diff --git a/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessor.cpp b/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessor.cpp
index f091b364b..ad2bd7152 100644
--- a/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessor.cpp
+++ b/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessor.cpp
@@ -4,8 +4,8 @@
 #include "src/models/sparse/StandardRewardModel.h"
 #include "src/modelchecker/propositional/SparsePropositionalModelChecker.h"
 #include "src/modelchecker/results/ExplicitQualitativeCheckResult.h"
-#include "src/storage/BitVector.h"
 #include "src/transformer/StateDuplicator.h"
+#include "src/transformer/SubsystemBuilder.h"
 #include "src/utility/macros.h"
 #include "src/utility/vector.h"
 #include "src/utility/graph.h"
@@ -18,10 +18,11 @@ namespace storm {
         namespace helper {
             
             template<typename SparseModelType>
-            typename SparseMultiObjectivePreprocessor<SparseModelType>::PreprocessorData SparseMultiObjectivePreprocessor<SparseModelType>::preprocess(storm::logic::MultiObjectiveFormula const& originalFormula, SparseModelType const& originalModel) {
-                PreprocessorData data(std::move(originalModel));
-                //Initialize the state mapping.
-                data.newToOldStateIndexMapping = storm::utility::vector::buildVectorForRange(0, data.preprocessedModel.getNumberOfStates());
+            typename SparseMultiObjectivePreprocessor<SparseModelType>::PreprocessorData SparseMultiObjectivePreprocessor<SparseModelType>::preprocess(storm::logic::MultiObjectiveFormula const& originalFormula, SparseModelType const& originalModel, storm::storage::BitVector const& subsystem) {
+                
+                auto subsystemBuilderResult = storm::transformer::SubsystemBuilder<SparseModelType>::transform(originalModel, subsystem);
+                PreprocessorData data(originalModel, std::move(*subsystemBuilderResult.model), std::move(subsystemBuilderResult.newToOldStateIndexMapping));
+                
                 //Invoke preprocessing on the individual objectives
                 for(auto const& subFormula : originalFormula.getSubFormulas()){
                     STORM_LOG_DEBUG("Preprocessing objective " << *subFormula<< ".");
diff --git a/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessor.h b/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessor.h
index 10ce6f9bb..a3e91824f 100644
--- a/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessor.h
+++ b/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessor.h
@@ -3,6 +3,7 @@
 
 #include "src/logic/Formulas.h"
 #include "src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessorData.h"
+#include "src/storage/BitVector.h"
 
 namespace storm {
     namespace modelchecker {
@@ -25,8 +26,10 @@ namespace storm {
                  * Preprocesses the given model w.r.t. the given formulas.
                  * @param originalModel The considered model
                  * @param originalFormula the considered formula. The subformulas should only contain one OperatorFormula at top level, i.e., the formula is simple.
+                 * @param subsystem the states of the original model which should be considered. Choices that have a transition leading outside of the subsystem will be
+                 *                  removed. Hence, every state in the subsystem has to have one choice that stays inside the subsystem.
                  */
-                static PreprocessorData preprocess(storm::logic::MultiObjectiveFormula const& originalFormula, SparseModelType const& originalModel);
+                static PreprocessorData preprocess(storm::logic::MultiObjectiveFormula const& originalFormula, SparseModelType const& originalModel,  storm::storage::BitVector const& subsystem);
                 
             private:
                 
diff --git a/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessorData.h b/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessorData.h
index ae2015b48..31b5f22c6 100644
--- a/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessorData.h
+++ b/src/modelchecker/multiobjective/helper/SparseMultiObjectivePreprocessorData.h
@@ -17,8 +17,8 @@ namespace storm {
                 
                 enum class QueryType { Achievability, Numerical, Pareto };
                 
-                SparseModelType preprocessedModel;
                 SparseModelType const& originalModel;
+                SparseModelType preprocessedModel;
                 std::vector<uint_fast64_t> newToOldStateIndexMapping;
                 
                 QueryType queryType;
@@ -27,7 +27,7 @@ namespace storm {
                 
                 bool produceSchedulers;
                 
-                SparseMultiObjectivePreprocessorData(SparseModelType const& model) : preprocessedModel(model),  originalModel(model), produceSchedulers(false) {
+                SparseMultiObjectivePreprocessorData(SparseModelType const& originalModel, SparseModelType&& preprocessedModel, std::vector<uint_fast64_t>&& newToOldStateIndexMapping) : originalModel(originalModel), preprocessedModel(preprocessedModel), newToOldStateIndexMapping(newToOldStateIndexMapping), produceSchedulers(false) {
                     //Intentionally left empty
                 }
                 
diff --git a/src/transformer/StateDuplicator.h b/src/transformer/StateDuplicator.h
index 6733fd424..094e3e5ec 100644
--- a/src/transformer/StateDuplicator.h
+++ b/src/transformer/StateDuplicator.h
@@ -235,7 +235,7 @@ namespace storm {
             std::is_same<MT,storm::models::sparse::Ctmc<typename SparseModelType::ValueType>>::value,
             MT>::type
             createTransformedModel(MT const& originalModel,
-                                   StateDuplicatorReturnType& result,
+                                   StateDuplicatorReturnType const& result,
                                    storm::storage::SparseMatrix<typename MT::ValueType>& matrix,
                                    storm::models::sparse::StateLabeling& stateLabeling,
                                    std::unordered_map<std::string,
@@ -249,7 +249,7 @@ namespace storm {
             std::is_same<MT,storm::models::sparse::MarkovAutomaton<typename SparseModelType::ValueType>>::value,
             MT>::type
             createTransformedModel(MT const& originalModel,
-                                   StateDuplicatorReturnType& result,
+                                   StateDuplicatorReturnType const& result,
                                    storm::storage::SparseMatrix<typename MT::ValueType>& matrix,
                                    storm::models::sparse::StateLabeling& stateLabeling,
                                    std::unordered_map<std::string,
diff --git a/src/transformer/SubsystemBuilder.h b/src/transformer/SubsystemBuilder.h
new file mode 100644
index 000000000..8d692edd7
--- /dev/null
+++ b/src/transformer/SubsystemBuilder.h
@@ -0,0 +1,211 @@
+#ifndef STORM_TRANSFORMER_SUBSYSTEMBUILDER_H
+#define STORM_TRANSFORMER_SUBSYSTEMBUILDER_H
+
+
+#include <memory>
+#include <boost/optional.hpp>
+
+#include "src/models/sparse/StandardRewardModel.h"
+#include "src/utility/constants.h"
+#include "src/utility/graph.h"
+#include "src/utility/macros.h"
+#include "src/utility/vector.h"
+#include "src/models/sparse/Dtmc.h"
+#include "src/models/sparse/Mdp.h"
+#include "src/models/sparse/Ctmc.h"
+#include "src/models/sparse/MarkovAutomaton.h"
+
+#include "src/exceptions/InvalidArgumentException.h"
+#include "src/exceptions/InvalidStateException.h"
+
+namespace storm {
+    namespace transformer {
+        
+        /*
+         * Removes all states that are not part of the subsystem
+         */
+        template <typename SparseModelType>
+        class SubsystemBuilder {
+        public:
+
+            struct SubsystemBuilderReturnType {
+                // The resulting model
+                std::shared_ptr<SparseModelType> model;
+                // Gives for each state in the resulting model the corresponding state in the original model and vice versa.
+                // If a state does not exist in the other model, an invalid index is given.
+                std::vector<uint_fast64_t> newToOldStateIndexMapping;
+                std::vector<uint_fast64_t> oldToNewStateIndexMapping;
+                // marks the actions of the original model that are still available in the subsystem
+                storm::storage::BitVector subsystemActions;
+            };
+            
+            /*
+             * Removes all states that are not part of the subsystem
+             * all actions (i.e. rows) that lead outside of the subsystem are erased. Note that this might introduce deadlock states.
+             * 
+             * @param originalModel The model to be duplicated
+             * @param subsystem The states that will be kept
+             */
+            static SubsystemBuilderReturnType transform(SparseModelType const& originalModel, storm::storage::BitVector const& subsystem) {
+                STORM_LOG_DEBUG("Invoked subsystem builder on model with " << originalModel.getNumberOfStates() << " states.");
+                SubsystemBuilderReturnType result;
+                
+                uint_fast64_t subsystemStateCount = subsystem.getNumberOfSetBits();
+                STORM_LOG_THROW(subsystemStateCount != 0, storm::exceptions::InvalidArgumentException, "Invoked SubsystemBuilder for an empty subsystem.");
+                if(subsystemStateCount == subsystem.size()) {
+                    result.model = std::make_shared<SparseModelType>(originalModel);
+                    result.newToOldStateIndexMapping = storm::utility::vector::buildVectorForRange(0, result.model->getNumberOfStates());
+                    result.oldToNewStateIndexMapping = result.newToOldStateIndexMapping;
+                    result.subsystemActions = storm::storage::BitVector(result.model->getTransitionMatrix().getRowCount(), true);
+                    return result;
+                }
+                
+                result.newToOldStateIndexMapping.reserve(subsystemStateCount);
+                result.oldToNewStateIndexMapping = std::vector<uint_fast64_t>(subsystem.size(), std::numeric_limits<uint_fast64_t>::max());
+                result.subsystemActions = storm::storage::BitVector(result.model->getTransitionMatrix().getRowCount(), false);
+                for(auto subsysState : subsystem) {
+                    result.oldToNewStateIndexMapping[subsysState] = result.newToOldStateIndexMapping.size();
+                    result.newToOldStateIndexMapping.push_back(subsysState);
+                    for(uint_fast64_t row = originalModel.getTransitionMatrix().getRowGroupIndices()[subsysState]; row < originalModel.getTransitionMatrix().getRowGroupIndices()[subsysState+1]; ++row) {
+                        result.subsystemActions.set(row, true);
+                        for(auto const& entry : originalModel.getTransitionMatrix().getRow(row)) {
+                            if(!subsystem.get(entry.getColumn())) {
+                                result.subsystemActions.set(row, false);
+                                break;
+                            }
+                        }
+                    }
+                }
+                
+                // Transform the ingedients of the model
+                storm::storage::SparseMatrix<typename SparseModelType::ValueType> matrix = transformMatrix(originalModel.getTransitionMatrix(), result);
+                storm::models::sparse::StateLabeling labeling(matrix.getRowGroupCount());
+                for(auto const& label : originalModel.getStateLabeling().getLabels()){
+                    storm::storage::BitVector newBitVectorForLabel = transformStateBitVector(originalModel.getStateLabeling().getStates(label), subsystem);
+                    labeling.addLabel(label, std::move(newBitVectorForLabel));
+                }
+                std::unordered_map<std::string, typename SparseModelType::RewardModelType> rewardModels;
+                for(auto const& rewardModel : originalModel.getRewardModels()){
+                    rewardModels.insert(std::make_pair(rewardModel.first, transformRewardModel(rewardModel.second, originalModel.getTransitionMatrix().getRowGroupIndices(), subsystem, result)));
+                }
+                boost::optional<std::vector<storm::models::sparse::LabelSet>> choiceLabeling;
+                if(originalModel.hasChoiceLabeling()){
+                    choiceLabeling = transformActionValueVector<storm::models::sparse::LabelSet>(originalModel.getChoiceLabeling(), result.subsystemActions);
+                }
+                result.model = std::make_shared<SparseModelType>(createTransformedModel(originalModel, subsystem, result, matrix, labeling, rewardModels, choiceLabeling));
+                STORM_LOG_DEBUG("Subsystem Builder is done. Resulting model has " << result.model->getNumberOfStates() << " states.");
+                return result;
+            }
+            
+        private:
+            template<typename ValueType = typename SparseModelType::ValueType, typename RewardModelType = typename SparseModelType::RewardModelType>
+            static typename std::enable_if<std::is_same<RewardModelType, storm::models::sparse::StandardRewardModel<ValueType>>::value, RewardModelType>::type
+            transformRewardModel(RewardModelType const& originalRewardModel, std::vector<uint_fast64_t> const& originalRowGroupIndices, storm::storage::BitVector const& subsystem, SubsystemBuilderReturnType const& result) {
+                boost::optional<std::vector<ValueType>> stateRewardVector;
+                boost::optional<std::vector<ValueType>> stateActionRewardVector;
+                boost::optional<storm::storage::SparseMatrix<ValueType>> transitionRewardMatrix;
+                if(originalRewardModel.hasStateRewards()){
+                    stateRewardVector = transformStateValueVector(originalRewardModel.getStateRewardVector(), subsystem);
+                }
+                if(originalRewardModel.hasStateActionRewards()){
+                    stateActionRewardVector = transformActionValueVector(originalRewardModel.getStateActionRewardVector(), result.subsystemActions);
+                }
+                if(originalRewardModel.hasTransitionRewards()){
+                    transitionRewardMatrix = transformMatrix(originalRewardModel.getTransitionRewardMatrix(), result);
+                }
+                return RewardModelType(std::move(stateRewardVector), std::move(stateActionRewardVector), std::move(transitionRewardMatrix));
+            }
+            
+            template<typename ValueType = typename SparseModelType::ValueType>
+            static storm::storage::SparseMatrix<ValueType> transformMatrix(storm::storage::SparseMatrix<ValueType> const& originalMatrix, SubsystemBuilderReturnType const& result) {
+                // Build the builder
+                uint_fast64_t const numStates = result.newToOldStateIndexMapping.size();
+                uint_fast64_t const numRows = result.subsystemActions.getNumberOfSetBits();
+                uint_fast64_t numEntries = 0;
+                for(auto row : result.subsystemActions) {
+                    numEntries += originalMatrix.getRow(row).getNumberOfEntries();
+                }
+                storm::storage::SparseMatrixBuilder<ValueType> builder(numRows, numStates, numEntries, true, !originalMatrix.hasTrivialRowGrouping(), originalMatrix.hasTrivialRowGrouping() ? 0 : numStates);
+                
+                // Fill in the data
+                uint_fast64_t newRow = 0;
+                for(uint_fast64_t newState = 0; newState < numStates; ++newState){
+                    if(!originalMatrix.hasTrivialRowGrouping()){
+                        builder.newRowGroup(newRow);
+                    }
+                    uint_fast64_t oldState = result.newToOldStateIndexMapping[newState];
+                    for (uint_fast64_t oldRow = result.subsystemActions.getNextSetIndex(originalMatrix.getRowGroupIndices()[oldState]); oldRow < originalMatrix.getRowGroupIndices()[oldState+1]; oldRow = result.subsystemActions.getNextSetIndex(oldRow+1)){
+                        for(auto const& entry : originalMatrix.getRow(oldRow)){
+                            builder.addNextValue(newRow, result.oldToNewStateIndexMapping[entry.getColumn()], entry.getValue());
+                        }
+                        ++newRow;
+                    }
+                }
+                return builder.build();
+            }
+            
+            
+            template<typename ValueType = typename SparseModelType::ValueType>
+            static std::vector<ValueType> transformActionValueVector(std::vector<ValueType> const& originalVector, storm::storage::BitVector const& subsystemActions) {
+                std::vector<ValueType> v;
+                v.reserve(subsystemActions.getNumberOfSetBits());
+                for(auto action : subsystemActions){
+                    v.push_back(originalVector[action]);
+                }
+                return v;
+            }
+            
+            template<typename ValueType = typename SparseModelType::ValueType>
+            static std::vector<ValueType> transformStateValueVector(std::vector<ValueType> const& originalVector, storm::storage::BitVector const& subsystem) {
+                std::vector<ValueType> v;
+                v.reserve(subsystem.getNumberOfSetBits());
+                for(auto state : subsystem){
+                    v.push_back(originalVector[state]);
+                }
+                return v;
+            }
+            
+            static storm::storage::BitVector transformStateBitVector(storm::storage::BitVector const& originalBitVector, storm::storage::BitVector const& subsystem) {
+                return originalBitVector % subsystem;
+            }
+            
+            
+            template<typename MT = SparseModelType>
+            static typename std::enable_if<
+            std::is_same<MT,storm::models::sparse::Dtmc<typename SparseModelType::ValueType>>::value ||
+            std::is_same<MT,storm::models::sparse::Mdp<typename SparseModelType::ValueType>>::value ||
+            std::is_same<MT,storm::models::sparse::Ctmc<typename SparseModelType::ValueType>>::value,
+            MT>::type
+            createTransformedModel(MT const& originalModel,
+                                   storm::storage::BitVector const& subsystem,
+                                   SubsystemBuilderReturnType const& result,
+                                   storm::storage::SparseMatrix<typename MT::ValueType>& matrix,
+                                   storm::models::sparse::StateLabeling& stateLabeling,
+                                   std::unordered_map<std::string,
+                                   typename MT::RewardModelType>& rewardModels,
+                                   boost::optional<std::vector<typename storm::models::sparse::LabelSet>>& choiceLabeling ) {
+                return MT(std::move(matrix), std::move(stateLabeling), std::move(rewardModels), std::move(choiceLabeling));
+            }
+            
+            template<typename MT = SparseModelType>
+            static typename std::enable_if<
+            std::is_same<MT,storm::models::sparse::MarkovAutomaton<typename SparseModelType::ValueType>>::value,
+            MT>::type
+            createTransformedModel(MT const& originalModel,
+                                   storm::storage::BitVector const& subsystem,
+                                   SubsystemBuilderReturnType const& result,
+                                   storm::storage::SparseMatrix<typename MT::ValueType>& matrix,
+                                   storm::models::sparse::StateLabeling& stateLabeling,
+                                   std::unordered_map<std::string,
+                                   typename MT::RewardModelType>& rewardModels,
+                                   boost::optional<std::vector<typename storm::models::sparse::LabelSet>>& choiceLabeling ) {
+                storm::storage::BitVector markovianStates = transformStateBitVector(originalModel.getMarkovianStates(), subsystem);
+                std::vector<typename MT::ValueType> exitRates = transformStateValueVector(originalModel.getExitRates(), subsystem);
+                return MT(std::move(matrix), std::move(stateLabeling), std::move(markovianStates), std::move(exitRates), true, std::move(rewardModels), std::move(choiceLabeling));
+            }
+            
+            
+        };
+    }
+}
+#endif // STORM_TRANSFORMER_SUBSYSTEMBUILDER_H