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Axiomatizing Team Equivalence for Finite-State Machines

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The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy

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

Abstract

Finite-state machines, a simple class of finite Petri nets, were equipped in [10] with a truly concurrent, bisimulation-based, behavioral equivalence, called team equivalence, which conservatively extends bisimulation equivalence on labeled transition systems and which is checked in a distributed manner, without necessarily building a global model of the overall behavior. The process algebra CFM [9] is expressive enough to represent all and only the finite-state machines, up to net isomorphism. Here we first prove that this equivalence is a congruence for the operators of CFM, then we show some algebraic properties of team equivalence and, finally, we provide a finite, sound and complete, axiomatization for team equivalence over CFM.

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Notes

  1. 1.

    The open net semantics for open CFM extends the net semantics in Table 2 with \([\![x ]\!]_{I} = (\{x\}, \emptyset , \emptyset , \{x\})\), so that, e.g., the semantics of a.x is \((\{a.x\}, \{a\}, \{(a.x,a,x)\}, a.x)\).

  2. 2.

    Note that if C has been already encountered while scanning the original term p, then the resulting term is C itself, and so the proof does not loop; indeed, to be precise, induction is on the syntactic definition parametrized w.r.t. a set of already encountered constants (initially empty); however, this parametrization is not explicit in the proof.

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Acknowledgments

The anonymous referees are thanked for their useful comments and suggestions. Catuscia Palamidessi is thanked for her illuminating scientific work.

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Authors and Affiliations

  1. Dipartimento di Informatica — Scienza e Ingegneria, Università di Bologna, Mura A. Zamboni, 7, 40127, Bologna, Italy

    Roberto Gorrieri

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  1. Roberto Gorrieri
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Correspondence to Roberto Gorrieri .

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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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Gorrieri, R. (2019). Axiomatizing Team Equivalence for Finite-State Machines. 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_2

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  • DOI: https://doi.org/10.1007/978-3-030-31175-9_2

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-31175-9

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