Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-31T10:24:46.068Z Has data issue: false hasContentIssue false
  • English
  • Français

Processes as terms: non-well-founded models for bisimulation

Published online by Cambridge University Press:  04 March 2009

J. J. M. M. Rutten
J. J. M. M. Rutten
Affiliation:
CWI, Kruislaan 413, 1098 SJ Amsterdam, The netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

A compositional semantics characterizing bisimulation equivalence is derived from transition system specifications in the SOS style, satisfying certain syntactic syntactic conditions. We use Aczel's nonstandard set theory for solving a recursive equation for a domain fo processes. It contains non-well-founded elements modelling possibly infinite behaviour. Semantic interpretations of syntactic operators are obtained by defining the operational semantics for terms consisting of both syntactic and semantic (processes)entities. Finally, we return to standard set theory by observing that a similar, though less general, result can be obtained with the use of complete metric spaces.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 2 , Issue 3 , September 1992 , pp. 257 - 275
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramsky, s. (1991) A domain equation for bisimulation. Information and Computation, 92 161–218.CrossRefGoogle Scholar
Aczel, P. (1988) Non-well-founded sets, number 14 in CSLI Lecture Notes.Google Scholar
America, p. and Rutten, J. J. M. M. (1989) Solving reflexive domain equations in a category of complete metric spaces. Journal of Computer and System Sciences, 39(3) 343–375.CrossRefGoogle Scholar
Barwise, J. (1975) Admissible sets and structures, Springer-Verlag.CrossRefGoogle Scholar
Barwise, J. and Etchemendy, J. (1988) The Liar: An Essay in Truth and Circularity, Oxford University Press.Google Scholar
de Bakker, J. W. and Zucker, J. I. (1982) Processes and the denotational semantics of concurrency. Information and Control, 54 70–120CrossRefGoogle Scholar
Engelking, R. (1977) General Topology, Polish Scientific Publishers.Google Scholar
Forti, M. and Honsell, F. (1983) Set theory with free construction principles. Annali Scuola Normale Superiore, Pisa, X(3) 493–522.Google Scholar
Groote, J. F. and Vanndrager, F. (1989) Structured operational semantics and bisimulation as a congruence. In: Ausiello, G., Dezani-Ciancaglini, M., and Rocca, S. Ronchi Della, Editors, Processdings 16th ICALP, Lecture Notes in Computer Science 372 423–438. Springer-verlag. To appear in Information and Computation.Google Scholar
Mislove, M. W., Moss, L. S. and Oles, F. J. (1989) Non-well-founded sets obtained from ideal fixed points. In Proc. Of the Fourth IEEE Symposium on Logic in Computer Science 263–272. To appear in Information and Computation.Google Scholar
Nivat, M. (1979) Infinite words, infinite trees, infinite computations. In: Bakker, J. W. de and Leeuwen, J. van, editors, Foundations of Computer Science III, Part 2, Math. Centre Tracts 109 3–52.Google Scholar
Park, D. M. R. (1981) Concurrency and automata on infinite sequences. In: Deussen, P., editor, Proceedings 5th GI conference, Lecture Notes in COmputer Science 104 15–32. Springer-verlag.Google Scholar
Plotkin, G. D. (1981) A Structural approach to Operational semantics, Technical Report DAIMI FN-19, Aarhus University, Computer Science Department.Google Scholar
Rutten, J. J. M. M. (1990) Deriving denotational models for bisimulation from Structured Operational Semantics. In: Broy, M. and Jones, C. B., editors, Programming concepts and methods, proceedings of the IFIP Working Group 2.2/2.3 Working Conference, Sea of Galile 155–177. North-Holland.Google Scholar
Rutten, J. J. M. M. (1991) Hereditarily-finite sets and complete metric spaces. Technical report CS-R9148, Centre for Mathematics and Computer Science, Amsterdam.Google Scholar
van Glabbeek, R. J. and Rutten, J. J. M. M. (1989) The Processes of De Bakker and Zucker represent bisimulation equivalence classes. In: J. W. de Bakker, 25 jaar semantiek 243–246, CWI, Amsterdam.Google Scholar