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Bisimulation for labelled Markov processes
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Bisimulation for Labelled Markov Processes
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LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Approximating labelled Markov processes
Information and Computation
Semi-pullbacks and bisimulation in categories of Markov processes
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Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
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Theoretical Computer Science - Selected papers of CMCS'03
Semi-pullbacks and bisimulations in categories of stochastic relations
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Electronic Notes in Theoretical Computer Science (ENTCS)
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CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Coalgebraic Logic over Measurable Spaces: Behavioral and Logical Equivalence
Electronic Notes in Theoretical Computer Science (ENTCS)
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We introduce a new notion of bisimulation, called event bisimulation on labelled Markov processes and compare it with the, now standard, notion of probabilistic bisimulation, originally due to Larsen and Skou. Event bisimulation uses a sub σ-algebra as the basic carrier of information rather than an equivalence relation. The resulting notion is thus based on measurable subsets rather than on points: hence the name. Event bisimulation applies smoothly for general measure spaces; bisimulation, on the other hand, is known only to work satisfactorily for analytic spaces. We prove the logical characterization theorem for event bisimulation without having to invoke any of the subtle aspects of analytic spaces that feature prominently in the corresponding proof for ordinary bisimulation. These complexities only arise when we show that on analytic spaces the two concepts coincide. We show that the concept of event bisimulation arises naturally from taking the cocongruence point of view for probabilistic systems. We show that the theory can be given a pleasing categorical treatment in line with general coalgebraic principles. As an easy application of these ideas we develop a notion of "almost sure" bisimulation; the theory comes almost "for free" once we modify Giry's monad appropriately.