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A characterization of concurrency-like relations

  • Ryszard Janicki
Conference paper
Part of the Lecture Notes in Computer Science book series (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 ↣ 2 U , 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.

Keywords

Partial Order Minimal Cover Maximal Chain Concurrent System Concurrent Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [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. [2]
    Genrich H.J., A position in panel discussion, MFCS'75 Symposium, Marianskie Laznie, 1975.Google Scholar
  3. [3]
    Harrary F., Graph Theory, Addison-Wesllay, Mass., 1967.Google Scholar
  4. [4]
    Janicki R., Synthesis of Concurrent Schemes, Lecture Notes in Comp. Sci., vol. 64, Springer-Verlag, 1978, 298–307.Google Scholar
  5. [5]
    Knuth E., Petri Nets and Trace Languages, Proc. of the 1st European Conf. on Parallel and Distr. Processing, Toulouse, 1979.Google Scholar
  6. [6]
    Marczewski E., Sur deux propriétés des classes d'ensembles, Fund. Math., 33 (1945), 303–307.Google Scholar
  7. [7]
    Mazurkiewicz A., Concurrent Program Schemes and Their Interpretations, DAIMI PB-78, Aarhus Univ., Department of Comp. Sci., 1977.Google Scholar
  8. [8]
    Pawlak Z., On the Notion of a Computer, Logic Meth. and Phil. Sci., 3 (1968), 255–267.Google Scholar
  9. [9]
    Peterson T.L., Petri Nets, ASM Computing Surveys 9, 3 (1977), 223–252.CrossRefGoogle Scholar
  10. [10]
    Petri C.A., Concepts of Net Theory, MFCS'73 Proc., Math. Inst. of Slovak Acad. of Sci., 1973, 137–146.Google Scholar
  11. [11]
    Petri C.A., Non-Sequential Processes, ISF Report 77-01, Gesellshaft für Mathematik und Datenverarbeitung, Bonn, 1977.Google Scholar
  12. [12]
    Petri C.A., Concurrency as a Basis of Systems Thinking, ISF Report 78-06, Gesellshaft für Mathematik und Datenverarbeitung, Bonn, 1978.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Ryszard Janicki
    • 1
  1. 1.Institute of MathematicsWarsaw Technical UniversityWarsawPoland

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