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A Logic Characteristic for Timed Extensions of Partial Order Based Equivalences

  • Natalya S. Gribovskaya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7162)

Abstract

The intention of the paper is to provide a uniform logic characteristic for timed extensions of partial order based equivalences (pomset trace equivalence, history preserving bisimulation and hereditary history preserving bisimulation) in the setting of timed event structures. For this purpose, we use open maps based characterizations of the equivalences, provided in [10], and the logics of path assertions from [6].

Keywords

Timed event structures timed partial order equivalences logic characteristic category theory 

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References

  1. 1.
    Boudol, G., Castellani, I.: Concurrency and atomicity. Theoretical Computer Science 59, 25–84 (1989)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cattani, G.L., Sassone, V.: Higher dimentional transition systems. In: 11th Annual IEEE Symp. on Logic in Computer Science, pp. 55–62. IEEE Comp. Soc. Press, Washington (1996)Google Scholar
  3. 3.
    Gribovskaya, N.S., Virbitskaite, I.B.: Timed Delay Bisimulation is an Equivalence Relation for Timed Transition Systems. Fundamenta Informaticae 93(1-3), 127–142 (2009)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Hune, T., Nielsen, M.: Bisimulation and open maps for timed transition systems. Fundamenta Informaticae 38, 61–77 (1999)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Joyal, A., Moerdijk, I.: A completeness theorem for open maps. Annual Pure Applied Logic 70, 51–86 (1997)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Joyal, A., Nielsen, M., Winskel, G.: Bisimulation from open maps. Information and Computation 127(2), 164–185 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Katoen, J.-P., Langerak, R., Latella, D., Brinksma, E.: On Specifying Real-time Systems in a Causality-based Setting. In: Jonsson, B., Parrow, J. (eds.) FTRTFT 1996. LNCS, vol. 1135, pp. 385–404. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  8. 8.
    Nielsen, M., Cheng, A.: Observing Behaviour Categorically. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 263–278. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  9. 9.
    Oshevskaya, E.S.: Open Maps Bisimulations for Higher Dimensional Automata Models. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds.) FCT 2009. LNCS, vol. 5699, pp. 274–286. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Virbitskaite, I.B., Gribovskaya, N.S.: Open maps and observational equivalences for timed partial order models. Fundamenta Informaticae 60(1-4), 383–399 (2004)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Virbitskaite, I.B., Gribovskaya, N.S., Best, E.: A Categorical View of Timed Behaviours. Fundamenta Informaticae 102(1), 129–143 (2010)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Winskel, G.: An Introduction to Event Structures. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop. LNCS, vol. 354, pp. 364–397. Springer, Heidelberg (1989)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Natalya S. Gribovskaya
    • 1
  1. 1.A.P. Ershov Institute of Informatics SystemsSB RASNovosibirskRussia

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