Probabilistic Reachability for Parametric Markov Models
Proceedings of the 16th International SPIN Workshop on Model Checking Software
Correctness issues of symbolic bisimulation computation for markov chains
MMB&DFT'10 Proceedings of the 15th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
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Bisimulation minimization is one of the classical means to fight the infamous state space explosion problem in verification. Particularly in stochastic verification, numerical algorithms are applied, which do not scale beyond systems of moderate size. To alleviate this problem, symbolic bisimulation minimization has been usedeffectively to reduce very large symbolically represented state spaces to moderate size explicit representations. But even this minimization may fail due to time or memory limitations. This paper presents a symbolic algorithm which relies on a hybrid symbolic partition representation. It dynamically converts between two knownrepresentations in order to provide a trade-off between memory consumption and runtime. The conversion itself is logarithmic in the partition size. We show how to apply it for the minimization of Markov chains, but the same techniques can be adapted in a straightforward way to other models like labeled transition systems or interactive Markov chains.