modelchecker {
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/*!
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* @brief
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* Interface for all model checkers that can verify PRCTL formulae over DTMCs represented as a sparse matrix.
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*/
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template<class Type>
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class SparseDtmcPrctlModelChecker : public AbstractModelChecker<Type> {
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public:
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/*!
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* Constructs a SparseDtmcPrctlModelChecker with the given model.
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*
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* @param model The DTMC to be checked.
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*/
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explicit SparseDtmcPrctlModelChecker(storm::models::Dtmc<Type> const& model) : AbstractModelChecker<Type>(model) {
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// Intentionally left empty.
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}
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/*!
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* Copy constructs a SparseDtmcPrctlModelChecker from the given model checker. In particular, this means that the newly
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* constructed model checker will have the model of the given model checker as its associated model.
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*/
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explicit SparseDtmcPrctlModelChecker(storm::modelchecker::SparseDtmcPrctlModelChecker<Type> const& modelChecker) : AbstractModelChecker<Type>(modelChecker) {
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// Intentionally left empty.
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}
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/*!
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* Virtual destructor. Needs to be virtual, because this class has virtual methods.
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*/
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virtual ~SparseDtmcPrctlModelChecker() {
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// Intentionally left empty.
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}
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/*!
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* Returns a constant reference to the DTMC associated with this model checker.
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* @returns A constant reference to the DTMC associated with this model checker.
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*/
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storm::models::Dtmc<Type> const& getModel() const {
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return AbstractModelChecker<Type>::template getModel<storm::models::Dtmc<Type>>();
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}
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/*!
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* Checks the given formula that is a P/R operator without a bound.
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*
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* @param formula The formula to check.
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* @returns The set of states satisfying the formula represented by a bit vector.
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*/
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std::vector<Type>* checkNoBoundOperator(storm::property::prctl::AbstractNoBoundOperator<Type> const& formula) const {
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// Check if the operator was an optimality operator and report a warning in that case.
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if (formula.isOptimalityOperator()) {
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LOG4CPLUS_WARN(logger, "Formula contains min/max operator, which is not meaningful over deterministic models.");
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}
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return formula.check(*this, false);
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}
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/*!
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* Checks the given formula that is a bounded-until formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bounds 0 and 1. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bounds 0 and 1.
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* @returns The probabilities for the given formula to hold on every state of the model associated with this model
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* checker. If the qualitative flag is set, exact probabilities might not be computed.
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*/
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virtual std::vector<Type>* checkBoundedUntil(storm::property::prctl::BoundedUntil<Type> const& formula, bool qualitative) const {
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// First, we need to compute the states that satisfy the sub-formulas of the bounded until-formula.
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storm::storage::BitVector* leftStates = formula.getLeft().check(*this);
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storm::storage::BitVector* rightStates = formula.getRight().check(*this);
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// Copy the matrix before we make any changes.
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storm::storage::SparseMatrix<Type> tmpMatrix(*this->getModel().getTransitionMatrix());
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// Make all rows absorbing that violate both sub-formulas or satisfy the second sub-formula.
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tmpMatrix.makeRowsAbsorbing(~(*leftStates | *rightStates) | *rightStates);
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// Create the vector with which to multiply.
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std::vector<Type>* result = new std::vector<Type>(this->getModel().getNumberOfStates());
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storm::utility::setVectorValues(result, *rightStates, storm::utility::constGetOne<Type>());
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// Perform the matrix vector multiplication as often as required by the formula bound.
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this->performMatrixVectorMultiplication(tmpMatrix, *result, nullptr, formula.getBound());
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// Delete obsolete intermediates and return result.
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delete leftStates;
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delete rightStates;
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return result;
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}
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/*!
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* Checks the given formula that is a next formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bounds 0 and 1. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bounds 0 and 1.
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* @returns The probabilities for the given formula to hold on every state of the model associated with this model
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* checker. If the qualitative flag is set, exact probabilities might not be computed.
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*/
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virtual std::vector<Type>* checkNext(storm::property::prctl::Next<Type> const& formula, bool qualitative) const {
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// First, we need to compute the states that satisfy the child formula of the next-formula.
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storm::storage::BitVector* nextStates = formula.getChild().check(*this);
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// Create the vector with which to multiply and initialize it correctly.
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std::vector<Type>* result = new std::vector<Type>(this->getModel().getNumberOfStates());
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storm::utility::setVectorValues(result, *nextStates, storm::utility::constGetOne<Type>());
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// Delete obsolete intermediate.
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delete nextStates;
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// Perform one single matrix-vector multiplication.
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this->performMatrixVectorMultiplication(*this->getModel().getTransitionMatrix(), *result);
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// Return result.
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return result;
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}
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/*!
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* Checks the given formula that is a bounded-eventually formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bounds 0 and 1. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bounds 0 and 1.
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* @returns The probabilities for the given formula to hold on every state of the model associated with this model
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* checker. If the qualitative flag is set, exact probabilities might not be computed.
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*/
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virtual std::vector<Type>* checkBoundedEventually(storm::property::prctl::BoundedEventually<Type> const& formula, bool qualitative) const {
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// Create equivalent temporary bounded until formula and check it.
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storm::property::prctl::BoundedUntil<Type> temporaryBoundedUntilFormula(new storm::property::prctl::Ap<Type>("true"), formula.getChild().clone(), formula.getBound());
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return this->checkBoundedUntil(temporaryBoundedUntilFormula, qualitative);
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}
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/*!
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* Checks the given formula that is an eventually formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bounds 0 and 1. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bounds 0 and 1.
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* @returns The probabilities for the given formula to hold on every state of the model associated with this model
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* checker. If the qualitative flag is set, exact probabilities might not be computed.
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*/
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virtual std::vector<Type>* checkEventually(storm::property::prctl::Eventually<Type> const& formula, bool qualitative) const {
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// Create equivalent temporary until formula and check it.
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storm::property::prctl::Until<Type> temporaryUntilFormula(new storm::property::prctl::Ap<Type>("true"), formula.getChild().clone());
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return this->checkUntil(temporaryUntilFormula, qualitative);
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}
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/*!
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* Checks the given formula that is a globally formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bounds 0 and 1. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bounds 0 and 1.
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* @returns The probabilities for the given formula to hold on every state of the model associated with this model
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* checker. If the qualitative flag is set, exact probabilities might not be computed.
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*/
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virtual std::vector<Type>* checkGlobally(storm::property::prctl::Globally<Type> const& formula, bool qualitative) const {
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// Create "equivalent" (equivalent up to negation) temporary eventually formula and check it.
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storm::property::prctl::Eventually<Type> temporaryEventuallyFormula(new storm::property::prctl::Not<Type>(formula.getChild().clone()));
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std::vector<Type>* result = this->checkEventually(temporaryEventuallyFormula, qualitative);
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// Now subtract the resulting vector from the constant one vector to obtain final result.
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storm::utility::subtractFromConstantOneVector(result);
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return result;
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}
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/*!
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* Check the given formula that is an until formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bounds 0 and 1. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bounds 0 and 1.
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* @returns The probabilities for the given formula to hold on every state of the model associated with this model
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* checker. If the qualitative flag is set, exact probabilities might not be computed.
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*/
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virtual std::vector<Type>* checkUntil(storm::property::prctl::Until<Type> const& formula, bool qualitative) const {
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// First, we need to compute the states that satisfy the sub-formulas of the until-formula.
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storm::storage::BitVector* leftStates = formula.getLeft().check(*this);
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storm::storage::BitVector* rightStates = formula.getRight().check(*this);
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// Then, we need to identify the states which have to be taken out of the matrix, i.e.
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// all states that have probability 0 and 1 of satisfying the until-formula.
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std::pair<storm::storage::BitVector, storm::storage::BitVector> statesWithProbability01 = storm::utility::graph::performProb01(this->getModel(), *leftStates, *rightStates);
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storm::storage::BitVector statesWithProbability0 = std::move(statesWithProbability01.first);
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storm::storage::BitVector statesWithProbability1 = std::move(statesWithProbability01.second);
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// Delete intermediate results that are obsolete now.
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delete leftStates;
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delete rightStates;
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// Perform some logging.
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LOG4CPLUS_INFO(logger, "Found " << statesWithProbability0.getNumberOfSetBits() << " 'no' states.");
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LOG4CPLUS_INFO(logger, "Found " << statesWithProbability1.getNumberOfSetBits() << " 'yes' states.");
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storm::storage::BitVector maybeStates = ~(statesWithProbability0 | statesWithProbability1);
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LOG4CPLUS_INFO(logger, "Found " << maybeStates.getNumberOfSetBits() << " 'maybe' states.");
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// Create resulting vector.
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std::vector<Type>* result = new std::vector<Type>(this->getModel().getNumberOfStates());
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// Only try to solve system if there are states for which the probability is unknown.
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uint_fast64_t maybeStatesSetBitCount = maybeStates.getNumberOfSetBits();
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if (maybeStatesSetBitCount > 0 && !qualitative) {
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// Now we can eliminate the rows and columns from the original transition probability matrix.
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storm::storage::SparseMatrix<Type> submatrix = this->getModel().getTransitionMatrix()->getSubmatrix(maybeStates);
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// Converting the matrix from the fixpoint notation to the form needed for the equation
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// system. That is, we go from x = A*x + b to (I-A)x = b.
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submatrix.convertToEquationSystem();
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// Initialize the x vector with 0.5 for each element. This is the initial guess for
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// the iterative solvers. It should be safe as for all 'maybe' states we know that the
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// probability is strictly larger than 0.
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std::vector<Type> x(maybeStatesSetBitCount, Type(0.5));
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// Prepare the right-hand side of the equation system. For entry i this corresponds to
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// the accumulated probability of going from state i to some 'yes' state.
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std::vector<Type> b = this->getModel().getTransitionMatrix()->getConstrainedRowSumVector(maybeStates, statesWithProbability1);
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// Now solve the created system of linear equations.
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this->solveEquationSystem(submatrix, x, b);
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// Set values of resulting vector according to result.
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storm::utility::setVectorValues<Type>(result, maybeStates, x);
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} else if (qualitative) {
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// If we only need a qualitative result, we can safely assume that the results will only be compared to
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// bounds which are either 0 or 1. Setting the value to 0.5 is thus safe.
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storm::utility::setVectorValues<Type>(result, maybeStates, Type(0.5));
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}
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// Set values of resulting vector that are known exactly.
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storm::utility::setVectorValues<Type>(result, statesWithProbability0, storm::utility::constGetZero<Type>());
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storm::utility::setVectorValues<Type>(result, statesWithProbability1, storm::utility::constGetOne<Type>());
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return result;
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}
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/*!
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* Checks the given formula that is an instantaneous reward formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bound 0. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bound 0.
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* @returns The reward values for the given formula for every state of the model associated with this model
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* checker. If the qualitative flag is set, exact values might not be computed.
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*/
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virtual std::vector<Type>* checkInstantaneousReward(storm::property::prctl::InstantaneousReward<Type> const& formula, bool qualitative) const {
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// Only compute the result if the model has a state-based reward model.
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if (!this->getModel().hasStateRewards()) {
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LOG4CPLUS_ERROR(logger, "Missing (state-based) reward model for formula.");
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throw storm::exceptions::InvalidPropertyException() << "Missing (state-based) reward model for formula.";
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}
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// Initialize result to state rewards of the model.
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std::vector<Type>* result = new std::vector<Type>(*this->getModel().getStateRewardVector());
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// Perform the actual matrix-vector multiplication as long as the bound of the formula is met.
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this->performMatrixVectorMultiplication(*this->getModel().getTransitionMatrix(), *result, nullptr, formula.getBound());
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// Return result.
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return result;
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}
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/*!
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* Check the given formula that is a cumulative reward formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bound 0. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bound 0.
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* @returns The reward values for the given formula for every state of the model associated with this model
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* checker. If the qualitative flag is set, exact values might not be computed.
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*/
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virtual std::vector<Type>* checkCumulativeReward(storm::property::prctl::CumulativeReward<Type> const& formula, bool qualitative) const {
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// Only compute the result if the model has at least one reward model.
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if (!this->getModel().hasStateRewards() && !this->getModel().hasTransitionRewards()) {
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LOG4CPLUS_ERROR(logger, "Missing reward model for formula.");
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throw storm::exceptions::InvalidPropertyException() << "Missing reward model for formula.";
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}
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// Compute the reward vector to add in each step based on the available reward models.
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std::vector<Type> totalRewardVector;
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if (this->getModel().hasTransitionRewards()) {
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totalRewardVector = this->getModel().getTransitionMatrix()->getPointwiseProductRowSumVector(*this->getModel().getTransitionRewardMatrix());
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if (this->getModel().hasStateRewards()) {
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gmm::add(*this->getModel().getStateRewardVector(), totalRewardVector);
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}
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} else {
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totalRewardVector = std::vector<Type>(*this->getModel().getStateRewardVector());
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}
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// Initialize result to either the state rewards of the model or the null vector.
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std::vector<Type>* result = nullptr;
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if (this->getModel().hasStateRewards()) {
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result = new std::vector<Type>(*this->getModel().getStateRewardVector());
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} else {
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result = new std::vector<Type>(this->getModel().getNumberOfStates());
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}
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// Perform the actual matrix-vector multiplication as long as the bound of the formula is met.
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this->performMatrixVectorMultiplication(*this->getModel().getTransitionMatrix(), *result, &totalRewardVector, formula.getBound());
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// Return result.
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return result;
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}
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/*!
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* Checks the given formula that is a reachability reward formula.
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*
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* @param formula The formula to check.
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* @param qualitative A flag indicating whether the formula only needs to be evaluated qualitatively, i.e. if the
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* results are only compared against the bound 0. If set to true, this will most likely results that are only
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* qualitatively correct, i.e. do not represent the correct value, but only the correct relation with respect to the
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* bound 0.
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* @returns The reward values for the given formula for every state of the model associated with this model
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* checker. If the qualitative flag is set, exact values might not be computed.
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*/
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virtual std::vector<Type>* checkReachabilityReward(storm::property::prctl::ReachabilityReward<Type> const& formula, bool qualitative) const {
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// Only compute the result if the model has at least one reward model.
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if (!this->getModel().hasStateRewards() && !this->getModel().hasTransitionRewards()) {
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LOG4CPLUS_ERROR(logger, "Missing reward model for formula. Skipping formula");
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throw storm::exceptions::InvalidPropertyException() << "Missing reward model for formula.";
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}
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// Determine the states for which the target predicate holds.
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storm::storage::BitVector* targetStates = formula.getChild().check(*this);
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// Determine which states have a reward of infinity by definition.
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storm::storage::BitVector trueStates(this->getModel().getNumberOfStates(), true);
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storm::storage::BitVector infinityStates = storm::utility::graph::performProb1(this->getModel(), trueStates, *targetStates);
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infinityStates.complement();
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// Create resulting vector.
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std::vector<Type>* result = new std::vector<Type>(this->getModel().getNumberOfStates());
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// Check whether there are states for which we have to compute the result.
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storm::storage::BitVector maybeStates = ~(*targetStates) & ~infinityStates;
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const int maybeStatesSetBitCount = maybeStates.getNumberOfSetBits();
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if (maybeStatesSetBitCount > 0) {
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// Now we can eliminate the rows and columns from the original transition probability matrix.
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storm::storage::SparseMatrix<Type> submatrix = this->getModel().getTransitionMatrix()->getSubmatrix(maybeStates);
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// Converting the matrix from the fixpoint notation to the form needed for the equation
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// system. That is, we go from x = A*x + b to (I-A)x = b.
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submatrix.convertToEquationSystem();
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// Initialize the x vector with 1 for each element. This is the initial guess for
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// the iterative solvers.
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std::vector<Type> x(maybeStatesSetBitCount, storm::utility::constGetOne<Type>());
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// Prepare the right-hand side of the equation system.
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std::vector<Type> b(maybeStatesSetBitCount);
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if (this->getModel().hasTransitionRewards()) {
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// If a transition-based reward model is available, we initialize the right-hand
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// side to the vector resulting from summing the rows of the pointwise product
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// of the transition probability matrix and the transition reward matrix.
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std::vector<Type> pointwiseProductRowSumVector = this->getModel().getTransitionMatrix()->getPointwiseProductRowSumVector(*this->getModel().getTransitionRewardMatrix());
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storm::utility::selectVectorValues(&b, maybeStates, pointwiseProductRowSumVector);
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if (this->getModel().hasStateRewards()) {
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// If a state-based reward model is also available, we need to add this vector
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// as well. As the state reward vector contains entries not just for the states
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// that we still consider (i.e. maybeStates), we need to extract these values
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// first.
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std::vector<Type> subStateRewards(maybeStatesSetBitCount);
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storm::utility::selectVectorValues(&subStateRewards, maybeStates, *this->getModel().getStateRewardVector());
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gmm::add(subStateRewards, b);
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}
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} else {
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// If only a state-based reward model is available, we take this vector as the
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// right-hand side. As the state reward vector contains entries not just for the
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// states that we still consider (i.e. maybeStates), we need to extract these values
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// first.
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storm::utility::selectVectorValues(&b, maybeStates, *this->getModel().getStateRewardVector());
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}
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// Now solve the resulting equation system.
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this->solveEquationSystem(submatrix, x, b);
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// Set values of resulting vector according to result.
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storm::utility::setVectorValues<Type>(result, maybeStates, x);
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}
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// Set values of resulting vector that are known exactly.
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storm::utility::setVectorValues(result, *targetStates, storm::utility::constGetZero<Type>());
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storm::utility::setVectorValues(result, infinityStates, storm::utility::constGetInfinity<Type>());
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// Delete temporary storages and return result.
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delete targetStates;
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return result;
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}
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private:
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/*!
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* Performs (repeated) matrix-vector multiplication with the given parameters, i.e. computes x[i+1] = A*x[i] + b
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* until x[n], where x[0] = x.
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*
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* @param A The matrix that is to be multiplied against the vector.
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* @param x The initial vector that is to be multiplied against the matrix. This is also the output parameter,
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* i.e. after the method returns, this vector will contain the computed values.
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* @param b If not null, this vector is being added to the result after each matrix-vector multiplication.
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* @param n Specifies the number of iterations the matrix-vector multiplication is performed.
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* @returns The result of the repeated matrix-vector multiplication as the content of the parameter vector.
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*/
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virtual void performMatrixVectorMultiplication(storm::storage::SparseMatrix<Type> const& A, std::vector<Type>& x, std::vector<Type>* b = nullptr, uint_fast64_t n = 1) const = 0;
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|
|
|
/*!
|
|
* Solves the equation system A*x = b given by the parameters.
|
|
*
|
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* @param A The matrix specifying the coefficients of the linear equations.
|
|
* @param x The solution vector x. The initial values of x represent a guess of the real values to the solver, but
|
|
* may be ignored.
|
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* @param b The right-hand side of the equation system.
|
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* @returns The solution vector x of the system of linear equations as the content of the parameter x.
|
|
*/
|
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virtual void solveEquationSystem(storm::storage::SparseMatrix<Type> const& A, std::vector<Type>& x, std::vector<Type> const& b) const = 0;
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};
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} // namespace modelchecker
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} // namespace storm
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#endif /* STORM_MODELCHECKER_SPARSEDTMCPRCTLMODELCHECKER_H_ */
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