Skip to main content
SpringerLink
Log in

Reasoning about the past

  • Invited Papers
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

In this extended abstract, we briefly recall the abstract (categorical) notion of bisimulation from open morphisms, as introduced by Joyal, Nielsen and Winskel. The approach is applicable across a wide range of models of computation, and any such bisimulation comes automatically with characteristic logics and games, which in their general formulations treat the future and the past (of computations) on an equal footing. This raises a number of questions concerning properties of such logics and games for concrete well known models from concurrency theory, in particular questions on the power of reasoning about the past.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bednarczyk, M., Categories of Asynchronous Systems. Ph.D. Thesis in Computer Science, Univ. of Sussex, Report No. 1/88, 1988.

    Google Scholar 

  2. Cattani, G.L., Fiore, M., Winskel,G., A Theory of Recursive Domains with Applications to Concurrency. To appear in Proceedings of LICS'98.

    Google Scholar 

  3. De Nicola, R., Montanari, U., and Vaandrager, F., Back and Forth Bisimulations. Proceedings of CONCUR'90, Springer Lecture Notes in Computer Science 458, pp. 152–165, 1990.

    Google Scholar 

  4. Hoare, C.A.R., Communicating Sequential Processes. Prentice Hall,1985.

    Google Scholar 

  5. Hune, T., Nielsen, M., Timed Bisimulation and Open Maps. In this volume.

    Google Scholar 

  6. Joyal, A., Nielsen, M. and Winskell, G., Bisimulation from Open Maps. Information and Computation, 127, no. 2, pp. 164–185, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  7. Jurdzinski, M., Nielsen, M., On the Power of Past Modalities. In preparation.

    Google Scholar 

  8. Keller, R.M., Formal Verification of Parallel Programs. CACM, 19(7), pp. 371–384, 1976.

    MATH  Google Scholar 

  9. Lichtenstein, O., Pnueli, A., and Zuck, L., The Glory of the Past. Springer Lecture Notes in Computer Science 193, pp. 196–218, 1985.

    MATH  MathSciNet  Google Scholar 

  10. MacLane, S., and Moerdijk, I., Sheaves in geometry and logic: a first introduction to topos theory, Springer, 1992.

    Google Scholar 

  11. Mazurkiewicz, A., Basic notions of trace theory. In de Bakker, de Roever and Rozenberg (eds.), Linear Time, Branching Time and Partial Orders in Logics and Models for Concurrency, Springer Lecture Notes in Computer Science 354, pp. 285–363, 1988.

    Google Scholar 

  12. Milner,A.J.R.G., Communication and concurrency. Prentice Hall, 1989.

    Google Scholar 

  13. Nielsen, M., Plotkin, G. and Winskel, G., Petri nets, Event structures and Domains, part 1. Theoretical Computer Science 13, pp. 85–108, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  14. Nielsen, M., Cheng, A., Observing Behaviour Categorically. Proc. of FST&TCS'15, Springer Lecture Notes in Computer Science 1026, pp. 263–278, 1995.

    MathSciNet  Google Scholar 

  15. Nielsen, M., and Clausen, C., Bisimulations, Games, and Logic. Proc. of CONCUR'94, Springer Lecture Notes in Computer Science 836, pp. 385–400, 1994.

    Google Scholar 

  16. Nielsen, M., and Winskel, G., Petri nets and bisimulations. Theoretical Computer Science, 153, pp. 211–244, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  17. Penczek, W., Kuiper, R., Traces and Logic. In The Book of Traces, eds. Diekert, V., Rozenberg, G., World Scientific, pp. 307–390, 1994.

    Google Scholar 

  18. Petri, C.A. Kommunikation mit Automaten. PhD thesis, Institut für Instrumentelle Mathematik, Bonn, Germany, 1962.

    Google Scholar 

  19. Pratt, V.R., Modelling concurrency with partial orders. International Journal of Parallel Programming, 15(1), pp. 33–71, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  20. Shields, M.W., Concurrent Machines, Comput. J., 28, pp. 449–465, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  21. Stirling, C., Games and Modal Mu-Calculus. Lecture Notes in Computer Science 1055, pp. 298 ff., 1996.

    Google Scholar 

  22. Thiagarajan, P.S., Elementary Net Systems. Springer Lecture Notes in Computer Science 254, pp. 26–59, 1986.

    Article  MathSciNet  Google Scholar 

  23. Vardi, M.Y., The Taming of the Converse: Reasoning about Two-way Computations. Springer Lecture Notes in Computer Science 193, pp. 413–424, 1985.

    MATH  MathSciNet  Google Scholar 

  24. Winskel, G., Event structures. Springer Lecture Notes in Computer Science 255, pp. 325–392, 1987.

    MATH  MathSciNet  Google Scholar 

  25. Winskel, G., and Nielsen, M., Models for concurrency. In the Handbook of Logic in Computer Science, vol. IV, ed. Abramsky, Gabbay and Maibaum, Oxford University Press, pp. 1–148, 1995.

    Google Scholar 

  26. Winskel, G., A Presheaf Semantics of Value-Passing Processes. In the proc. of CONCUR'96, Springer Lecture Notes in Computer Science 1119, pp. 98–114, 1996.

    MathSciNet  Google Scholar 

  27. Winskel, G., and Nielsen, M., Presheaves as Transition Systems, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 29, pp. 129–140, 1997.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Aarhus, Denmark

    Mogens Nielsen

  2. Centre of the Danish National Research Foundation, Basic Research in Computer Science, Denmark

    Mogens Nielsen

Authors
  1. Mogens Nielsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Luboš Brim Jozef Gruska Jiří Zlatuška

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nielsen, M. (1998). Reasoning about the past. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055761

Download citation

  • DOI: https://doi.org/10.1007/BFb0055761

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation