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An efficient algorithm for branching bisimulation and stuttering equivalence

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Automata, Languages and Programming (ICALP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 443))

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Abstract

This paper presents an efficient algorithm for the Relational Coarsest Partition with Stuttering problem (RCPS). The RCPS problem is closely related to the problem of deciding stuttering equivalence on finite state Kripke structures (see Browne, Clarke & Grumberg [3]), and to the problem of deciding branching bisimulation equivalence on finite state labelled transition systems (see Van Glabbeek & Weijland [12]). If n is the number of states and m the number of transitions, then our algorithm has time complexity O(n·(n+m)) and space complexity O(n+m). The algorithm induces algorithms for branching bisimulation and stuttering equivalence which have the same complexity. Since for Kripke structures m⩽n 2, this confirms a conjecture of Browne, Clarke & Grumberg [3], that their O(n 5)-time algorithm for stuttering equivalence is not optimal.

Note: The research of the authors was supported by RACE project no. 1046, Specification and Programming Environment for Communication Software (SPECS). The research of the second author was also supported by ESPRIT project no. 3006 CONCUR.

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands

    Jan Friso Groote & Frits Vaandrager

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  1. Jan Friso Groote
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  2. Frits Vaandrager
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Michael S. Paterson

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© 1990 Springer-Verlag Berlin Heidelberg

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Groote, J.F., Vaandrager, F. (1990). An efficient algorithm for branching bisimulation and stuttering equivalence. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032063

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  • DOI: https://doi.org/10.1007/BFb0032063

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  • Print ISBN: 978-3-540-52826-5

  • Online ISBN: 978-3-540-47159-2

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