Bisimulation through probabilistic testing (preliminary report)
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Edge-valued binary decision diagrams for multi-level hierarchical verification
DAC '92 Proceedings of the 29th ACM/IEEE Design Automation Conference
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
A compositional approach to performance modelling
A compositional approach to performance modelling
An Efficient Algorithm for Aggregating PEPA Models
IEEE Transactions on Software Engineering
Multi-Terminal Binary Decision Diagrams: An Efficient DataStructure for Matrix Representation
Formal Methods in System Design
Algebric Decision Diagrams and Their Applications
Formal Methods in System Design
Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications
IEEE Transactions on Computers
Formal Verification Using Edge-Valued Binary Decision Diagrams
IEEE Transactions on Computers
Aggregation Methods for Large Markov Chains
Proceedings of the International Workshop on Computer Performance and Reliability
Stochastic process algebras: integrating qualitative and quantitative modelling
Proceedings of the 7th IFIP WG6.1 International Conference on Formal Description Techniques VII
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Symbolic Bisimulation Minimisation
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
Exploiting Symmetries in Stochastic Process Algebras
Proceedings of the 12th European Simulation Multiconference on Simulation - Past, Present and Future
A Data Structure for the Efficient Kronecker Solution of GSPNs
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS
ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS
Optimal state-space lumping in Markov chains
Information Processing Letters
Probabilistic symbolic model checking with PRISM: a hybrid approach
International Journal on Software Tools for Technology Transfer (STTT) - Special section on tools and algorithms for the construction and analysis of systems
A distributed algorithm for strong bisimulation reduction of state spaces
International Journal on Software Tools for Technology Transfer (STTT) - Special section on parallel and distributed model checking
Generating BDDs for symbolic model checking in CCS
Distributed Computing
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International Journal on Software Tools for Technology Transfer (STTT) - Special section on formal methods for industrial critical systems
On the use of exact lumpability in partially symmetricalWell-formed Nets
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Solution of large markov models using lumping techniques and symbolic data structures
Solution of large markov models using lumping techniques and symbolic data structures
Numerical vs. statistical probabilistic model checking
International Journal on Software Tools for Technology Transfer (STTT)
Compositional Performability Evaluation for STATEMATE
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Analysis of Markov reward models using zero-suppressed multi-terminal BDDs
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Optimization techniques for BDD-based bisimulation computation
Proceedings of the 17th ACM Great Lakes symposium on VLSI
Cell Cycle Control in Eukaryotes: A BioSpi model
Electronic Notes in Theoretical Computer Science (ENTCS)
Signature-based Symbolic Algorithm for Optimal Markov Chain Lumping
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Probabilistic model checking of complex biological pathways
Theoretical Computer Science
Compositional Dependability Evaluation for STATEMATE
IEEE Transactions on Software Engineering
Bisimulation minimisation mostly speeds up probabilistic model checking
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
A symbolic algorithm for optimal Markov chain lumping
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Symmetry reduction for probabilistic model checking
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Sigref: a symbolic bisimulation tool box
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
PRISM: a tool for automatic verification of probabilistic systems
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Stochastic Petri net models of polling systems
IEEE Journal on Selected Areas in Communications
Reduced base model construction methods for stochastic activity networks
IEEE Journal on Selected Areas in Communications
Counterexample generation for Markov chains using SMT-based bounded model checking
FMOODS'11/FORTE'11 Proceedings of the joint 13th IFIP WG 6.1 and 30th IFIP WG 6.1 international conference on Formal techniques for distributed systems
Knowledge acquisition in inconsistent multi-scale decision systems
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Comparison of scheduling schemes for on-demand IaaS requests
Journal of Systems and Software
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State space lumping is one of the classical means to fight the state space explosion problem in state-based performance evaluation and verification. Particularly when numerical algorithms are applied to analyze a Markov model, one often observes that those algorithms do not scale beyond systems of moderate size. To alleviate this problem, symbolic lumping algorithms have been devised to effectively reduce very large-but symbolically represented-Markov models to moderate size explicit representations. This lumping step partitions the Markov model in such a way that any numerical analysis carried out on the lumped model is guaranteed to produce exact results for the original system. But even this lumping preprocessing may fail due to time or memory limitations. This paper discusses the two main approaches to symbolic lumping, and combines them to improve on their respective limitations. The algorithm automatically converts between known symbolic partition representations in order to provide a trade-off between memory consumption and runtime. We show how to apply this algorithm for the lumping of Markov chains, but the same techniques can be adapted in a straightforward way to other models like Markov reward models, labeled transition systems, or interactive Markov chains.