Timed Equivalences for Timed Event Structures

  • M. V. Andreeva
  • I. B. Virbitskaite
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3606)


The intention of the paper is to develop a framework for observational equivalences in the setting of a real-time partial order model. In particular, we introduce a family of equivalences of linear time – branching time spectrum based on interleaving, causal trees and partial order semantics, in the setting of event structures with dense time domain. We study the relationships between these approaches and show their discriminating power. Furthermore, when dealing with particular subclasses of the model under consideration there is no difference between a more concrete or a more abstract approach.


Partial Order Event Structure Time Equivalence Labelling Function Causal Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aceto, L.: History Preserving, Causal and Mixed-ordering Equivalence over Stable Event Structures. Fundamenta Informaticae 17(4), 319–331 (1992)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Aceto, L., De Nicola, R., Fantechi, A.: Testing Equivalences for Event Structures. In: Venturini Zilli, M. (ed.) Mathematical Models for the Semantics of Parallelism. LNCS, vol. 280, pp. 1–20. Springer, Heidelberg (1987)Google Scholar
  3. 3.
    Alur, R., Dill, D.: The Theory of Timed Automata. Theoretical Computer Science 126, 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Alur, R., Henzinger, T.A.: Logics and Models of Real Time: a Survey. In: Huizing, C., de Bakker, J.W., Rozenberg, G., de Roever, W.-P. (eds.) REX 1991. LNCS, vol. 600, pp. 74–106. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  5. 5.
    Andreeva, M.V., Bozhenkova, E.N., Virbitskaite, I.B.: Analysis of Timed Concurrent Models Based on Testing Equivalence. Fundamenta Informaticae 43(1-4), 1–20 (2000)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Andreeva, M.A., Virbitskaite, I.B.: Timed Equivalences for Timed Event Structures. Available from,
  7. 7.
    Baier, C., Katoen, J.-P., Latella, D.: Metric Semantics for True Concurrent Real Time. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 568–579. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  8. 8.
    Čerāns, K.: Decidability of Bisimulation Equivalences for Parallel Timer Processes. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 302–315. Springer, Heidelberg (1993)Google Scholar
  9. 9.
    Darondeau, P., Degano, P.: Causal Trees: Interleaving + Causality. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 239–255. Springer, Heidelberg (1990)Google Scholar
  10. 10.
    De Nicola, R., Hennessy, M.: Testing Equivalence for Processes. Theoretical Computer Science 34, 83–133 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    van Glabbeek, R.J.: The Linear Time – Branching Time Spectrum II: The Semantics of Sequential Systems with Silent Moves. Extended Abstract. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 66–81. Springer, Heidelberg (1993)Google Scholar
  12. 12.
    van Glabbeek, R.J., Goltz, U.: Equivalence Notions for Concurrent Systems and Refinement of Actions. In: Kreczmar, A., Mirkowska, G. (eds.) MFCS 1989. LNCS, vol. 379, pp. 237–248. Springer, Heidelberg (1989)Google Scholar
  13. 13.
    Goltz, U., Wehrheim, H.: Causal Testing. In: Penczek, W., Szałas, A. (eds.) MFCS 1996. LNCS, vol. 1113, pp. 394–406. Springer, Heidelberg (1996)Google Scholar
  14. 14.
    Hennessy, M., Milner, R.: Algebraic Laws for Nondeterminism and Concurrency. Journal of ACM 32, 137–162 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Hoare, C.A.R.: Communicating sequential processes. Prentice-Hall, London (1985)zbMATHGoogle Scholar
  16. 16.
    Maggiolo-Schettini, A., Winkowski, J.: Towards an Algebra for Timed Behaviours. Theoretical Computer Science 103, 335–363 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Milner, R.: Communication and Concurrency. Prentice-Hall, London (1989)zbMATHGoogle Scholar
  18. 18.
    Murphy, D.: Time and Duration in Noninterleaving Concurrency. Fundamenta Informaticae 19, 403–416 (1993)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Steffen, B., Weise, C.: Deciding Testing Equivalence for Real-Time Processes with Dense Time. In: Borzyszkowski, A.M., Sokolowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 703–713. Springer, Heidelberg (1993)Google Scholar
  20. 20.
    Virbitskaite, I.B.: An Observation Semantics for Timed Event Structures. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds.) PSI 2001. LNCS, vol. 2244, pp. 215–225. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  21. 21.
    Virbitskaite, I.B., Gribovskaya, N.S.: Open Maps and Observational Equivalences for Timed Partial Order Models. Fundamenta Informaticae 60(1-4), 383–399 (2004)zbMATHMathSciNetGoogle Scholar
  22. 22.
    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. LNCS, vol. 354, pp. 364–397. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  23. 23.
    Weise, C., Lenzkes, D.: Efficient Scaling-Invariant Checking of Timed Bisimulation. In: Reischuk, R., Morvan, M. (eds.) STACS 1997. LNCS, vol. 1200, pp. 176–188. Springer, Heidelberg (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • M. V. Andreeva
    • 1
  • I. B. Virbitskaite
    • 1
  1. 1.A.P. Ershov Institute of Informatics SystemsSiberian Division of the Russian Academy of SciencesNovosibirskRussia

Personalised recommendations