Universal models in categories for process synchronization

  • Anna Labella
  • Alberto Pettorossi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 280)


In the first part of the paper we show how to construct categorical models for Milner's CCS [Mil80], Hoare's CSP [Hoa78], and similarly defined calculi for synchronized and parallel computations.

We consider a generic category C of processes with morphisms which are labelled by strings of actions belonging to a monoid A. We define the synchronization between two processes in C as a functor (if it exists) from a subcategory of C × C into C. We introduce the notions of categorical semantics and good categorical semantics for processes.

In the second part of the paper we show that the Categories of Trees we will define, is optimal for most synchronizations described in the literature. That result is presented also in the framework of the Enriched Category Theory [Law74] for indicating its meaning in terms of an internal logic [Law74].


Boolean Algebra Universal Model Atomic Action Label Tree Internal Logic 
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8. References

  1. [Hoa78]
    Hoare, C. A. R.: "Communicating Sequential Processes" Comm. A.C.M., Vol. 21 n.8 (1978), 666–677.Google Scholar
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    Kasangian, S. and A. Labella: "Enriched Categories for the Semantics of Distributed Calculi" (to appear) (1987).Google Scholar
  3. [Kel82]
    Kelly, G.M.: "Basic Concepts of Enriched Category Theory", Cambridge University Press, Cambridge, U.K. (1982).Google Scholar
  4. [LaP85]
    Labella, A. and A. Pettorossi: "Categorical Models of Process Cooperation". Proc. Workshop on Category Theory and Computer Science, University of Surrey, Guilford, U.K., Lecture Notes in Computer Science n.240, Springer-Verlag, (1985), 282–298.Google Scholar
  5. [Law74]
    Lawvere, F.W.: "Metric Spaces, Generalized Logic, and Closed Categories". Rendiconti del Seminario Matematico e Fisico, Milano, Italy, (1974), 135–166.Google Scholar
  6. [Mil80]
    Milner, R.: "A Calculus for Communicating Systems" Lecture Notes in Computer Science n.92, Springer-Verlag, Berlin (1980).Google Scholar
  7. [Mil83]
    Milner, R.: "Calculi for Synchrony and Asynchrony" Theoretical Computer Science n.25, (1983), 267–310.Google Scholar
  8. [Win83]
    Winskel, G.: "Synchronization Trees" Lecture Notes in Computer Science n.154 Proc. ICALP '83, Springer-Verlag, (1983), 695-711.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Anna Labella
    • 1
  • Alberto Pettorossi
    • 2
  1. 1.Department of MathematicsUniversity of Roma "La Sapienza"RomaItaly
  2. 2.IASI - CNRRomaItaly

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