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Modelling concurrency with semi-commutations

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  • Conference paper
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Mathematical Foundations of Computer Science 1992 (MFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 629))

Abstract

The aim of this paper is to propose a mathematical tool, as well general as precise, for reasoning about concurrent systems. Ordered semi-commutative monoids are chosen for this purpose; their directed subsets represent processes of concurrent systems. Properties of such processes are proved; the main one is the diamond property. Infinite semitraces and their graphs are defined. Special sequences of actions, called linearizations and fair linearizations, are distinguished in order to represent finite and infinite processes. Finally, the approach is applied for modelling behaviours of general Petri-nets. Some kind of fairness, oriented on tokens, is introduced. It is shown that complete processes of general petri-nets, contrary to those of elementary nets, are not always fair.

A more complete version of this paper, with full proofs, broader comments and additional examples, is available as Report 714/1991 of LRI of University Paris-Sud.

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References

  1. M.Clerbout/M.Latteux: Semi-Commutations; Information and Computation 73, 1987.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Polish Academy of Sciences, PO Box 22, PKiN 00-901, Warszawa

    Edward Ochmański

Authors
  1. Edward Ochmański
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Editor information

Ivan M. Havel Václav Koubek

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© 1992 Springer-Verlag Berlin Heidelberg

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Ochmański, E. (1992). Modelling concurrency with semi-commutations. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-55808-X_40

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  • DOI: https://doi.org/10.1007/3-540-55808-X_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55808-8

  • Online ISBN: 978-3-540-47291-9

  • eBook Packages: Springer Book Archive

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