Enriched categories for local and interaction calculi

  • Stefano Kasangian
  • Anna Labella
  • Alberto Pettorossi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 283)


The construction of models for distributed computations plays a very important role in designing and developing parallel computing systems. Various algebraic approaches have been proposed in the past as, for instance, the communicating computing agents of [Mil80], [BeK85], and [BHR84].

In our work we propose a general method for defining the categorical models for classes of algebras of distributed computing agents. If the static and dynamic operations [Mil80] of the algebras enjoy suitable properties, we can construct enriched categories which are models of distributed computations, including also the case of concurrent finite automata which cooperate via protocols. The construction is uniform with respect to the particular algebra one may wish to consider.


Categorical Model Binary String Atomic Action Finite State Automaton Free Monoid 
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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9. References

  1. [AsR86]
    Astesiano, E. and Reggio, G.: "A Syntax-Directed Approach to the Semantics of Concurrent Languages" Proc. Information Processing 86. (H-J. Kugler, ed.) Elsevier Science Publ. (North Holland) (1986), 571–576.Google Scholar
  2. [AuB84]
    Austry, D. and Boudol, G.: "Algèbre de Processus et Synchronisation" Theoretical Computer Science 30 (1984), 91–131.Google Scholar
  3. [BeK85]
    Bergstra, J.A. and Klop, J.W.: "Algebra of Communicating Processes with Abstraction". Theoretical Computer Science Vol.37, No.1 (1985), 77–121.Google Scholar
  4. [Bet80]
    Betti, R. "Automi e categorie chiuse" Boll. Unione Matem. Ital. (5) 17–13 (1980), 44–58.Google Scholar
  5. [BHR84]
    Brookes, S.D., Hoare, C.A.R., and Roscoe, A.W.: "A Theory of Communicating Sequential Processes" J.A.C.M. 31, 3 (1984), 560–599.Google Scholar
  6. [Car85]
    Cardelli, L.: "AMBER" Proc. Treizième Ecole de Printemps d'Informatique Theorique, La Val D'Ajol, Vosges (France) (May 1985).Google Scholar
  7. [DeM85]
    Degano, P. and Montanari, U.: "Specification Languages for Distributed Systems". Proc. Mathematical Foundations of Software Development LNCS n.185 Springer-Verlag, Berlin (1985), 29–51.Google Scholar
  8. [EiK65]
    Eilenberg, S. and Kelly, G.M.: "Closed Categories" Proc. of the Conference on Categorical Algebra. La Jolla 1965, Springer-Verlag (1966), 421–562.Google Scholar
  9. [GMY84]
    Gouda, M.G., Manning, E.G., and Yu, Y.T.: "On Progress of Communication between Two Finite State Machines" Information and Control 63 (1984), 200–216.Google Scholar
  10. [GoB84]
    Goguen, J., and Burstall, R.M.: "Some Fundamental Algebraic Tools for the Semantics of Computation, Part 1: Comma Categories, Colimits, Signature and Theories". Theoretical Computer Science 31(2), (1984), 175–209.Google Scholar
  11. [HAB78]
    Hewitt, C., Atkinson, R., and Baker, H.: "Semantics of Communicating Parallel Processes" Proc. Summer School on Foundations of Artificial Intelligence, ISI, Università di Pisa, Pisa (June 1978).Google Scholar
  12. [Hen83]
    Hennessy, M.: "Synchronous and Asynchronous Experiments on Processes" Information and Control 59 (1983), 36–83.Google Scholar
  13. [Hoa78]
    Hoare, C.A.R.: "Communicating Sequential Processes" Communications A.C.M. Vol.21, n.8, (1978), 666–677.Google Scholar
  14. [KaL87]
    Kasangian, S. and Labella, A.: "Enriched Categorical Semantics for Distributed Calculi" (forthcoming paper) (1987).Google Scholar
  15. [Kel82]
    Kelly, G.M.: "Basic Concepts of Enriched Category Theory", Cambridge University Press, Cambridge (1982).Google Scholar
  16. [KKR83]
    Kasangian, S., Kelly, G.M., and Rossi, F.: "Cofibrations and the Realization of Nondeterministic Automata" Cahiers de Topologie et Géométrie Différentielle. XXIV 1 (1983), 23–46.Google Scholar
  17. [LaP86]
    Labella, A. and Pettorossi, A.: "Categorical Models of Process Cooperation" Proc. Category Theory and Computer Programming, Guildford, U.K., September 1985, Lecture Notes in Computer Science n.240, Springer-Verlag, Berlin (1986), 282–298.Google Scholar
  18. [Law73]
    Lawvere, F.W.: "Metric Spaces, Generalized Logic, and Closed Categories" Rendiconti del Seminario Matematico e Fisico, Milano 43 (1973), 135–166.Google Scholar
  19. [Mac71]
    Mac Lane, S.: "Categories for the Working Mathematician". Springer Verlag Berlin (1971).Google Scholar
  20. [Maz78]
    Mazurkiewicz, A.: "Concurrent Program Schemes and their Interpretations" DAIMI PB 78 Aarhus University Publ., Denmark, (1978).Google Scholar
  21. [Mil79]
    Milne, G.: "Synchronized Behaviour Algebras: A Model for Interacting Systems" Department of Computer Science, University of Southern California, Los Angeles, USA, (1979).Google Scholar
  22. [Mil80]
    Milner, R.: "A Calculus of Communicating Systems" LNCS n.92 Springer-Verlag, Berlin (1980).Google Scholar
  23. [Mil83]
    Milner, R.: "Calculi for Synchrony and Asynchrony" Theoretical Computer Science 25 (1983), 267–310.Google Scholar
  24. [Pet62]
    Petri, C.A.: "Fundamentals of a Theory of Asynchronous Information Flow" In: Proceedings of IFIP Congress 62, North-Holland, Amsterdam (1962).Google Scholar
  25. [Plo81]
    Plotkin, G.: "Lectures Notes on Domain Theory". Computer Science Department, Edinburgh University, Edinburgh (Scotland) (1981).Google Scholar
  26. [Plo82]
    Plotkin, G.: "An Operational Semantics for CSP". Proc. Formal Description of Programming Concepts II (ed. D. Bjørner), IFIP TC-2, Garmisch-Partenkirchen, Germany (1982), 199–223.Google Scholar
  27. [TaW82]
    Taylor, R. and Wilson, P.: "OCCAM: Process-Oriented Language Meets Demands of Distributed Processing". Electronics, Mac Graw Hill (November 1982).Google Scholar
  28. [Win84]
    Winskel, G.: "Categories of Models for Concurrency" LNCS.197 Seminar on Concurrency. Carnegie-Mellon University, Pittsburgh July 9–11, 1984, Springer-Verlag (1985), 246–267.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Stefano Kasangian
    • 1
  • Anna Labella
    • 2
  • Alberto Pettorossi
    • 3
  1. 1.Dipartimento di MatematicaUniversità di MilanoMilanoItaly
  2. 2.Dipartimento di MatematicaUniversità di Roma "La Sapienza"RomaItaly
  3. 3.IASI-CNRRomaItaly

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