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Axiomatizing an Algebra of Step Reactions for Synchronous Languages

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CONCUR 2002 — Concurrency Theory (CONCUR 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2421))

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Abstract

This paper introduces a novel algebra for reasoning about step reactions in synchronous languages, such as macro steps in Harel, Pnueli and Shalev’s Statecharts and instantaneous reactions in Berry’s Esterel. The algebra describes step reactions in terms of configurations which can both be read in a standard operational as well as in a model- theoretic fashion. The latter arises by viewing configurations as propositional formulas, interpreted intuitionistically over finite linear Kripke structures. Previous work by the authors showed the adequacy of this approach by establishing compositionality and full-abstraction results for Statecharts and Esterel. The present paper generalizes this work in an algebraic setting and, as its main result, provides a sound and complete equational axiomatization of step reactions. This yields, for the first time in the literature, a complete axiomatization of Statecharts macro steps, which can also be applied, modulo encoding, to Esterel reactions.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Sheffield University, 211 Portobello Street, S1 4DP, Sheffield, UK

    Gerald Lüttgen

  2. Fakultät für Wirtschaftsinformatik und Angewandte Informatik, Universität Bamberg, 96045, Bamberg, Germany

    Michael Mendler

Authors
  1. Gerald Lüttgen
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  2. Michael Mendler
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Masaryk University Brno, Botanicka 68a, 60200, Brno, Czech Republic

    Luboš Brim , Mojmír Křetínský  & Antonín Kučera ,  & 

  2. Faculty of Electrical Engineering and Informatics, Department of Computer Science, Technical University of Ostrava (VSB), 17. listopadu 15, 70833, Ostrava-Poruba, Czech Republic

    Petr Jančar

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Lüttgen, G., Mendler, M. (2002). Axiomatizing an Algebra of Step Reactions for Synchronous Languages. In: Brim, L., Křetínský, M., Kučera, A., Jančar, P. (eds) CONCUR 2002 — Concurrency Theory. CONCUR 2002. Lecture Notes in Computer Science, vol 2421. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45694-5_26

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  • DOI: https://doi.org/10.1007/3-540-45694-5_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44043-7

  • Online ISBN: 978-3-540-45694-0

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