Metrics for labelled Markov processes

  • Authors:
  • Josée Desharnais;Vineet Gupta;Radha Jagadeesan;Prakash Panangaden

  • Affiliations:
  • Département d'Informatique, Université Laval, Québec, Canada G1K 7P4;Google Inc., 2400 Bayshore Parkway, Mountain View, CA;School of CTI DePaul University, 243 S. Wabash Avenue, Chicago, IL;School of Computer Science, McGill University, 3480 University Street, Montréal PQ, Canada H3A 2A7

  • Venue:
  • Theoretical Computer Science - Logic, semantics and theory of programming
  • Year:
  • 2004

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Abstract

The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behavior has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Hutchinson metric.