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The fixed point theory of unbounded non-determinism

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Formal Aspects of Computing

Abstract

This paper presents a fixed point theorem for the infinite traces model of CSP. Unlike any other model of CSP, there is no complete partial order over the infinite traces model whose fixed point theory agrees with the operational semantics (A. W. Roscoe, Oxford University Computing Laboratory Technical Monograph PRG-67, 1988). This arises from the introduction of unbounded non-determinism. However, the subset of pre-deterministic processes, that is those which describe the behaviour of a process on some run of its implementation, do form a subset for which the usual order is complete. By requiring that each CSP operator has a monotonic implementation which preserves pre-determinism, it is possible to show that all CSP operators have a least fixed point. In effect, it is the requirement that all operators have a methodical implementation.

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References

  1. Barrett, G.: The Semantics of Priority and Fairness in occam.Proc. MFPSV, Lecture Notes in Computer Science, Springer-Verlag LNCS 442, 194–208 (1989).

  2. Barrett, G and Goldsmith, M. H.: Classifying Unbounded Nondeterminism in CSP. in Category Theory and Topology in Computer Science, OUP (1991).

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  6. Roscoe, A. W.:Two Papers on CSP. Oxford University Computing Laboratory Technical Monograph PRG-67, July 1988.

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Authors and Affiliations

  1. INMOS Limited, 1000 Aztec West, BS12 4SQ, Almondsbury, Bristol, UK

    Geoff Barrett

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  1. Geoff Barrett
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Additional information

The author carried out the research for this paper on the Espirit Genesis project at the Programming Research Group, Oxford University.

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Barrett, G. The fixed point theory of unbounded non-determinism. Formal Aspects of Computing 3, 110–128 (1991). https://doi.org/10.1007/BF01898399

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  • DOI: https://doi.org/10.1007/BF01898399

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