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A complete theory of deterministic event structures

  • Session: True Concurrency
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CONCUR '95: Concurrency Theory (CONCUR 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 962))

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Abstract

We present an ω-complete algebra of a class of deterministic event structures, which are labelled prime event structures where the labelling function satisfies a certain distinctness condition. The operators of the algebra are summation, sequential composition and join. Each of these gives rise to a monoid; in addition a number of distributivity properties hold. Summation loosely corresponds to choice and join to parallel composition, with however some nonstandard aspects.

The space of models is a complete partial order (in fact a complete lattice) in which all operators are continuous; hence minimal fixpoints can be defined inductively. Moreover, the submodel relation can be captured within the algebra by summation (x⊑y iff x+y=y); therefore the effect of fixpoints can be captured by an infinitary proof rule, yielding a complete proof system for recursively defined deterministic event structures.

The research reported in this paper was partially supported by the HCM Cooperation Network “EXPRESS” (Expressiveness of Languages for Concurrency) and the Esprit Basic Research Working Group 6067 CALIBAN (Causal Calculi Based on Nets).

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Authors and Affiliations

  1. Institut für Informatik, University of Hildesheim, Germany

    Arend Rensink

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  1. Arend Rensink
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Insup Lee Scott A. Smolka

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© 1995 Springer-Verlag Berlin Heidelberg

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Rensink, A. (1995). A complete theory of deterministic event structures. In: Lee, I., Smolka, S.A. (eds) CONCUR '95: Concurrency Theory. CONCUR 1995. Lecture Notes in Computer Science, vol 962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60218-6_12

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  • DOI: https://doi.org/10.1007/3-540-60218-6_12

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  • Print ISBN: 978-3-540-60218-7

  • Online ISBN: 978-3-540-44738-2

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