#ifndef STORM_UTILITY_GRAPH_H_
#define STORM_UTILITY_GRAPH_H_
#include <set>
#include <limits>
#include "storm/utility/OsDetection.h"
#include "storm/storage/sparse/StateType.h"
#include "storm/storage/PartialScheduler.h"
#include "storm/models/sparse/NondeterministicModel.h"
#include "storm/models/sparse/DeterministicModel.h"
#include "storm/storage/dd/DdType.h"
#include "storm/solver/OptimizationDirection.h"
namespace storm {
namespace storage {
class BitVector;
template<typename VT> class SparseMatrix;
}
namespace models {
namespace symbolic {
template<storm::dd::DdType Type, typename ValueType>
class Model;
template<storm::dd::DdType Type, typename ValueType>
class DeterministicModel;
template<storm::dd::DdType Type, typename ValueType>
class NondeterministicModel;
template<storm::dd::DdType Type, typename ValueType>
class StochasticTwoPlayerGame;
}
}
namespace dd {
template<storm::dd::DdType Type>
class Bdd;
template<storm::dd::DdType Type, typename ValueType>
class Add;
}
namespace utility {
namespace graph {
/*!
* Performs a forward depth-first search through the underlying graph structure to identify the states that
* are reachable from the given set only passing through a constrained set of states until some target
* have been reached.
*
* @param transitionMatrix The transition relation of the graph structure to search.
* @param initialStates The set of states from which to start the search.
* @param constraintStates The set of states that must not be left.
* @param targetStates The target states that may not be passed.
* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
* @param maximalSteps The maximal number of steps to reach the psi states.
*/
template<typename T>
storm::storage::BitVector getReachableStates(storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::BitVector const& initialStates, storm::storage::BitVector const& constraintStates, storm::storage::BitVector const& targetStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0);
/*!
* Retrieves a set of states that covers als BSCCs of the system in the sense that for every BSCC exactly
* one state is included in the cover.
*
* @param transitionMatrix The transition relation of the graph structure.
*/
template<typename T>
storm::storage::BitVector getBsccCover(storm::storage::SparseMatrix<T> const& transitionMatrix);
/*!
* Performs a breadth-first search through the underlying graph structure to compute the distance from all
* states to the starting states of the search.
*
* @param transitionMatrix The transition relation of the graph structure to search.
* @param initialStates The set of states from which to start the search.
* @param subsystem The subsystem to consider.
* @return The distances of each state to the initial states of the sarch.
*/
template<typename T>
std::vector<uint_fast64_t> getDistances(storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::BitVector const& initialStates, boost::optional<storm::storage::BitVector> const& subsystem = boost::none);
/*!
* Performs a backward depth-first search trough the underlying graph structure
* of the given model to determine which states of the model have a positive probability
* of satisfying phi until psi. The resulting states are written to the given bit vector.
*
* @param backwardTransitions The reversed transition relation of the graph structure to search.
* @param phiStates A bit vector of all states satisfying phi.
* @param psiStates A bit vector of all states satisfying psi.
* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
* @param maximalSteps The maximal number of steps to reach the psi states.
* @return A bit vector with all indices of states that have a probability greater than 0.
*/
template <typename T>
storm::storage::BitVector performProbGreater0(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0);
/*!
* Computes the set of states of the given model for which all paths lead to
* the given set of target states and only visit states from the filter set
* before. In order to do this, it uses the given set of states that
* characterizes the states that possess at least one path to a target state.
* The results are written to the given bit vector.
*
* @param backwardTransitions The reversed transition relation of the graph structure to search.
* @param phiStates A bit vector of all states satisfying phi.
* @param psiStates A bit vector of all states satisfying psi.
* @param statesWithProbabilityGreater0 A reference to a bit vector of states that possess a positive
* probability mass of satisfying phi until psi.
* @return A bit vector with all indices of states that have a probability greater than 1.
*/
template <typename T>
storm::storage::BitVector performProb1(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, storm::storage::BitVector const& statesWithProbabilityGreater0);
/*!
* Computes the set of states of the given model for which all paths lead to
* the given set of target states and only visit states from the filter set
* before. In order to do this, it uses the given set of states that
* characterizes the states that possess at least one path to a target state.
* The results are written to the given bit vector.
*
* @param backwardTransitions The reversed transition relation of the graph structure to search.
* @param phiStates A bit vector of all states satisfying phi.
* @param psiStates A bit vector of all states satisfying psi.
* @return A bit vector with all indices of states that have a probability greater than 1.
*/
template <typename T>
storm::storage::BitVector performProb1(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
/*!
* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi until psi in a
* deterministic model.
*
* @param model The model whose graph structure to search.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @return A pair of bit vectors such that the first bit vector stores the indices of all states
* with probability 0 and the second stores all indices of states with probability 1.
*/
template <typename T>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::models::sparse::DeterministicModel<T> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
/*!
* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi until psi in a
* deterministic model.
*
* @param backwardTransitions The backward transitions of the model whose graph structure to search.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @return A pair of bit vectors such that the first bit vector stores the indices of all states
* with probability 0 and the second stores all indices of states with probability 1.
*/
template <typename T>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01(storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
/*!
* Computes the set of states that has a positive probability of reaching psi states after only passing
* through phi states before.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @param stepBound If given, this number indicates the maximal amount of steps allowed.
* @return All states with positive probability.
*/
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProbGreater0(storm::models::symbolic::Model<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, boost::optional<uint_fast64_t> const& stepBound = boost::optional<uint_fast64_t>());
/*!
* Computes the set of states that have a probability of one of reaching psi states after only passing
* through phi states before.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @param statesWithProbabilityGreater0 The set of states with a positive probability of satisfying phi
* until psi as a BDD.
* @return All states with probability 1.
*/
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProb1(storm::models::symbolic::Model<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::dd::Bdd<Type> const& statesWithProbabilityGreater0);
/*!
* Computes the set of states that have a probability of one of reaching psi states after only passing
* through phi states before.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @return All states with probability 1.
*/
template <storm::dd::DdType Type, typename ValueType>
storm::dd::Bdd<Type> performProb1(storm::models::symbolic::Model<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates);
/*!
* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi until psi in a
* deterministic model.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @return A pair of BDDs that represent all states with probability 0 and 1, respectively.
*/
template <storm::dd::DdType Type, typename ValueType>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01(storm::models::symbolic::DeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates);
/*!
* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi until psi in a
* deterministic model.
*
* @param model The (symbolic) model for which to compute the set of states. This is used for retrieving the
* manager and information about the meta variables.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @return A pair of BDDs that represent all states with probability 0 and 1, respectively.
*/
template <storm::dd::DdType Type, typename ValueType>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01(storm::models::symbolic::Model<Type, ValueType> const& model, storm::dd::Add<Type, ValueType> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates);
/*!
* Computes a scheduler for the given states that chooses an action that stays completely in the very same set.
* Note that this assumes that there is a legal choice for each of the states.
*
* @param states The set of states for which to compute the scheduler that stays in this very set.
* @param transitionMatrix The transition matrix.
*/
template <typename T>
storm::storage::PartialScheduler computeSchedulerStayingInStates(storm::storage::BitVector const& states, storm::storage::SparseMatrix<T> const& transitionMatrix);
/*!
* Computes a scheduler for the given states that chooses an action that has at least one successor in the
* given set of states. Note that this assumes that there is a legal choice for each of the states.
*
* @param states The set of states for which to compute the scheduler that chooses an action with a successor
* in this very set.
* @param transitionMatrix The transition matrix.
*/
template <typename T>
storm::storage::PartialScheduler computeSchedulerWithOneSuccessorInStates(storm::storage::BitVector const& states, storm::storage::SparseMatrix<T> const& transitionMatrix);
/*!
* Computes a scheduler for the ProbGreater0E-States such that in the induced system the given psiStates are reachable via phiStates
*
* @param transitionMatrix The transition matrix of the system.
* @param backwardTransitions The reversed transition relation.
* @param phiStates The set of states satisfying phi.
* @param psiStates The set of states satisfying psi.
* @param rowFilter If given, the returned scheduler will only pick choices such that rowFilter is true for the corresponding matrixrow.
* @return A Scheduler for the ProbGreater0E-States
*
* @note No choice is defined for ProbGreater0E-States if all the probGreater0-choices violate the row filter.
* This also holds for states that only reach psi via such states.
*/
template <typename T>
storm::storage::PartialScheduler computeSchedulerProbGreater0E(storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, boost::optional<storm::storage::BitVector> const& rowFilter = boost::none);
/*!
* Computes a scheduler for the given states that have a scheduler that has a probability 0.
*
* @param prob0EStates The states that have a scheduler achieving probablity 0.
* @param transitionMatrix The transition matrix of the system.
*/
template <typename T>
storm::storage::PartialScheduler computeSchedulerProb0E(storm::storage::BitVector const& prob0EStates, storm::storage::SparseMatrix<T> const& transitionMatrix);
/*!
* Computes a scheduler for the given prob1EStates such that in the induced system the given psiStates are reached with probability 1.
*
* @param prob1EStates The states that have a scheduler achieving probablity 1.
* @param transitionMatrix The transition matrix of the system.
* @param backwardTransitions The reversed transition relation.
* @param phiStates The set of states satisfying phi.
* @param psiStates The set of states satisfying psi.
* @return A scheduler for the Prob1E-States
*/
template <typename T>
storm::storage::PartialScheduler computeSchedulerProb1E(storm::storage::BitVector const& prob1EStates, storm::storage::SparseMatrix<T> const& transitionMatrix, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
/*!
* Computes the sets of states that have probability greater 0 of satisfying phi until psi under at least
* one possible resolution of non-determinism in a non-deterministic model. Stated differently,
* this means that these states have a probability greater 0 of satisfying phi until psi if the
* scheduler tries to minimize this probability.
*
* @param model The model whose graph structure to search.
* @param backwardTransitions The reversed transition relation of the model.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
* @param maximalSteps The maximal number of steps to reach the psi states.
* @return A bit vector that represents all states with probability 0.
*/
template <typename T>
storm::storage::BitVector performProbGreater0E(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0) ;
template <typename T>
storm::storage::BitVector performProb0A(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
/*!
* Computes the sets of states that have probability 0 of satisfying phi until psi under all
* possible resolutions of non-determinism in a non-deterministic model. Stated differently,
* this means that these states have probability 0 of satisfying phi until psi even if the
* scheduler tries to maximize this probability.
*
* @param model The model whose graph structure to search.
* @param backwardTransitions The reversed transition relation of the model.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
* @param maximalSteps The maximal number of steps to reach the psi states.
* @return A bit vector that represents all states with probability 0.
*/
template <typename T, typename RM>
storm::storage::BitVector performProb0A(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
/*!
* Computes the sets of states that have probability 1 of satisfying phi until psi under at least
* one possible resolution of non-determinism in a non-deterministic model. Stated differently,
* this means that these states have probability 1 of satisfying phi until psi if the
* scheduler tries to maximize this probability.
*
* @param model The model whose graph structure to search.
* @param backwardTransitions The reversed transition relation of the model.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @return A bit vector that represents all states with probability 1.
*/
template <typename T>
storm::storage::BitVector performProb1E(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
/*!
* Computes the sets of states that have probability 1 of satisfying phi until psi under at least
* one possible resolution of non-determinism in a non-deterministic model. Stated differently,
* this means that these states have probability 1 of satisfying phi until psi if the
* scheduler tries to maximize this probability.
*
* @param model The model whose graph structure to search.
* @param backwardTransitions The reversed transition relation of the model.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @return A bit vector that represents all states with probability 1.
*/
template <typename T, typename RM>
storm::storage::BitVector performProb1E(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template <typename T>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
/*!
* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi
* until psi in a non-deterministic model in which all non-deterministic choices are resolved
* such that the probability is maximized.
*
* @param model The model whose graph structure to search.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @return A pair of bit vectors that represent all states with probability 0 and 1, respectively.
*/
template <typename T, typename RM>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Max(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
/*!
* Computes the sets of states that have probability greater 0 of satisfying phi until psi under any
* possible resolution of non-determinism in a non-deterministic model. Stated differently,
* this means that these states have a probability greater 0 of satisfying phi until psi if the
* scheduler tries to maximize this probability.
*
* @param model The model whose graph structure to search.
* @param backwardTransitions The reversed transition relation of the model.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @param useStepBound A flag that indicates whether or not to use the given number of maximal steps for the search.
* @param maximalSteps The maximal number of steps to reach the psi states.
* @return A bit vector that represents all states with probability 0.
*/
template <typename T>
storm::storage::BitVector performProbGreater0A(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool useStepBound = false, uint_fast64_t maximalSteps = 0);
/*!
* Computes the sets of states that have probability 0 of satisfying phi until psi under at least
* one possible resolution of non-determinism in a non-deterministic model. Stated differently,
* this means that these states have probability 0 of satisfying phi until psi if the
* scheduler tries to minimize this probability.
*
* @param model The model whose graph structure to search.
* @param backwardTransitions The reversed transition relation of the model.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @return A bit vector that represents all states with probability 0.
*/
template <typename T, typename RM>
storm::storage::BitVector performProb0E(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template <typename T>
storm::storage::BitVector performProb0E(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
/*!
* Computes the sets of states that have probability 1 of satisfying phi until psi under all
* possible resolutions of non-determinism in a non-deterministic model. Stated differently,
* this means that these states have probability 1 of satisfying phi until psi even if the
* scheduler tries to minimize this probability.
*
* @param model The model whose graph structure to search.
* @param backwardTransitions The reversed transition relation of the model.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @return A bit vector that represents all states with probability 0.
*/
template <typename T, typename RM>
storm::storage::BitVector performProb1A(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template <typename T>
storm::storage::BitVector performProb1A( storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
template <typename T>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::storage::SparseMatrix<T> const& transitionMatrix, std::vector<uint_fast64_t> const& nondeterministicChoiceIndices, storm::storage::SparseMatrix<T> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) ;
/*!
* Computes the sets of states that have probability 0 or 1, respectively, of satisfying phi
* until psi in a non-deterministic model in which all non-deterministic choices are resolved
* such that the probability is minimized.
*
* @param model The model whose graph structure to search.
* @param phiStates The set of all states satisfying phi.
* @param psiStates The set of all states satisfying psi.
* @return A pair of bit vectors that represent all states with probability 0 and 1, respectively.
*/
template <typename T, typename RM>
std::pair<storm::storage::BitVector, storm::storage::BitVector> performProb01Min(storm::models::sparse::NondeterministicModel<T, RM> const& model, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates);
/*!
* Computes the set of states for which there exists a scheduler that achieves a probability greater than
* zero of satisfying phi until psi.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @return A BDD representing all such states.
*/
template <storm::dd::DdType Type, typename ValueType = double>
storm::dd::Bdd<Type> performProbGreater0E(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates);
/*!
* Computes the set of states for which there does not exist a scheduler that achieves a probability greater
* than zero of satisfying phi until psi.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The phi states of the model.
* @param psiStates The psi states of the model.
* @return A BDD representing all such states.
*/
template <storm::dd::DdType Type, typename ValueType = double>
storm::dd::Bdd<Type> performProb0A(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates);
/*!
* Computes the set of states for which all schedulers achieve a probability greater than zero of satisfying
* phi until psi.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @return A BDD representing all such states.
*/
template <storm::dd::DdType Type, typename ValueType = double>
storm::dd::Bdd<Type> performProbGreater0A(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates);
/*!
* Computes the set of states for which there exists a scheduler that achieves probability zero of satisfying
* phi until psi.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @return A BDD representing all such states.
*/
template <storm::dd::DdType Type, typename ValueType = double>
storm::dd::Bdd<Type> performProb0E(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates) ;
/*!
* Computes the set of states for which all schedulers achieve probability one of satisfying phi until psi.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @param statesWithProbabilityGreater0A The states of the model that have a probability greater zero under
* all schedulers.
* @return A BDD representing all such states.
*/
template <storm::dd::DdType Type, typename ValueType = double>
storm::dd::Bdd<Type> performProb1A(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::dd::Bdd<Type> const& statesWithProbabilityGreater0A);
/*!
* Computes the set of states for which there exists a scheduler that achieves probability one of satisfying
* phi until psi.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @param statesWithProbabilityGreater0E The states of the model that have a scheduler that achieves a value
* greater than zero.
* @return A BDD representing all such states.
*/
template <storm::dd::DdType Type, typename ValueType = double>
storm::dd::Bdd<Type> performProb1E(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::dd::Bdd<Type> const& statesWithProbabilityGreater0E);
template <storm::dd::DdType Type, typename ValueType = double>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01Max(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates);
template <storm::dd::DdType Type, typename ValueType = double>
std::pair<storm::dd::Bdd<Type>, storm::dd::Bdd<Type>> performProb01Min(storm::models::symbolic::NondeterministicModel<Type, ValueType> const& model, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates);
template <storm::dd::DdType Type>
struct GameProb01Result {
GameProb01Result() = default;
GameProb01Result(storm::dd::Bdd<Type> const& player1States, storm::dd::Bdd<Type> const& player2States, boost::optional<storm::dd::Bdd<Type>> const& player1Strategy = boost::none, boost::optional<storm::dd::Bdd<Type>> const& player2Strategy = boost::none) : player1States(player1States), player2States(player2States), player1Strategy(player1Strategy), player2Strategy(player2Strategy) {
// Intentionally left empty.
}
bool hasPlayer1Strategy() const {
return static_cast<bool>(player1Strategy);
}
storm::dd::Bdd<Type> const& getPlayer1Strategy() const {
return player1Strategy.get();
}
boost::optional<storm::dd::Bdd<Type>> const& getOptionalPlayer1Strategy() {
return player1Strategy;
}
bool hasPlayer2Strategy() const {
return static_cast<bool>(player2Strategy);
}
storm::dd::Bdd<Type> const& getPlayer2Strategy() const {
return player2Strategy.get();
}
boost::optional<storm::dd::Bdd<Type>> const& getOptionalPlayer2Strategy() {
return player2Strategy;
}
storm::dd::Bdd<Type> const& getPlayer1States() const {
return player1States;
}
storm::dd::Bdd<Type> const& getPlayer2States() const {
return player2States;
}
storm::dd::Bdd<Type> player1States;
storm::dd::Bdd<Type> player2States;
boost::optional<storm::dd::Bdd<Type>> player1Strategy;
boost::optional<storm::dd::Bdd<Type>> player2Strategy;
};
/*!
* Computes the set of states that have probability 0 given the strategies of the two players.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @param producePlayer1Strategy A flag indicating whether the strategy of player 1 shall be produced.
* @param producePlayer2Strategy A flag indicating whether the strategy of player 2 shall be produced.
*/
template <storm::dd::DdType Type, typename ValueType>
GameProb01Result<Type> performProb0(storm::models::symbolic::StochasticTwoPlayerGame<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::OptimizationDirection const& player1Strategy, storm::OptimizationDirection const& player2Strategy, bool producePlayer1Strategy = false, bool producePlayer2Strategy = false);
/*!
* Computes the set of states that have probability 1 given the strategies of the two players.
*
* @param model The (symbolic) model for which to compute the set of states.
* @param transitionMatrix The transition matrix of the model as a BDD.
* @param phiStates The BDD containing all phi states of the model.
* @param psiStates The BDD containing all psi states of the model.
* @param producePlayer1Strategy A flag indicating whether the strategy of player 1 shall be produced.
* @param producePlayer2Strategy A flag indicating whether the strategy of player 2 shall be produced.
* @param player1Candidates If given, this set constrains the candidates of player 1 states that are considered.
*/
template <storm::dd::DdType Type, typename ValueType>
GameProb01Result<Type> performProb1(storm::models::symbolic::StochasticTwoPlayerGame<Type, ValueType> const& model, storm::dd::Bdd<Type> const& transitionMatrix, storm::dd::Bdd<Type> const& phiStates, storm::dd::Bdd<Type> const& psiStates, storm::OptimizationDirection const& player1Strategy, storm::OptimizationDirection const& player2Strategy, bool producePlayer1Strategy = false, bool producePlayer2Strategy = false, boost::optional<storm::dd::Bdd<Type>> const& player1Candidates = boost::none);
/*!
* Performs a topological sort of the states of the system according to the given transitions.
*
* @param matrix A square matrix representing the transition relation of the system.
* @return A vector of indices that is a topological sort of the states.
*/
template <typename T>
std::vector<uint_fast64_t> getTopologicalSort(storm::storage::SparseMatrix<T> const& matrix);
/*!
* A class needed to compare the distances for two states in the Dijkstra search.
*/
template<typename T>
struct DistanceCompare {
bool operator()(std::pair<T, uint_fast64_t> const& lhs, std::pair<T, uint_fast64_t> const& rhs) const {
return lhs.first > rhs.first || (lhs.first == rhs.first && lhs.second > rhs.second);
}
};
/*!
* Performs a Dijkstra search from the given starting states to determine the most probable paths to all other states
* by only passing through the given state set.
*
* @param model The model whose state space is to be searched.
* @param transitions The transitions wrt to which to compute the most probable paths.
* @param startingStates The starting states of the Dijkstra search.
* @param filterStates A set of states that must not be left on any path.
*/
template <typename T>
std::pair<std::vector<T>, std::vector<uint_fast64_t>> performDijkstra(storm::models::sparse::Model<T> const& model,
storm::storage::SparseMatrix<T> const& transitions,
storm::storage::BitVector const& startingStates,
storm::storage::BitVector const* filterStates = nullptr);
} // namespace graph
} // namespace utility
} // namespace storm
#endif /* STORM_UTILITY_GRAPH_H_ */