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International Conference on Concurrency Theory

CONCUR 2003: CONCUR 2003 - Concurrency Theory pp 508–522Cite as

Quantitative Relations and Approximate Process Equivalences

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2761))

Abstract

We introduce a characterisation of probabilistic transition systems (PTS) in terms of linear operators on some suitably defined vector space representing the set of states. Various notions of process equivalences can then be re-formulated as abstract linear operators related to the concrete PTS semantics via a probabilistic abstract interpretation. These process equivalences can be turned into corresponding approximate notions by identifying processes whose abstract operators “differ” by a given quantity, which can be calculated as the norm of the difference operator. We argue that this number can be given a statistical interpretation in terms of the tests needed to distinguish two behaviours.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Universitá di Pisa, Italy

    Alessandra Di Pierro

  2. Department of Computing, Imperial College, London, UK

    Chris Hankin & Herbert Wiklicky

Authors
  1. Alessandra Di Pierro
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  2. Chris Hankin
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  3. Herbert Wiklicky
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Editor information

Editors and Affiliations

  1. Université Paris 7, PPS, Case 7014, 75205, Paris Cedex 13, France

    Roberto Amadio

  2. LIF, CNRS, Aix-Marseille Université, France

    Denis Lugiez

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© 2003 Springer-Verlag Berlin Heidelberg

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Di Pierro, A., Hankin, C., Wiklicky, H. (2003). Quantitative Relations and Approximate Process Equivalences. In: Amadio, R., Lugiez, D. (eds) CONCUR 2003 - Concurrency Theory. CONCUR 2003. Lecture Notes in Computer Science, vol 2761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45187-7_33

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  • DOI: https://doi.org/10.1007/978-3-540-45187-7_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40753-9

  • Online ISBN: 978-3-540-45187-7

  • eBook Packages: Springer Book Archive

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