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The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy pp 139–162Cite as

A Complete Axiomatization of Branching Bisimilarity for a Simple Process Language with Probabilistic Choice

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11760))

Abstract

This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a basic, recursion-free process language with non-deterministic as well as probabilistic choice. The proof of completeness of the axiomatization builds on the completeness of strong probabilistic bisimilarity on the one hand and on the notion of a concrete process, i.e. a process that does not display (partially) inert \(\tau \)-moves, on the other hand. The approach is first presented for the non-deterministic fragment of the calculus and next generalized to incorporate probabilistic choice, too.

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Author information

Authors and Affiliations

  1. Data61, CSIRO, Sydney, Australia

    Rob J. van Glabbeek

  2. Computer Science and Engineering, University of New South Wales, Sydney, Australia

    Rob J. van Glabbeek

  3. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Jan Friso Groote & Erik P. de Vink

Authors
  1. Rob J. van Glabbeek
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  2. Jan Friso Groote
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  3. Erik P. de Vink
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Correspondence to Erik P. de Vink .

Editor information

Editors and Affiliations

  1. Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Mário S. Alvim

  2. University of Athens, Athens, Greece

    Kostas Chatzikokolakis

  3. Federal University of Rio Grande do Norte - UFRN, Natal, Brazil

    Carlos Olarte

  4. CNRS & University Javeriana Cali, Palaiseau, France

    Frank Valencia

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van Glabbeek, R.J., Groote, J.F., de Vink, E.P. (2019). A Complete Axiomatization of Branching Bisimilarity for a Simple Process Language with Probabilistic Choice. In: Alvim, M., Chatzikokolakis, K., Olarte, C., Valencia, F. (eds) The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy. Lecture Notes in Computer Science(), vol 11760. Springer, Cham. https://doi.org/10.1007/978-3-030-31175-9_9

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  • DOI: https://doi.org/10.1007/978-3-030-31175-9_9

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