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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Continuity Properties of Distances for Markov Processes
verfasst von : Manfred Jaeger, Hua Mao, Kim Guldstrand Larsen, Radu Mardare
Erschienen in: Quantitative Evaluation of Systems
Verlag: Springer International Publishing
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In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable continuity properties for such distances are identified. We then establish a number of results that show that these two properties are in conflict, and not simultaneously fulfilled by any of our candidate natural distance functions. An impossibility result is derived that explains to some extent the fundamental difficulty we encounter.