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Asynchronous cellular automata for pomsets without auto-concurrency

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Book cover CONCUR '96: Concurrency Theory (CONCUR 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1119))

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Abstract

This paper extends to pomsets without auto-concurrency the fundamental notion of asynchronous cellular automata (ACA) which was originally introduced for traces by Zielonka. We generalize to pomsets the notion of asynchronous mapping introduced by Zielonka and we show how to construct a deterministic ACA from an asynchronous mapping. Our main result generalizes Büchi's theorem for a class of pomsets without auto-concurrency which satisfy a natural axiom. This axiom ensures that an asynchronous cellular automaton works on the pomset as a concurrent read owner write machine. More precisely, we prove the equivalence between non deterministic ACA, deterministic ACA and monadic second order logic for this class of pomsets.

This research was partly carried out during a stay of the second author in Dresden.

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References

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Author information

Authors and Affiliations

  1. Institut für Algebra, Technische Universität Dresden, D-01062, Dresden

    Manfred Droste

  2. LITP, IBP, Université Paris 7, 2 place Jussieu, F-75251, Paris Cedex 05

    Paul Gastin

Authors
  1. Manfred Droste
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  2. Paul Gastin
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Editor information

Ugo Montanari Vladimiro Sassone

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© 1996 Springer-Verlag Berlin Heidelberg

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Droste, M., Gastin, P. (1996). Asynchronous cellular automata for pomsets without auto-concurrency. In: Montanari, U., Sassone, V. (eds) CONCUR '96: Concurrency Theory. CONCUR 1996. Lecture Notes in Computer Science, vol 1119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61604-7_80

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  • DOI: https://doi.org/10.1007/3-540-61604-7_80

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  • Print ISBN: 978-3-540-61604-7

  • Online ISBN: 978-3-540-70625-0

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