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Revert back to older version ae0e423a4e [formerly e3f9d7a533] 

Former-commit-id: 9f72a10358
tempestpy_adaptions
PBerger 8 years ago
parent
bdf415d416
commit
1985c708ea
4 changed files with 42 additions and 66 deletions
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  1. 78
      src/modelchecker/abstraction/GameBasedMdpModelChecker.cpp
  2. 12
      src/solver/SymbolicGameSolver.cpp
  3. 2
      src/solver/SymbolicGameSolver.h
  4. 16
      test/functional/solver/FullySymbolicGameSolverTest.cpp

78
src/modelchecker/abstraction/GameBasedMdpModelChecker.cpp
View File

@ -400,14 +400,16 @@ namespace storm {
};
template<storm::dd::DdType Type, typename ValueType>
MaybeStateResult<Type, ValueType> solveMaybeStates(storm::OptimizationDirection const& player1Direction, storm::OptimizationDirection const& player2Direction, storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& prob0States, storm::dd::Bdd<Type> const& prob1States, boost::optional<MaybeStateResult<Type, ValueType>> startInfo = boost::none) {
MaybeStateResult<Type, ValueType> solveMaybeStates(storm::OptimizationDirection const& player1Direction, storm::OptimizationDirection const& player2Direction, storm::abstraction::MenuGame<Type, ValueType> const& game, storm::dd::Bdd<Type> const& maybeStates, storm::dd::Bdd<Type> const& prob1States, boost::optional<MaybeStateResult<Type, ValueType>> startInfo = boost::none) {
STORM_LOG_TRACE("Performing quantative solution step. Player 1: " << player1Direction << ", player 2: " << player2Direction << ".");
// Compute the ingredients of the equation system.
storm::dd::Add<Type, ValueType> maybeStatesAdd = game.getReachableStates().template toAdd<ValueType>();
// Compute the ingredients of the equation system.
storm::dd::Add<Type, ValueType> maybeStatesAdd = maybeStates.template toAdd<ValueType>();
storm::dd::Add<Type, ValueType> submatrix = maybeStatesAdd * game.getTransitionMatrix();
storm::dd::Add<Type, ValueType> subvector = game.getManager().template getAddZero<ValueType>();
storm::dd::Add<Type, ValueType> prob1StatesAsColumn = prob1States.template toAdd<ValueType>().swapVariables(game.getRowColumnMetaVariablePairs());
storm::dd::Add<Type, ValueType> subvector = submatrix * prob1StatesAsColumn;
subvector = subvector.sumAbstract(game.getColumnVariables());
// Cut away all columns targeting non-maybe states.
submatrix *= maybeStatesAdd.swapVariables(game.getRowColumnMetaVariablePairs());
@ -419,16 +421,12 @@ namespace storm {
} else {
startVector = game.getManager().template getAddZero<ValueType>();
}
// Set all target- and Prob1-states to 1 and all Prob0-states to 0
startVector = prob0States.ite(game.getManager().template getAddZero<ValueType>(), startVector);
startVector = prob1States.ite(game.getManager().template getAddOne<ValueType>(), startVector);
// Create the solver and solve the equation system.
storm::utility::solver::SymbolicGameSolverFactory<Type, ValueType> solverFactory;
std::unique_ptr<storm::solver::SymbolicGameSolver<Type, ValueType>> solver = solverFactory.create(submatrix, game.getReachableStates(), game.getIllegalPlayer1Mask(), game.getIllegalPlayer2Mask(), game.getRowVariables(), game.getColumnVariables(), game.getRowColumnMetaVariablePairs(), game.getPlayer1Variables(), game.getPlayer2Variables());
std::unique_ptr<storm::solver::SymbolicGameSolver<Type, ValueType>> solver = solverFactory.create(submatrix, maybeStates, game.getIllegalPlayer1Mask(), game.getIllegalPlayer2Mask(), game.getRowVariables(), game.getColumnVariables(), game.getRowColumnMetaVariablePairs(), game.getPlayer1Variables(), game.getPlayer2Variables());
solver->setGeneratePlayersStrategies(true);
auto values = solver->solveGame(player1Direction, player2Direction, startVector, subvector, prob0States, prob1States, startInfo ? boost::make_optional(startInfo.get().player1Strategy) : boost::none, startInfo ? boost::make_optional(startInfo.get().player2Strategy) : boost::none);
auto values = solver->solveGame(player1Direction, player2Direction, startVector, subvector, startInfo ? boost::make_optional(startInfo.get().player1Strategy) : boost::none, startInfo ? boost::make_optional(startInfo.get().player2Strategy) : boost::none);
return MaybeStateResult<Type, ValueType>(values, solver->getPlayer1Strategy(), solver->getPlayer2Strategy());
}
@ -527,14 +525,14 @@ namespace storm {
storm::dd::Add<Type, ValueType> minResult = prob01.min.second.getPlayer1States().template toAdd<ValueType>();
storm::dd::Add<Type, ValueType> maxResult = prob01.max.second.getPlayer1States().template toAdd<ValueType>();
storm::dd::Add<Type, ValueType> initialStatesAdd = game.getInitialStates().template toAdd<ValueType>();
// The minimal value after qualitative checking can only be zero. It it was 1, we could have given
// the result right away.
ValueType minValue = storm::utility::zero<ValueType>();
MaybeStateResult<Type, ValueType> minMaybeStateResult(game.getManager().template getAddZero<ValueType>(), game.getManager().getBddZero(), game.getManager().getBddZero());
if (!maybeMin.isZero()) {
minMaybeStateResult = solveMaybeStates(player1Direction, storm::OptimizationDirection::Minimize, game, prob01.min.first.getPlayer1States(), prob01.min.second.getPlayer1States());
minResult = minMaybeStateResult.values;
minMaybeStateResult = solveMaybeStates(player1Direction, storm::OptimizationDirection::Minimize, game, maybeMin, prob01.min.second.getPlayer1States());
minResult += minMaybeStateResult.values;
storm::dd::Add<Type, ValueType> initialStateMin = initialStatesAdd * minResult;
// Here we can only require a non-zero count of *at most* one, because the result may actually be 0.
STORM_LOG_ASSERT(initialStateMin.getNonZeroCount() <= 1, "Wrong number of results for initial states. Expected <= 1, but got " << initialStateMin.getNonZeroCount() << ".");
@ -553,8 +551,8 @@ namespace storm {
ValueType maxValue = storm::utility::one<ValueType>();
MaybeStateResult<Type, ValueType> maxMaybeStateResult(game.getManager().template getAddZero<ValueType>(), game.getManager().getBddZero(), game.getManager().getBddZero());
if (!maybeMax.isZero()) {
maxMaybeStateResult = solveMaybeStates(player1Direction, storm::OptimizationDirection::Maximize, game, prob01.max.first.getPlayer1States(), prob01.max.second.getPlayer1States(), boost::make_optional(minMaybeStateResult));
maxResult = maxMaybeStateResult.values;
maxMaybeStateResult = solveMaybeStates(player1Direction, storm::OptimizationDirection::Maximize, game, maybeMax, prob01.max.second.getPlayer1States(), boost::make_optional(minMaybeStateResult));
maxResult += maxMaybeStateResult.values;
storm::dd::Add<Type, ValueType> initialStateMax = (initialStatesAdd * maxResult);
// Unlike in the min-case, we can require a non-zero count of 1 here, because if the max was in
// fact 0, the result would be 0, which would have been detected earlier by the graph algorithms.
@ -579,30 +577,16 @@ namespace storm {
// If we arrived at this point, it means that we have all qualitative and quantitative information
// about the game, but we could not yet answer the query. In this case, we need to refine.
// Redirect all player 1 choices of the min strategy to that of the max strategy if this leads to a player 2 state that has the same prob.
// Get all relevant strategies.
storm::dd::Bdd<Type> minPlayer1Strategy = minMaybeStateResult.player1Strategy;
storm::dd::Bdd<Type> minPlayer2Strategy = minMaybeStateResult.player2Strategy;
storm::dd::Bdd<Type> maxPlayer1Strategy = maxMaybeStateResult.player1Strategy;
storm::dd::Bdd<Type> maxPlayer2Strategy = maxMaybeStateResult.player2Strategy;
storm::dd::Add<Type, ValueType> matrix = game.getTransitionMatrix();
storm::dd::Add<Type, ValueType> minResultTmp = minResult.swapVariables(game.getRowColumnMetaVariablePairs());
storm::dd::Add<Type, ValueType> minValuesForPlayer1UnderMinP1Strategy = (matrix * minPlayer1Strategy.template toAdd<ValueType>() * minPlayer2Strategy.template toAdd<ValueType>() * minResultTmp).sumAbstract(game.getColumnVariables()).sumAbstract(game.getPlayer2Variables());
storm::dd::Add<Type, ValueType> minValuesForPlayer1UnderMaxP1Strategy = (matrix * maxPlayer1Strategy.template toAdd<ValueType>() * minPlayer2Strategy.template toAdd<ValueType>() * minResultTmp).sumAbstract(game.getColumnVariables()).sumAbstract(game.getPlayer2Variables());
// This BDD has a 1 for every state (s) that can switch the strategy.
storm::dd::Bdd<Type> minIsGreaterOrEqual = minValuesForPlayer1UnderMinP1Strategy.greaterOrEqual(minValuesForPlayer1UnderMaxP1Strategy);
minPlayer1Strategy = minIsGreaterOrEqual.existsAbstract(game.getPlayer1Variables()).ite(maxPlayer1Strategy, minPlayer1Strategy);
// Start by extending the quantitative strategies by the qualitative ones.
minMaybeStateResult.player1Strategy |= prob01.min.first.getPlayer1Strategy() || prob01.min.second.getPlayer1Strategy();
storm::dd::Bdd<Type> tmp = (prob01.min.first.getPlayer2Strategy().existsAbstract(game.getPlayer2Variables()) && prob01.min.second.getPlayer2Strategy().existsAbstract(game.getPlayer2Variables()));
STORM_LOG_ASSERT(tmp.isZero(), "wth?");
tmp = prob01.min.first.getPlayer2Strategy().existsAbstract(game.getPlayer2Variables()) && minPlayer2Strategy.existsAbstract(game.getPlayer2Variables());
tmp = prob01.min.first.getPlayer2Strategy().existsAbstract(game.getPlayer2Variables()) && minMaybeStateResult.player2Strategy.existsAbstract(game.getPlayer2Variables());
if (!tmp.isZero()) {
tmp = tmp && prob01.min.first.getPlayer2Strategy().exclusiveOr(minPlayer2Strategy).existsAbstract(game.getPlayer2Variables());
tmp = tmp && prob01.min.first.getPlayer2Strategy().exclusiveOr(minMaybeStateResult.player2Strategy).existsAbstract(game.getPlayer2Variables());
(tmp && prob01.min.first.getPlayer2Strategy()).template toAdd<ValueType>().exportToDot("prob0_strat.dot");
(tmp && minPlayer2Strategy).template toAdd<ValueType>().exportToDot("maybe_strat.dot");
(tmp && minMaybeStateResult.player2Strategy).template toAdd<ValueType>().exportToDot("maybe_strat.dot");
if (!tmp.isZero()) {
storm::dd::Add<Type, ValueType> values = (tmp.template toAdd<ValueType>() * game.getTransitionMatrix() * minResult.swapVariables(game.getRowColumnMetaVariablePairs())).sumAbstract(game.getColumnVariables());
tmp.template toAdd<ValueType>().exportToDot("illegal.dot");
@ -611,20 +595,20 @@ namespace storm {
STORM_LOG_ASSERT(tmp.isZero(), "ddduuuudde?");
}
STORM_LOG_ASSERT(tmp.isZero(), "wth2?");
//tmp = prob01.min.second.getPlayer2Strategy().existsAbstract(game.getPlayer2Variables()) && minPlayer2Strategy;
tmp = prob01.min.second.getPlayer2Strategy().existsAbstract(game.getPlayer2Variables()) && minMaybeStateResult.player2Strategy;
//(minMaybeStateResult.player2Strategy && (prob01.min.first.getPlayer2Strategy() || prob01.min.second.getPlayer2Strategy())).template toAdd<ValueType>().exportToDot("strat_overlap.dot");
//minMaybeStateResult.player2Strategy |= prob01.min.first.getPlayer2Strategy() || prob01.min.second.getPlayer2Strategy();
//maxMaybeStateResult.player1Strategy |= prob01.max.first.getPlayer1Strategy() || prob01.max.second.getPlayer1Strategy();
//maxMaybeStateResult.player2Strategy |= prob01.max.first.getPlayer2Strategy() || prob01.max.second.getPlayer2Strategy();
(minMaybeStateResult.player2Strategy && (prob01.min.first.getPlayer2Strategy() || prob01.min.second.getPlayer2Strategy())).template toAdd<ValueType>().exportToDot("strat_overlap.dot");
minMaybeStateResult.player2Strategy |= prob01.min.first.getPlayer2Strategy() || prob01.min.second.getPlayer2Strategy();
maxMaybeStateResult.player1Strategy |= prob01.max.first.getPlayer1Strategy() || prob01.max.second.getPlayer1Strategy();
maxMaybeStateResult.player2Strategy |= prob01.max.first.getPlayer2Strategy() || prob01.max.second.getPlayer2Strategy();
// Make sure that all strategies are still valid strategies.
STORM_LOG_ASSERT(minPlayer1Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer1Variables()).getMax() <= 1, "Player 1 strategy for min is illegal.");
STORM_LOG_ASSERT(maxPlayer1Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer1Variables()).getMax() <= 1, "Player 1 strategy for max is illegal.");
STORM_LOG_ASSERT(minPlayer2Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer2Variables()).getMax() <= 1, "Player 2 strategy for min is illegal.");
STORM_LOG_ASSERT(maxPlayer2Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer2Variables()).getMax() <= 1, "Player 2 strategy for max is illegal.");
STORM_LOG_ASSERT(minMaybeStateResult.player1Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer1Variables()).getMax() <= 1, "Player 1 strategy for min is illegal.");
STORM_LOG_ASSERT(maxMaybeStateResult.player1Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer1Variables()).getMax() <= 1, "Player 1 strategy for max is illegal.");
STORM_LOG_ASSERT(minMaybeStateResult.player2Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer2Variables()).getMax() <= 1, "Player 2 strategy for min is illegal.");
STORM_LOG_ASSERT(maxMaybeStateResult.player2Strategy.template toAdd<ValueType>().sumAbstract(game.getPlayer2Variables()).getMax() <= 1, "Player 2 strategy for max is illegal.");
refineAfterQuantitativeCheck(abstractor, game, minResult, maxResult, prob01, std::make_pair(minPlayer1Strategy, minPlayer2Strategy), std::make_pair(maxPlayer1Strategy, maxPlayer2Strategy), transitionMatrixBdd);
refineAfterQuantitativeCheck(abstractor, game, minResult, maxResult, prob01, std::make_pair(minMaybeStateResult.player1Strategy, minMaybeStateResult.player2Strategy), std::make_pair(maxMaybeStateResult.player1Strategy, maxMaybeStateResult.player2Strategy), transitionMatrixBdd);
}
}
@ -649,7 +633,7 @@ namespace storm {
return std::make_pair(prob0, prob1);
}
template<storm::dd::DdType Type, typename ModelType>
storm::expressions::Expression GameBasedMdpModelChecker<Type, ModelType>::getExpression(storm::logic::Formula const& formula) {
STORM_LOG_THROW(formula.isBooleanLiteralFormula() || formula.isAtomicExpressionFormula() || formula.isAtomicLabelFormula(), storm::exceptions::InvalidPropertyException, "The target states have to be given as label or an expression.");
@ -663,11 +647,11 @@ namespace storm {
}
return result;
}
template class GameBasedMdpModelChecker<storm::dd::DdType::CUDD, storm::models::symbolic::Dtmc<storm::dd::DdType::CUDD, double>>;
template class GameBasedMdpModelChecker<storm::dd::DdType::CUDD, storm::models::symbolic::Mdp<storm::dd::DdType::CUDD, double>>;
template class GameBasedMdpModelChecker<storm::dd::DdType::Sylvan, storm::models::symbolic::Dtmc<storm::dd::DdType::Sylvan, double>>;
template class GameBasedMdpModelChecker<storm::dd::DdType::Sylvan, storm::models::symbolic::Mdp<storm::dd::DdType::Sylvan, double>>;
}
}
}

12
src/solver/SymbolicGameSolver.cpp
View File

@ -25,16 +25,12 @@ namespace storm {
}
template<storm::dd::DdType Type, typename ValueType>
storm::dd::Add<Type, ValueType> SymbolicGameSolver<Type, ValueType>::solveGame(OptimizationDirection player1Goal, OptimizationDirection player2Goal, storm::dd::Add<Type, ValueType> const& x, storm::dd::Add<Type, ValueType> const& b, storm::dd::Bdd<Type> const& prob0States, storm::dd::Bdd<Type> const& prob1States, boost::optional<storm::dd::Bdd<Type>> const& basePlayer1Strategy, boost::optional<storm::dd::Bdd<Type>> const& basePlayer2Strategy) {
storm::dd::Add<Type, ValueType> SymbolicGameSolver<Type, ValueType>::solveGame(OptimizationDirection player1Goal, OptimizationDirection player2Goal, storm::dd::Add<Type, ValueType> const& x, storm::dd::Add<Type, ValueType> const& b, boost::optional<storm::dd::Bdd<Type>> const& basePlayer1Strategy, boost::optional<storm::dd::Bdd<Type>> const& basePlayer2Strategy) {
// Set up the environment.
storm::dd::Add<Type, ValueType> xCopy = x;
uint_fast64_t iterations = 0;
bool converged = false;
// Constants
storm::dd::Add<Type, ValueType> const addOne = A.getDdManager().template getAddOne<ValueType>();
storm::dd::Add<Type, ValueType> const addZero = A.getDdManager().template getAddZero<ValueType>();
// Prepare some data storage in case we need to generate strategies.
if (generatePlayer1Strategy) {
if (basePlayer1Strategy) {
@ -53,7 +49,7 @@ namespace storm {
previousPlayer2Values = (player2Strategy.get().template toAdd<ValueType>() * (this->A.multiplyMatrix(x.swapVariables(this->rowColumnMetaVariablePairs), this->columnMetaVariables) + b)).sumAbstract(this->player2Variables);
} else {
player2Strategy = A.getDdManager().getBddZero();
previousPlayer2Values = addZero;
previousPlayer2Values = A.getDdManager().template getAddZero<ValueType>();
}
}
@ -107,10 +103,6 @@ namespace storm {
tmp = newValues;
}
// Fix Prob0 and Prob1 States
tmp = prob0States.ite(addZero, tmp);
tmp = prob1States.ite(addOne, tmp);
// Now check if the process already converged within our precision.
converged = xCopy.equalModuloPrecision(tmp, this->precision, this->relative);

2
src/solver/SymbolicGameSolver.h
View File

@ -70,7 +70,7 @@ namespace storm {
* then this strategy can be used to generate a strategy that only differs from the given one if it has to.
* @return The solution vector.
*/
virtual storm::dd::Add<Type, ValueType> solveGame(OptimizationDirection player1Goal, OptimizationDirection player2Goal, storm::dd::Add<Type, ValueType> const& x, storm::dd::Add<Type, ValueType> const& b, storm::dd::Bdd<Type> const& prob0States, storm::dd::Bdd<Type> const& prob1States, boost::optional<storm::dd::Bdd<Type>> const& basePlayer1Strategy = boost::none, boost::optional<storm::dd::Bdd<Type>> const& basePlayer2Strategy = boost::none);
virtual storm::dd::Add<Type, ValueType> solveGame(OptimizationDirection player1Goal, OptimizationDirection player2Goal, storm::dd::Add<Type, ValueType> const& x, storm::dd::Add<Type, ValueType> const& b, boost::optional<storm::dd::Bdd<Type>> const& basePlayer1Strategy = boost::none, boost::optional<storm::dd::Bdd<Type>> const& basePlayer2Strategy = boost::none);
// Setters that enable the generation of the players' strategies.
void setGeneratePlayer1Strategy(bool value);

16
test/functional/solver/FullySymbolicGameSolverTest.cpp
View File

@ -49,25 +49,25 @@ TEST(FullySymbolicGameSolverTest, Solve_Cudd) {
storm::dd::Add<storm::dd::DdType::CUDD, double> b = manager->getEncoding(state.first, 2).template toAdd<double>() + manager->getEncoding(state.first, 4).template toAdd<double>();
// Now solve the game with different strategies for the players.
storm::dd::Add<storm::dd::DdType::CUDD> result = solver->solveGame(storm::OptimizationDirection::Minimize, storm::OptimizationDirection::Minimize, x, b, manager->getBddZero(), manager->getBddZero());
storm::dd::Add<storm::dd::DdType::CUDD> result = solver->solveGame(storm::OptimizationDirection::Minimize, storm::OptimizationDirection::Minimize, x, b);
result *= manager->getEncoding(state.first, 1).template toAdd<double>();
result = result.sumAbstract({state.first});
EXPECT_NEAR(0, result.getValue(), storm::settings::getModule<storm::settings::modules::NativeEquationSolverSettings>().getPrecision());
x = manager->getAddZero<double>();
result = solver->solveGame(storm::OptimizationDirection::Minimize, storm::OptimizationDirection::Maximize, x, b, manager->getBddZero(), manager->getBddZero());
result = solver->solveGame(storm::OptimizationDirection::Minimize, storm::OptimizationDirection::Maximize, x, b);
result *= manager->getEncoding(state.first, 1).template toAdd<double>();
result = result.sumAbstract({state.first});
EXPECT_NEAR(0.5, result.getValue(), storm::settings::getModule<storm::settings::modules::NativeEquationSolverSettings>().getPrecision());
x = manager->getAddZero<double>();
result = solver->solveGame(storm::OptimizationDirection::Maximize, storm::OptimizationDirection::Minimize, x, b, manager->getBddZero(), manager->getBddZero());
result = solver->solveGame(storm::OptimizationDirection::Maximize, storm::OptimizationDirection::Minimize, x, b);
result *= manager->getEncoding(state.first, 1).template toAdd<double>();
result = result.sumAbstract({state.first});
EXPECT_NEAR(0.2, result.getValue(), storm::settings::getModule<storm::settings::modules::NativeEquationSolverSettings>().getPrecision());
x = manager->getAddZero<double>();
result = solver->solveGame(storm::OptimizationDirection::Maximize, storm::OptimizationDirection::Maximize, x, b, manager->getBddZero(), manager->getBddZero());
result = solver->solveGame(storm::OptimizationDirection::Maximize, storm::OptimizationDirection::Maximize, x, b);
result *= manager->getEncoding(state.first, 1).template toAdd<double>();
result = result.sumAbstract({state.first});
EXPECT_NEAR(0.99999892625817599, result.getValue(), storm::settings::getModule<storm::settings::modules::NativeEquationSolverSettings>().getPrecision());
@ -114,25 +114,25 @@ TEST(FullySymbolicGameSolverTest, Solve_Sylvan) {
storm::dd::Add<storm::dd::DdType::Sylvan, double> b = manager->getEncoding(state.first, 2).template toAdd<double>() + manager->getEncoding(state.first, 4).template toAdd<double>();
// Now solve the game with different strategies for the players.
storm::dd::Add<storm::dd::DdType::Sylvan> result = solver->solveGame(storm::OptimizationDirection::Minimize, storm::OptimizationDirection::Minimize, x, b, manager->getBddZero(), manager->getBddZero());
storm::dd::Add<storm::dd::DdType::Sylvan> result = solver->solveGame(storm::OptimizationDirection::Minimize, storm::OptimizationDirection::Minimize, x, b);
result *= manager->getEncoding(state.first, 1).template toAdd<double>();
result = result.sumAbstract({state.first});
EXPECT_NEAR(0, result.getValue(), storm::settings::getModule<storm::settings::modules::NativeEquationSolverSettings>().getPrecision());
x = manager->getAddZero<double>();
result = solver->solveGame(storm::OptimizationDirection::Minimize, storm::OptimizationDirection::Maximize, x, b, manager->getBddZero(), manager->getBddZero());
result = solver->solveGame(storm::OptimizationDirection::Minimize, storm::OptimizationDirection::Maximize, x, b);
result *= manager->getEncoding(state.first, 1).template toAdd<double>();
result = result.sumAbstract({state.first});
EXPECT_NEAR(0.5, result.getValue(), storm::settings::getModule<storm::settings::modules::NativeEquationSolverSettings>().getPrecision());
x = manager->getAddZero<double>();
result = solver->solveGame(storm::OptimizationDirection::Maximize, storm::OptimizationDirection::Minimize, x, b, manager->getBddZero(), manager->getBddZero());
result = solver->solveGame(storm::OptimizationDirection::Maximize, storm::OptimizationDirection::Minimize, x, b);
result *= manager->getEncoding(state.first, 1).template toAdd<double>();
result = result.sumAbstract({state.first});
EXPECT_NEAR(0.2, result.getValue(), storm::settings::getModule<storm::settings::modules::NativeEquationSolverSettings>().getPrecision());
x = manager->getAddZero<double>();
result = solver->solveGame(storm::OptimizationDirection::Maximize, storm::OptimizationDirection::Maximize, x, b, manager->getBddZero(), manager->getBddZero());
result = solver->solveGame(storm::OptimizationDirection::Maximize, storm::OptimizationDirection::Maximize, x, b);
result *= manager->getEncoding(state.first, 1).template toAdd<double>();
result = result.sumAbstract({state.first});
EXPECT_NEAR(0.99999892625817599, result.getValue(), storm::settings::getModule<storm::settings::modules::NativeEquationSolverSettings>().getPrecision());
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