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标题：Bisimulation for Labelled Markov Processes
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作者：Richard Blute ; Josée Desharnais ; Abbas Edalat 等
期刊名称：BRICS Report Series
印刷版ISSN：0909-0878
出版年度：1997
卷号：4
期号：4
出版社：Aarhus University
摘要：In this paper we introduce a new class of labelled transition systems - Labelled Markov Processes - and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems where the state space is not necessarily discrete, it 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 completely 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 result that we prove is that a notion of bisimulation for Markov processes on Polish spaces, which extends the Larsen-Skou denition for discrete systems, is indeed an equivalence relation. This turns out to be a rather hard mathematical result which, as far as we know, embodies a new result in pure probability theory. This work heavily uses continuous mathematics which is becoming an important part of work on hybrid systems.