[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Partial-congruence factorization of bisimilarity induced by open maps

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1443))

Included in the following conference series:

Abstract

We investigate some relationships between bisimilaxity defined by open maps and behavioural equivalence factorized by indistinguishability relations. This is done in the setting of a concrete category supporting algebraic constructions of subobject and quotient. Some sufficient condition is found for bisimilarity to be factorizable by the greatest open congruences. We also find a necessary and sufficient condition for a factorization of bisimilarity: quotients by all maximal open congruences are isomorphic. The general results are motivated and illustrated by important examples: transition systems, event structures and presheaves.

This work was supported by the KBN grant 8 T11C 046 14.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abramsky, C.-H. Luke Ong. Full Abstraction in the Lazy Lambda Calculus. Information and Computation 105(2), 159–267, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  2. Benson, D.B., Ben-Schachar, O. Bisimulation of automata. Information and Computation, 79, 60–83, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bidoit, M., Hennicker, R., Wirsing, M. Behavioural and abstractor specifications. Science of Computer Programming 25(2–3):149–186, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  4. Bidoit, M., Tarlecki, A. Regular algebras: a framework for observational specifications with recursive definitions. Report LIENS-95-12, Ecole Norm. Sup., 1995.

    Google Scholar 

  5. Bidoit, M., Tarlecki A. Behavioural satisfaction and equivalence in concrete model categories. Proc. 20th CAAP'96, Linköping, Springer-Verlag.

    Google Scholar 

  6. Castellani, I. Bisimulation and abstraction homomorphisms. Proc. of CAAP'85, Springer-Verlag LNCS, 1985.

    Google Scholar 

  7. Cattani, G.L., Winskel, G. Presheaf models for concurrency. Computer Science Logic CSL'96, LNCS 1258. Preliminary version: BRICS Report RS-96-35.

    Google Scholar 

  8. Cheng, A., Nielsen, M. Open maps (at) work. Research series RS-95-23, BRICS, Department of Comp. Sc., University of Aarhus, 1995.

    Google Scholar 

  9. Giarratana, V., Gimona, F., Montanari, U. Observability concepts in abstract data type specification. Proc. 5th Intl. Symp. Mathematical Foundations of Computer Science, Gdansk 1976, LNCS 45, Springer-Verlag 1976, 576–587.

    Google Scholar 

  10. Van Glabeek, R.J., Goltz, U. Equivalence notions for concurrent systems and refinement of actions. Proc. of MFCS, Springer-Verlag LNCS vol. 379, 1989.

    Google Scholar 

  11. Gordon, A. A tutorial on co-induction and functional programming. Proc.of the 1994 Glasgow Workshop on Functional Programming, Springer Workshops in Computing, 1995, 78–95.

    Google Scholar 

  12. Joyal, A., Moerdijk, I. A completeness theorem for open maps. Annals of Pure and Applied Logic 70(1994), 51–86.

    Article  MATH  MathSciNet  Google Scholar 

  13. Joyal, A., Nielsen, G. Winskel, Bisimulation and open maps. Proc. 8th Annual Symposium on Logic in Computer Science LICS'93, 1993, 418–427.

    Google Scholar 

  14. Lasota, S. Open Maps as a Bridge between Algebraic Observational Equivalence and Bisimilarity. Proc. 12th Workshop on Algebraic Developement Techniques, Tarquinia, 1997, LNCS 1376.

    Google Scholar 

  15. Lasota, S. Partial-Congruence Factorization of Bisimilarity Induced by Open Maps. The full version of this paper, available at http://zls.mimuw.edu.pl/~sl.

    Google Scholar 

  16. Milner, R. Communication and concurrency. Prentice-Hall International Series in Computer Science, C. A. R. Hoare series editor, 1989.

    Google Scholar 

  17. Nielsen, M., Winskel, G. Models for concurrency. Chapter 1 of The Handbook of Logic in Computer Science, vol. 4, Oxford University Press, 1995.

    Google Scholar 

  18. Park, D.M.R. Concurrency and Automata on Infinite Sequences. Proc. 5th G.I. Conference, Lecture Notes in Computer Science 104, Springer-Verlag, 1981.

    Google Scholar 

  19. Reichel, H. Behavioural equivalence — a unifying concept for initial and final specification methods. Proc. 3rd Hungarian Computer Science Conference, Mathematical Models in Computer Systems, M. Arato, L. Varga, eds., Budapest, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Kim G. Larsen Sven Skyum Glynn Winskel

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lasota, S. (1998). Partial-congruence factorization of bisimilarity induced by open maps. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055043

Download citation

  • DOI: https://doi.org/10.1007/BFb0055043

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64781-2

  • Online ISBN: 978-3-540-68681-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics