Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
9. References
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.
Austry, D. and Boudol, G.: "Algèbre de Processus et Synchronisation" Theoretical Computer Science 30 (1984), 91–131.
Bergstra, J.A. and Klop, J.W.: "Algebra of Communicating Processes with Abstraction". Theoretical Computer Science Vol.37, No.1 (1985), 77–121.
Betti, R. "Automi e categorie chiuse" Boll. Unione Matem. Ital. (5) 17–13 (1980), 44–58.
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.
Cardelli, L.: "AMBER" Proc. Treizième Ecole de Printemps d'Informatique Theorique, La Val D'Ajol, Vosges (France) (May 1985).
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.
Eilenberg, S. and Kelly, G.M.: "Closed Categories" Proc. of the Conference on Categorical Algebra. La Jolla 1965, Springer-Verlag (1966), 421–562.
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.
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.
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).
Hennessy, M.: "Synchronous and Asynchronous Experiments on Processes" Information and Control 59 (1983), 36–83.
Hoare, C.A.R.: "Communicating Sequential Processes" Communications A.C.M. Vol.21, n.8, (1978), 666–677.
Kasangian, S. and Labella, A.: "Enriched Categorical Semantics for Distributed Calculi" (forthcoming paper) (1987).
Kelly, G.M.: "Basic Concepts of Enriched Category Theory", Cambridge University Press, Cambridge (1982).
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.
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.
Lawvere, F.W.: "Metric Spaces, Generalized Logic, and Closed Categories" Rendiconti del Seminario Matematico e Fisico, Milano 43 (1973), 135–166.
Mac Lane, S.: "Categories for the Working Mathematician". Springer Verlag Berlin (1971).
Mazurkiewicz, A.: "Concurrent Program Schemes and their Interpretations" DAIMI PB 78 Aarhus University Publ., Denmark, (1978).
Milne, G.: "Synchronized Behaviour Algebras: A Model for Interacting Systems" Department of Computer Science, University of Southern California, Los Angeles, USA, (1979).
Milner, R.: "A Calculus of Communicating Systems" LNCS n.92 Springer-Verlag, Berlin (1980).
Milner, R.: "Calculi for Synchrony and Asynchrony" Theoretical Computer Science 25 (1983), 267–310.
Petri, C.A.: "Fundamentals of a Theory of Asynchronous Information Flow" In: Proceedings of IFIP Congress 62, North-Holland, Amsterdam (1962).
Plotkin, G.: "Lectures Notes on Domain Theory". Computer Science Department, Edinburgh University, Edinburgh (Scotland) (1981).
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.
Taylor, R. and Wilson, P.: "OCCAM: Process-Oriented Language Meets Demands of Distributed Processing". Electronics, Mac Graw Hill (November 1982).
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kasangian, S., Labella, A., Pettorossi, A. (1987). Enriched categories for local and interaction calculi. In: Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds) Category Theory and Computer Science. Lecture Notes in Computer Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18508-9_20
Download citation
DOI: https://doi.org/10.1007/3-540-18508-9_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18508-6
Online ISBN: 978-3-540-48006-8
eBook Packages: Springer Book Archive