Logics and Bisimulation Games for Concurrency, Causality and Conflict

  • Julian Gutierrez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5504)


Based on a simple axiomatization of concurrent behaviour we define two ways of observing parallel computations and show that in each case they are dual to conflict and causality, respectively. We give a logical characterization to those dualities and show that natural fixpoint modal logics can be extracted from such a characterization. We also study the equivalences induced by such logics and prove that they are decidable and can be related with well-known bisimulations for interleaving and noninterleaving concurrency. Moreover, by giving a game-theoretical characterization to the equivalence induced by the main logic, which is called Separation Fixpoint Logic (SFL), we show that the equivalence SFL induces is strictly stronger than a history-preserving bisimulation (hpb) and strictly weaker than a hereditary history-preserving bisimulation (hhpb). Our study considers branching-time models of concurrency based on transition systems and petri net structures.


Modal and temporal logics Bisimulation games Behavioural equivalences Concurrent and reactive systems Petri nets 


  1. 1.
    Alur, R., Henzinger, T., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alur, R., Peled, D., Penczek, W.: Model-Checking of Causality Properties. In: LICS, pp. 90–100. IEEE Computer Society, Los Alamitos (1995)Google Scholar
  3. 3.
    Bradfield, J.: Truth and Games: Essays in Honour of Gabriel Sandu. In: Aho, T., Pietarinen, A. (eds.) Acta Philosophica Fennica. Independence: Logics and Concurrency, vol. 78, pp. 47–70. Phil. Soc. of Finland (2006)Google Scholar
  4. 4.
    Bradfield, J., Esparza, J., Mader, A.: A Causal Fixpoint Logic. Unpub. (1997)Google Scholar
  5. 5.
    Bradfield, J., Fröschle, S.: Independence-Friendly Modal Logic and True Concurrency. Nord. J. Comput. 9(1), 102–117 (2002)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Brookes, S.: A semantics for concurrent separation logic. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 16–34. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Fecher, H.: A Completed Hierarchy of True Concurrent Equivalences. Inf. Process. Lett. 89(5), 261–265 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Fröschle, S.: The Decidability Border of Hereditary History Preserving Bisimilarity. Inf. Process. Lett. 93(6), 289–293 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Fröschle, S., Hildebrandt, T.: On Plain and Hereditary History-Preserving Bisimulation. In: Kutyłowski, M., Wierzbicki, T., Pacholski, L. (eds.) MFCS 1999. LNCS, vol. 1672, pp. 354–365. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Glabbeek, R., Goltz, U.: Refinement of Actions and Equivalence Notions for Concurrent Systems. Acta Inf. 37(4/5), 229–327 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hayman, J., Winskel, G.: Independence and Concurrent Separation Logic. In: LICS, pp. 147–156. IEEE Computer Society, Los Alamitos (2006)Google Scholar
  12. 12.
    Hennessy, M., Milner, R.: Algebraic Laws for Nondeterminism and Concurrency. J. ACM 32(1), 137–161 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Joyal, A., Nielsen, M., Winskel, G.: Bisimulation from Open Maps. Inf. Comput. 127(2), 164–185 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Mazurkiewicz, A.: Trace Theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 279–324. Springer, Heidelberg (1987)Google Scholar
  15. 15.
    Nielsen, M., Clausen, C.: Games and Logics for a Noninterleaving Bisimulation. Nord. J. Comput. 2(2), 221–249 (1995)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Nielsen, M., Winskel, G.: Models for Concurrency. In: Handbook of Logic in Computer Science, vol. 4, pp. 1–148. Oxford University Press, Oxford (1995)Google Scholar
  17. 17.
    Penczek, W.: Branching Time and Partial Order in Temporal Logics. In: Time and Logic: A Computational Approach, pp. 179–228. UCL Press (1995)Google Scholar
  18. 18.
    Pym, D., Tofts, C.: A Calculus and Logic of Resources and Processes. Formal Asp. Comput. 18(4), 495–517 (2006)CrossRefzbMATHGoogle Scholar
  19. 19.
    Reynolds, J.: Separation Logic: A Logic for Shared Mutable Data Structures. In: LICS, pp. 55–74. IEEE Computer Society, Los Alamitos (2002)Google Scholar
  20. 20.
    Sims, É.-J.: Extending Separation Logic with Fixpoints and Postponed Substitution. Theor. Comput. Sci. 351(2), 258–275 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Stirling, C.: Modal and Temporal Properties of Processes. Springer, Heidelberg (2001)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Julian Gutierrez
    • 1
  1. 1.LFCS. School of InformaticsUniversity of Edinburgh, Informatics ForumEdinburghUK

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