Span(Graph): A categorical algebra of transition systems

  • Piergiulio Katis
  • N. Sabadini
  • R. F. C. Walters
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1349)


We have shown that a natural algebraic structure on Span(Graph) allows the compositional specification of concurrent systems. Hoare's parallel operation appears as a derived operation in this algebra. The simpler basic operations of our algebra are possible because we do not insist on interleaving semantics: interleaving prevents consideration of the identity span, as well as other natural constants such as the diagonal. We have given some examples of transforming systems using the equations of the algebra. Associated to the algebra there is a geometry which expresses the distributed nature of a concurrent system. This relation between algebra and geometry makes precise the relation between process algebras and circuit diagrams as used, for example, in Ebergen [E87].


Label Transition System Process Algebra Concurrent System Initial Vertex Distributive Category 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Piergiulio Katis
    • 1
  • N. Sabadini
    • 2
  • R. F. C. Walters
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SydneyN.S.W.Australia
  2. 2.Dipartimento di Scienze dell'InformazioneUniversità di MilanoMilanoItaly

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