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Timing and causality in process algebra

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Abstract

There has been considerable controversy in concurrency theory between the ‘interleaving’ and ‘true concurrency’ schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences; the latter adopts more complex semantic structures to avoid reducing concurrency to interleaving.

In this paper we show that the two approaches are not irreconcilable. We define a timed process algebra where occurrences are associated with intervals of time, and give it a transition system semantics. This semantics has many of the advantages of the interleaving approach; the algebra admits an expansion theorem, and bisimulation semantics can be used as usual. Our transition systems, however, incorporate timing information, and this enables us to express concurrency: merely adding timing appropriately generalises transition systems to asynchronous transition systems, showing that time gives a link between true concurrency and interleaving. Moreover, we can provide a complete axiomatisation of bisimulation for our algebra; a result that is often problematic in a timed setting.

Another advantage of incorporating timing information into the calculus is that it allows a particularly simple definition of action refinement; this we present. The paper concludes with a comparison of the equivalence we present with those in the literature, and an example system specification in our formalism.

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Authors and Affiliations

  1. School of Cognitive and Computing Science, University of Sussex, BN19QH, Brighton, England

    Luca Aceto

  2. BRICS Aalborg University, Fredrik Bajersvej 7E, DK-9220, Aalborg Ø, Denmark

    Luca Aceto

  3. Department of Computer Science, University of Birmingham, B15 2TT, Birmingham, England

    David Murphy

Authors
  1. Luca Aceto
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  2. David Murphy
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Aceto, L., Murphy, D. Timing and causality in process algebra. Acta Informatica 33, 317–350 (1996). https://doi.org/10.1007/s002360050047

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