Abstract
A categorial semantic domain for general (discrete event) systems based on labeled transition systems with full concurrency is constructed, where synchronization and hiding are functorial. Moreover, we claim that, within the proposed framework, a class of mappings stands for refinement. Then we prove that refinement satisfies the diagonal compositionality requirement, i.e., refinements compose (vertical) and distribute over system composition (horizontal).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
M. A. Arbib, E. G. Manes, Arrows, Structures and Functors — The Categorial Imperative, Academic Press, 1975.
A. Asperti, G. Longo, Categories, Types and Structures — An Introduction to the Working Computer Science, Foundations of Computing (M. Garey, A. Meyer Eds.), MIT Press, 1991.
M. A. Bednarczyk, Categories of Asynchronous Systems, Ph.D. thesis, technical report 1/88, University of Sussex, 1988.
H. D. Ehrich, A. Sernadas, Algebraic Implementation of Objects over Objects, Stepwise Refinement of Distributed Systems: Models, Formalisms, Correctness (J. de Bakker, W.-P. de Roever, G. Rozenberg Eds.), pp. 239–266, Springer-Verlag, 1990.
R. Gorrieri, Refinement, Atomicity and Transactions for Process Description Language, Ph.D. thesis, Università di Pisa, 1990.
C. A. R. Hoare, Communicating Sequential Processes, Prentice Hall, 1985.
A. Mazurkiewicz, Basic Notion of Trace Theory, REX 88: Linear Time, Branching Time and Partial Orders in Logic and Models for Concurrency (J. W. de Bakker, W.-P. de Roever, G. Rozenberg, Eds.), pp. 285–363, LNCS 354, Springer-Verlag, 1988.
P. B. Menezes, J. F. Costa, Synchronization in Petri Nets, preprint IST/DM/2-94, IST, Lisbon, 1993. Revised version accepted for publication in Fundamenta Informaticae.
P. B. Menezes, J. F. Costa, Compositional Refinement of Concurrent Systems, preprint IST/DM/26-94, IST, Lisbon, 1994. Revised version accepted for publication in the Journal of the Brazilian Computer Society — Special Issue on Parallel Computation.
P. B. Menezes, J. F. Costa, Object Refinement, preprint IST/DM/24-94, IST, Lisbon, 1994.
J. Meseguer, U. Montanari, Petri Nets are Monoids, Information and Computation 88, pp. 105–155, Academic Press, 1990.
R. Milner, Communication and Concurrency, Prentice Hall, 1989.
C. Rattray, The Shape of Complex Systems, EUROCAST 93: Computer Aided Systems Theory (F. Pichler, R. M. Díaz, Eds.), pp. 72–82, LNCS 763, Springer-Verlag, 1994.
W. Reisig, Petri Nets: An Introduction, EATCS Monographs on Theoretical Computer Science 4, Springer-Verlag, 1985.
V. Sassone, M. Nielsen, G. Winskel, A Classification of Models for Concurrency, CONCUR 93: 4th International Conference of Concurrency (E. Best, Ed.), pp. 82–96, LNCS 715, Springer-Verlag, 1993.
M. E. Szabo, Algebra of Proofs, Studies in Logic and the Foundations of Mathematics, vol. 88, North-Holland, 1978.
G. Winskel, Petri Nets, Algebras, Morphisms and Compositionality, Information and Computation 72, pp. 197–238, Academic Press, 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Menezes, P.B., Costa, J.F., Sernadas, A. (1996). Refinement mapping for general (discrete event) systems theory. In: Pichler, F., Díaz, R.M., Albrecht, R. (eds) Computer Aided Systems Theory — EUROCAST '95. EUROCAST 1995. Lecture Notes in Computer Science, vol 1030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034753
Download citation
DOI: https://doi.org/10.1007/BFb0034753
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60748-9
Online ISBN: 978-3-540-49358-7
eBook Packages: Springer Book Archive