A characterization of concurrency-like relations

  • Ryszard Janicki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 70)


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.


Partial Order Minimal Cover Maximal Chain Concurrent System Concurrent Process 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

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

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