#include "storm/storage/StronglyConnectedComponentDecomposition.h"
#include "storm/models/sparse/Model.h"
#include "storm/models/sparse/StandardRewardModel.h"
#include "storm/adapters/RationalFunctionAdapter.h"
#include "storm/utility/macros.h"
#include "storm/exceptions/UnexpectedException.h"
namespace storm {
namespace storage {
template <typename ValueType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition() : Decomposition() {
// Intentionally left empty.
}
template <typename ValueType>
template <typename RewardModelType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<ValueType, RewardModelType> const& model, bool dropNaiveSccs, bool onlyBottomSccs) : Decomposition() {
performSccDecomposition(model, dropNaiveSccs, onlyBottomSccs);
}
template <typename ValueType>
template <typename RewardModelType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<ValueType, RewardModelType> const& model, StateBlock const& block, bool dropNaiveSccs, bool onlyBottomSccs) {
storm::storage::BitVector subsystem(model.getNumberOfStates(), block.begin(), block.end());
performSccDecomposition(model.getTransitionMatrix(), subsystem, dropNaiveSccs, onlyBottomSccs);
}
template <typename ValueType>
template <typename RewardModelType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<ValueType, RewardModelType> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs) {
performSccDecomposition(model.getTransitionMatrix(), subsystem, dropNaiveSccs, onlyBottomSccs);
}
template <typename ValueType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition(storm::storage::SparseMatrix<ValueType> const& transitionMatrix, StateBlock const& block, bool dropNaiveSccs, bool onlyBottomSccs) {
storm::storage::BitVector subsystem(transitionMatrix.getRowGroupCount(), block.begin(), block.end());
performSccDecomposition(transitionMatrix, subsystem, dropNaiveSccs, onlyBottomSccs);
}
template <typename ValueType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition(storm::storage::SparseMatrix<ValueType> const& transitionMatrix, bool dropNaiveSccs, bool onlyBottomSccs) {
performSccDecomposition(transitionMatrix, storm::storage::BitVector(transitionMatrix.getRowGroupCount(), true), dropNaiveSccs, onlyBottomSccs);
}
template <typename ValueType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition(storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs) {
performSccDecomposition(transitionMatrix, subsystem, dropNaiveSccs, onlyBottomSccs);
}
template <typename ValueType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition(StronglyConnectedComponentDecomposition const& other) : Decomposition(other) {
// Intentionally left empty.
}
template <typename ValueType>
StronglyConnectedComponentDecomposition<ValueType>& StronglyConnectedComponentDecomposition<ValueType>::operator=(StronglyConnectedComponentDecomposition const& other) {
this->blocks = other.blocks;
return *this;
}
template <typename ValueType>
StronglyConnectedComponentDecomposition<ValueType>::StronglyConnectedComponentDecomposition(StronglyConnectedComponentDecomposition&& other) : Decomposition(std::move(other)) {
// Intentionally left empty.
}
template <typename ValueType>
StronglyConnectedComponentDecomposition<ValueType>& StronglyConnectedComponentDecomposition<ValueType>::operator=(StronglyConnectedComponentDecomposition&& other) {
this->blocks = std::move(other.blocks);
return *this;
}
template <typename ValueType>
void StronglyConnectedComponentDecomposition<ValueType>::performSccDecomposition(storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs) {
uint_fast64_t numberOfStates = transitionMatrix.getRowGroupCount();
// Set up the environment of the algorithm.
// Start with the two stacks it maintains.
std::vector<uint_fast64_t> s;
s.reserve(numberOfStates);
std::vector<uint_fast64_t> p;
p.reserve(numberOfStates);
// We also need to store the preorder numbers of states and which states have been assigned to which SCC.
std::vector<uint_fast64_t> preorderNumbers(numberOfStates);
storm::storage::BitVector hasPreorderNumber(numberOfStates);
storm::storage::BitVector stateHasScc(numberOfStates);
std::vector<uint_fast64_t> stateToSccMapping(numberOfStates);
uint_fast64_t sccCount = 0;
// Finally, we need to keep track of the states with a self-loop to identify naive SCCs.
storm::storage::BitVector statesWithSelfLoop(numberOfStates);
// Start the search for SCCs from every state in the block.
uint_fast64_t currentIndex = 0;
for (auto state : subsystem) {
if (!hasPreorderNumber.get(state)) {
performSccDecompositionGCM(transitionMatrix, state, statesWithSelfLoop, subsystem, currentIndex, hasPreorderNumber, preorderNumbers, s, p, stateHasScc, stateToSccMapping, sccCount);
}
}
// After we obtained the state-to-SCC mapping, we build the actual blocks.
this->blocks.resize(sccCount);
for (auto state : subsystem) {
this->blocks[stateToSccMapping[state]].insert(state);
}
// Now flag all trivial SCCs as such.
for (uint_fast64_t sccIndex = 0; sccIndex < sccCount; ++sccIndex) {
if (this->blocks[sccIndex].size() == 1) {
uint_fast64_t onlyState = *this->blocks[sccIndex].begin();
if (!statesWithSelfLoop.get(onlyState)) {
this->blocks[sccIndex].setIsTrivial(true);
}
}
}
// If requested, we need to drop some SCCs.
if (onlyBottomSccs || dropNaiveSccs) {
storm::storage::BitVector blocksToDrop(sccCount);
// If requested, we need to delete all naive SCCs.
if (dropNaiveSccs) {
for (uint_fast64_t sccIndex = 0; sccIndex < sccCount; ++sccIndex) {
if (this->blocks[sccIndex].isTrivial()) {
blocksToDrop.set(sccIndex);
}
}
}
// If requested, we need to drop all non-bottom SCCs.
if (onlyBottomSccs) {
for (uint_fast64_t state = 0; state < numberOfStates; ++state) {
// If the block of the state is already known to be dropped, we don't need to check the transitions.
if (!blocksToDrop.get(stateToSccMapping[state])) {
for (typename storm::storage::SparseMatrix<ValueType>::const_iterator successorIt = transitionMatrix.getRowGroup(state).begin(), successorIte = transitionMatrix.getRowGroup(state).end(); successorIt != successorIte; ++successorIt) {
if (subsystem.get(successorIt->getColumn()) && stateToSccMapping[state] != stateToSccMapping[successorIt->getColumn()]) {
blocksToDrop.set(stateToSccMapping[state]);
break;
}
}
}
}
}
// Create the new set of blocks by moving all the blocks we need to keep into it.
std::vector<block_type> newBlocks((~blocksToDrop).getNumberOfSetBits());
uint_fast64_t currentBlock = 0;
for (uint_fast64_t blockIndex = 0; blockIndex < this->blocks.size(); ++blockIndex) {
if (!blocksToDrop.get(blockIndex)) {
newBlocks[currentBlock] = std::move(this->blocks[blockIndex]);
++currentBlock;
}
}
// Now set this new set of blocks as the result of the decomposition.
this->blocks = std::move(newBlocks);
}
}
template <typename ValueType>
template <typename RewardModelType>
void StronglyConnectedComponentDecomposition<ValueType>::performSccDecomposition(storm::models::sparse::Model<ValueType, RewardModelType> const& model, bool dropNaiveSccs, bool onlyBottomSccs) {
// Prepare a block that contains all states for a call to the other overload of this function.
storm::storage::BitVector fullSystem(model.getNumberOfStates(), true);
// Call the overloaded function.
performSccDecomposition(model.getTransitionMatrix(), fullSystem, dropNaiveSccs, onlyBottomSccs);
}
template <typename ValueType>
void StronglyConnectedComponentDecomposition<ValueType>::performSccDecompositionGCM(storm::storage::SparseMatrix<ValueType> const& transitionMatrix, uint_fast64_t startState, storm::storage::BitVector& statesWithSelfLoop, storm::storage::BitVector const& subsystem, uint_fast64_t& currentIndex, storm::storage::BitVector& hasPreorderNumber, std::vector<uint_fast64_t>& preorderNumbers, std::vector<uint_fast64_t>& s, std::vector<uint_fast64_t>& p, storm::storage::BitVector& stateHasScc, std::vector<uint_fast64_t>& stateToSccMapping, uint_fast64_t& sccCount) {
// Prepare the stack used for turning the recursive procedure into an iterative one.
std::vector<uint_fast64_t> recursionStateStack;
recursionStateStack.reserve(transitionMatrix.getRowGroupCount());
recursionStateStack.push_back(startState);
while (!recursionStateStack.empty()) {
// Peek at the topmost state in the stack, but leave it on there for now.
uint_fast64_t currentState = recursionStateStack.back();
// If the state has not yet been seen, we need to assign it a preorder number and iterate over its successors.
if (!hasPreorderNumber.get(currentState)) {
preorderNumbers[currentState] = currentIndex++;
hasPreorderNumber.set(currentState, true);
s.push_back(currentState);
p.push_back(currentState);
for (auto const& successor : transitionMatrix.getRowGroup(currentState)) {
if (subsystem.get(successor.getColumn()) && successor.getValue() != storm::utility::zero<ValueType>()) {
if (currentState == successor.getColumn()) {
statesWithSelfLoop.set(currentState);
}
if (!hasPreorderNumber.get(successor.getColumn())) {
// In this case, we must recursively visit the successor. We therefore push the state
// onto the recursion stack.
recursionStateStack.push_back(successor.getColumn());
} else {
if (!stateHasScc.get(successor.getColumn())) {
while (preorderNumbers[p.back()] > preorderNumbers[successor.getColumn()]) {
p.pop_back();
}
}
}
}
}
} else {
// In this case, we have searched all successors of the current state and can exit the "recursion"
// on the current state.
if (currentState == p.back()) {
p.pop_back();
uint_fast64_t poppedState = 0;
do {
poppedState = s.back();
s.pop_back();
stateToSccMapping[poppedState] = sccCount;
stateHasScc.set(poppedState);
} while (poppedState != currentState);
++sccCount;
}
recursionStateStack.pop_back();
}
}
}
template <typename ValueType>
void StronglyConnectedComponentDecomposition<ValueType>::sortTopologically(storm::storage::SparseMatrix<ValueType> const& transitions, uint64_t* longestChainSize) {
// Get a mapping from state to the corresponding scc
STORM_LOG_THROW(this->size() < std::numeric_limits<uint32_t>::max(), storm::exceptions::UnexpectedException, "The number of SCCs is too large.");
std::vector<uint32_t> sccIndices(transitions.getRowGroupCount(), std::numeric_limits<uint32_t>::max());
uint32_t sccIndex = 0;
for (auto const& scc : *this) {
for (auto const& state : scc) {
sccIndices[state] = sccIndex;
}
++sccIndex;
}
// Prepare the resulting set of sorted sccs
std::vector<storm::storage::StronglyConnectedComponent> sortedSCCs;
sortedSCCs.reserve(this->size());
// Find a topological sort via DFS.
storm::storage::BitVector unsortedSCCs(this->size(), true);
std::vector<uint32_t> sccStack, chainSizes;
if (longestChainSize != nullptr) {
chainSizes.resize(this->size(), 1u);
*longestChainSize = 0;
}
uint32_t const token = std::numeric_limits<uint32_t>::max();
std::set<uint64_t> successorSCCs;
for (uint32_t firstUnsortedScc = 0; firstUnsortedScc < unsortedSCCs.size(); firstUnsortedScc = unsortedSCCs.getNextSetIndex(firstUnsortedScc + 1)) {
sccStack.push_back(firstUnsortedScc);
while (!sccStack.empty()) {
uint32_t currentSccIndex = sccStack.back();
if (currentSccIndex != token) {
// Check whether the SCC is still unprocessed
if (unsortedSCCs.get(currentSccIndex)) {
// Explore the successors of the scc.
storm::storage::StronglyConnectedComponent const& currentScc = this->getBlock(currentSccIndex);
// We first push a token on the stack in order to recognize later when all successors of this SCC have been explored already.
sccStack.push_back(token);
// Now add all successors that are not already sorted.
// Successors should only be added once, so we first prepare a set of them and add them afterwards.
successorSCCs.clear();
for (auto const& state : currentScc) {
for (auto const& entry : transitions.getRowGroup(state)) {
auto const& successorSCC = sccIndices[entry.getColumn()];
if (successorSCC != currentSccIndex && unsortedSCCs.get(successorSCC)) {
successorSCCs.insert(successorSCC);
}
}
}
sccStack.insert(sccStack.end(), successorSCCs.begin(), successorSCCs.end());
}
} else {
// all successors of the current scc have already been explored.
sccStack.pop_back(); // pop the token
currentSccIndex = sccStack.back();
storm::storage::StronglyConnectedComponent& scc = this->getBlock(currentSccIndex);
// Compute the longest chain size for this scc
if (longestChainSize != nullptr) {
uint32_t& currentChainSize = chainSizes[currentSccIndex];
for (auto const& state : scc) {
for (auto const& entry : transitions.getRowGroup(state)) {
auto const& successorSCC = sccIndices[entry.getColumn()];
if (successorSCC != currentSccIndex) {
currentChainSize = std::max(currentChainSize, chainSizes[successorSCC] + 1);
}
}
}
*longestChainSize = std::max<uint64_t>(*longestChainSize, currentChainSize);
}
unsortedSCCs.set(currentSccIndex, false);
sccStack.pop_back(); // pop the current scc index
sortedSCCs.push_back(std::move(scc));
}
}
}
this->blocks = std::move(sortedSCCs);
}
// Explicitly instantiate the SCC decomposition.
template class StronglyConnectedComponentDecomposition<double>;
template StronglyConnectedComponentDecomposition<double>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<double> const& model, bool dropNaiveSccs, bool onlyBottomSccs);
template StronglyConnectedComponentDecomposition<double>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<double> const& model, StateBlock const& block, bool dropNaiveSccs, bool onlyBottomSccs);
template StronglyConnectedComponentDecomposition<double>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<double> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs);
template class StronglyConnectedComponentDecomposition<float>;
template StronglyConnectedComponentDecomposition<float>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<float> const& model, bool dropNaiveSccs, bool onlyBottomSccs);
template StronglyConnectedComponentDecomposition<float>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<float> const& model, StateBlock const& block, bool dropNaiveSccs, bool onlyBottomSccs);
template StronglyConnectedComponentDecomposition<float>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<float> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs);
#ifdef STORM_HAVE_CARL
template class StronglyConnectedComponentDecomposition<storm::RationalNumber>;
template StronglyConnectedComponentDecomposition<storm::RationalNumber>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<storm::RationalNumber> const& model, bool dropNaiveSccs, bool onlyBottomSccs);
template StronglyConnectedComponentDecomposition<storm::RationalNumber>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<storm::RationalNumber> const& model, StateBlock const& block, bool dropNaiveSccs, bool onlyBottomSccs);
template StronglyConnectedComponentDecomposition<storm::RationalNumber>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<storm::RationalNumber> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs);
template class StronglyConnectedComponentDecomposition<storm::RationalFunction>;
template StronglyConnectedComponentDecomposition<storm::RationalFunction>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<storm::RationalFunction> const& model, bool dropNaiveSccs, bool onlyBottomSccs);
template StronglyConnectedComponentDecomposition<storm::RationalFunction>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<storm::RationalFunction> const& model, StateBlock const& block, bool dropNaiveSccs, bool onlyBottomSccs);
template StronglyConnectedComponentDecomposition<storm::RationalFunction>::StronglyConnectedComponentDecomposition(storm::models::sparse::Model<storm::RationalFunction> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs);
#endif
} // namespace storage
} // namespace storm