Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix Approach

We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are standardl...

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Bibliographic Details
Published inElectronic proceedings in theoretical computer science Vol. 13; no. Proc. QFM 2009; pp. 55 - 65
Main Author Trčka, Nikola
Format Journal Article
LanguageEnglish
Published Open Publishing Association 10.12.2009
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Summary:We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are standardly presented in real matrix theory. By interpreting the obtained matrix conditions for bisimulations in this setting, we automatically obtain the definitions of strong, weak, and branching bisimulation for Markov reward chains. The obtained strong and weak bisimulations are shown to coincide with some existing notions, while the obtained branching bisimulation is new, but its usefulness is questionable.
ISSN:2075-2180
2075-2180
DOI:10.4204/EPTCS.13.5