Continuity properties of distances for Markov processes

Manfred Jaeger, Hua Mao, Kim Guldstrand Larsen, Radu Mardare

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

5 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationQuantitative Evaluation of Systems - 11th International Conference, QEST 2014, Proceedings
EditorsGethin Norman, William Sanders
Place of PublicationCham
Number of pages16
ISBN (Print)9783319106953
Publication statusPublished - 1 Jan 2014
Event11th International Conference on Quantitative Evaluation of Systems, QEST 2014 - Florence, Italy
Duration: 8 Sep 201410 Sep 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8657 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th International Conference on Quantitative Evaluation of Systems, QEST 2014


  • distance function
  • hide Markov model
  • Markov process
  • continuity property
  • parameter continuity

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