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Semantics of Concurrent Computation pp 109–122Cite as

A characterization of concurrency-like relations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 70))

Abstract

In the paper algebraic properties of symmetric and irreflexive relations (called sir-relations) are discussed. Such relations are of importance in the Petri nets theory (Best[1], Petri[11,12], Mazurkiewicz[7]).

It was proved that for every sir-relation C≤ X×X there is a family of functions (called representations of C) of the form r:X ↣ U2 , where U is a set, such that (a,b)εC ⇔ r(a) ⌢ r(b) = ø. The properties of that family and the relationship between the theory of covers and the theory of sir-relations are discussed.

The notion of K-density for sir-relations is introduced, and some of its properties are proved.

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References

  1. Best E., A Theorem on the Characteristic of Non-Sequential Processes, Technical Report 116, Univ. of Newcastle upon Tyne, Comp. Labor., 1977.

    Google Scholar 

  2. Genrich H.J., A position in panel discussion, MFCS'75 Symposium, Marianskie Laznie, 1975.

    Google Scholar 

  3. Harrary F., Graph Theory, Addison-Wesllay, Mass., 1967.

    Google Scholar 

  4. Janicki R., Synthesis of Concurrent Schemes, Lecture Notes in Comp. Sci., vol. 64, Springer-Verlag, 1978, 298–307.

    Google Scholar 

  5. Knuth E., Petri Nets and Trace Languages, Proc. of the 1st European Conf. on Parallel and Distr. Processing, Toulouse, 1979.

    Google Scholar 

  6. Marczewski E., Sur deux propriétés des classes d'ensembles, Fund. Math., 33 (1945), 303–307.

    Google Scholar 

  7. Mazurkiewicz A., Concurrent Program Schemes and Their Interpretations, DAIMI PB-78, Aarhus Univ., Department of Comp. Sci., 1977.

    Google Scholar 

  8. Pawlak Z., On the Notion of a Computer, Logic Meth. and Phil. Sci., 3 (1968), 255–267.

    Google Scholar 

  9. Peterson T.L., Petri Nets, ASM Computing Surveys 9, 3 (1977), 223–252.

    Article  Google Scholar 

  10. Petri C.A., Concepts of Net Theory, MFCS'73 Proc., Math. Inst. of Slovak Acad. of Sci., 1973, 137–146.

    Google Scholar 

  11. Petri C.A., Non-Sequential Processes, ISF Report 77-01, Gesellshaft für Mathematik und Datenverarbeitung, Bonn, 1977.

    Google Scholar 

  12. Petri C.A., Concurrency as a Basis of Systems Thinking, ISF Report 78-06, Gesellshaft für Mathematik und Datenverarbeitung, Bonn, 1978.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Warsaw Technical University, Pl. Jednosci Robotniczej 1, 00-661, Warsaw, Poland

    Ryszard Janicki

Authors
  1. Ryszard Janicki
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Gilles Kahn

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© 1979 Springer-Verlag Berlin Heidelberg

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Janicki, R. (1979). A characterization of concurrency-like relations. In: Kahn, G. (eds) Semantics of Concurrent Computation. Lecture Notes in Computer Science, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022466

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  • DOI: https://doi.org/10.1007/BFb0022466

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09511-8

  • Online ISBN: 978-3-540-35163-4

  • eBook Packages: Springer Book Archive

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