Abstract
An alternative proof (to that from [3]) is presented for weak bisimilarity of transition systems to be abstractly definable by open maps [9]. This result arises from an observation that the categories (of transition systems) well suited for studying strong and weak bisimulations are related by an adjunction (for a suitable monad), giving a link between both bisimilarities.We formulate a generalization of this result, hopefully applicable also to other equivalences of processes.
This work was supported by the KBN grant 8 T11C 046 14
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References
Bidoit, M., Tarlecki A. Behavioural satisfaction and equivalence in concrete model categories. Proc. 20th Coll. on Trees in Algebra and Computing CAAP’96, Linköping, 241–256, LNCS 1059, 1996.
Cattani, G.L., Winskel, G. Presheaf models for concurrency. Computer Science Logic CSL’96, LNCS, Springer-Verlag. Preliminary version appeared as BRICS Report RS-96-35.
Cheng, A., Nielsen, M. Open maps (at) work. Research series RS-95-23, BRICS, Department of Computer Science, University of Aarhus, 1995.
Cheng, A., Nielsen, M. Open Maps, Behavioural Equivalences, and Congruences. Research series RS-96-2, BRICS, Department of Computer Science, University of Aarhus, 1996. A short version of this paper appeared in Proc. 20th Coll. on Trees in Algebra and Computing CAAP’96, Linköping, 257–272, LNCS 1059, 1996.
Van Glabeek, R.J., Goltz, U. Equivalence notions for concurrent systems and refinement of actions. Proc. of MFCS, Springer-Verlag LNCS vol. 379, 1989.
Hennesy, M. Algebraic Theory of Processes. MIT Press series in the foundations of computing, 1988.
Hoare, C.A.R. Communicating Sequential Processes. Prentice-Hall, 1985.
Joyal, A., Moerdijk, I. A completeness theorem for open maps. Annals of Pure and Applied Logic 70 (1994), 51–86.
Joyal, A., Nielsen, G. Winskel, Bisimulation and open maps. Proc. 8th Annual Symposium on Logic in Computer Science LICS’93, 1993, 418–427.
Lasota, S. Open Maps as a Bridge between Algebraic Observational Equivalence and Bisimilarity. Proc. 12th Workshop on Algebraic Developement Techniques, Tarquinia, 1997, LNCS 1376.
Mac Lane, S. Categories for the Working Mathematician. Springer, New York, 1971.
Milner, R. Communication and concurrency. Prentice-Hall International Series in Computer Science, C. A. R. Hoare series editor, 1989.
Nielsen, M., Winskel, G. Models for concurrency. Chapter 1 of The Handbook of Logic in Computer Science, vol. 4, Oxford University Press, eds.S. Abramsky, D. M. Gabbay and T.S. Gabbay, 1995.
Park, D.M.R. Concurrency and Automata on Infinite Sequences. Proc. 5th G.I. Conference, Lecture Notes in Computer Science 104, Springer-Verlag, 1981.
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Lasota, S. (1998). Weak Bisimilarity and Open Maps. In: Rovan, B. (eds) SOFSEM’ 98: Theory and Practice of Informatics. SOFSEM 1998. Lecture Notes in Computer Science, vol 1521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49477-4_30
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DOI: https://doi.org/10.1007/3-540-49477-4_30
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