Abstract

In this paper we introduce a new class of labeled transition systems - Labeled Markov Processes - and define bisimulation for them. Labeled Markov processes are probabilistic labeled transition systems where the state space is not necessarily discrete. The state space could be the reals, for example. We assume that it is a Polish space (the underlying topological space for a complete separable metric space). The mathematical theory of such systems is new from the point of view of the extant literature on probabilistic process algebra; of course, it uses classical ideas from measure theory and Markov process theory. The notion of bisimulation builds on the ideas of Larsen and Skou and of Joyal, Nielsen and Winskel. The main contribution is the development of a notion of bisimulation for Markov processes on Polish spaces, which extends the Larsen-Skou definition for discrete systems. The proof that bisimulation is an equivalence relation turns out to depend on hard mathematical result of...

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