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Cones and foci: A mechanical framework for protocol verification

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Abstract

We define a cones and foci proof method, which rephrases the question whether two system specifications are branching bisimilar in terms of proof obligations on relations between data objects. Compared to the original cones and foci method from Groote and Springintveld, our method is more generally applicable, because it does not require a preprocessing step to eliminate τ-loops. We prove soundness of our approach and present a set of rules to prove the reachability of focus points. Our method has been formalized and proved correct using PVS. Thus we have established a framework for mechanical protocol verification. We apply this framework to the Concurrent Alternating Bit Protocol.

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Notes

  1. To cover μCRL specifications with successful termination, LPEs should include a summand \( \sum_{a\in {\it Act} \cup\{\tau\}}\sum_{\ell: L_a}a(f_a(d,\ell)) \vartriangleleft h_a(d,\ell) \vartriangleright \delta \). The cones and foci method extends to this setting without any complication. However, this extension would complicate the matching criteria in Definition 3.3. For the sake of presentation, successful termination is not taken into account in this paper.

  2. LPEs exclude “unguarded” recursive specifications such as X = X, which can have multiple solutions.

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Acknowledgments

Jan Friso Groote is thanked for valuable discussions. This research is supported by the Dutch Technology Foundation STW under the project CES5008: Improving the quality of embedded systems using formal design and systematic testing.

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Authors and Affiliations

  1. CWI, Specification and Analysis of Embedded Systems Group, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Wan Fokkink & Jaco van de Pol

  2. Vrije Universiteit, Section of Theoretical Computer Science, 1081 HV, Amsterdam, The Netherlands

    Wan Fokkink

  3. INRIA Futurs and LIX, École Polytechnique, F-91128, Palaiseau Cedex, France

    Jun Pang

  4. Eindhoven University of Technology, Design and Analysis of Systems Group, 5600 MB, Eindhoven, The Netherlands

    Jaco van de Pol

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Fokkink, W., Pang, J. & van de Pol, J. Cones and foci: A mechanical framework for protocol verification. Form Method Syst Des 29, 1–31 (2006). https://doi.org/10.1007/s10703-006-0004-3

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