Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Bisimulation Minimization and Symbolic Model Checking
Formal Methods in System Design
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
Distributed state space minimization
International Journal on Software Tools for Technology Transfer (STTT) - Special section on formal methods for industrial critical systems
Numerical vs. statistical probabilistic model checking
International Journal on Software Tools for Technology Transfer (STTT)
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
Symbolic Partition Refinement with Dynamic Balancing of Time and Space
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Compositional Dependability Evaluation for STATEMATE
IEEE Transactions on Software Engineering
Comparative branching-time semantics for Markov chains
Information and Computation
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
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Electronic Notes in Theoretical Computer Science (ENTCS)
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Bisimulation reduction is a classical means to fight the infamous state space explosion problem, which limits the applicability of automated methods for verification like model checking. A signature-based method, originally developed by Blom and Orzan for labeled transition systems and adapted for Markov chains by Derisavi, has proved to be very efficient. It is possible to implement it symbolically using binary decision diagrams such that it is able to handle very large state spaces efficiently. We will show, however, that for Markov chains this algorithm suffers from numerical instabilities, which often result in too large quotient systems. We will present and experimentally evaluate two different approaches to avoid these problems: first the usage of rational arithmetic, and second an approach not only to represent the system structure but also the transition rates symbolically. In addition, this allows us to modify their actual values after the quotient computation.