Divide and Congruence: From Decomposition of Modalities to Preservation of Branching Bisimulation

  • Wan Fokkink
  • Rob van Glabbeek
  • Paulien de Wind
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4111)


We present a method for decomposing modal formulas for processes with the internal action τ. To decide whether a process algebra term satisfies a modal formula, one can check whether its subterms satisfy formulas that are obtained by decomposing the original formula. The decomposition uses the structural operational semantics that underlies the process algebra. We use this decomposition method to derive congruence formats for branching and rooted branching bisimulation equivalence.


Function Symbol Transition Rule Label Transition System Process Algebra Modal Formula 
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  1. 1.
    Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Information and Control 60(1/3), 109–137 (1984)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bloom, B.: Structural operational semantics for weak bisimulations. Theoretical Computer Science 146(1/2), 25–68 (1995)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bloom, B., Fokkink, W.J., van Glabbeek, R.J.: Precongruence formats for decorated trace semantics. ACM Transactions on Computational Logic 5(1), 26–78 (2004)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. Journal of the ACM 42(1), 232–268 (1995)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bol, R.N., Groote, J.F.: The meaning of negative premises in transition system specifications. Journal of the ACM 43(5), 863–914 (1996)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    De Nicola, R., Vaandrager, F.W.: Three logics for branching bisimulation. Journal of the ACM 42(2), 458–487 (1995)MATHCrossRefGoogle Scholar
  7. 7.
    Fokkink, W.J.: Rooted branching bisimulation as a congruence. Journal of Computer and System Sciences 60(1), 13–37 (2000)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Fokkink, W.J., van Glabbeek, R.J.: Ntyft/ntyxt rules reduce to ntree rules. Information and Computation 126(1), 1–10 (1996)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Fokkink, W.J., van Glabbeek, R.J., de Wind, P.: Compositionality of Hennessy-Milner logic by structural operational semantics. Theoretical Computer Science 354(3), 421–440 (2006)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Fokkink, W.J., van Glabbeek, R.J., de Wind, P.: Divide and congruence applied to η-bisimulation. In: Proc. SOS 2005. ENTCS. Elsevier, Amsterdam (to appear, 2005)Google Scholar
  11. 11.
    van Glabbeek, R.J.: The linear time-branching time spectrum II: The semantics of sequential systems with silent moves. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 66–81. Springer, Heidelberg (1993)Google Scholar
  12. 12.
    van Glabbeek, R.J.: The meaning of negative premises in transition system specifications II. Journal of Logic and Algebraic Programming 60/61, 229–258 (2004)CrossRefGoogle Scholar
  13. 13.
    van Glabbeek, R.J.: On cool congruence formats for weak bisimulations (extended abstract). In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 331–346. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    van Glabbeek, R.J., Weijland, W.P.: Branching time and abstraction in bisimulation semantics. Journal of the ACM 43(3), 555–600 (1996)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Groote, J.F.: Transition system specifications with negative premises. Theoretical Computer Science 118(2), 263–299 (1993)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Groote, J.F., Vaandrager, F.W.: Structured operational semantics and bisimulation as a congruence. Information and Computation 100(2), 202–260 (1992)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Hennessy, M.C.B., Milner, R.: Algebraic laws for non-determinism and concurrency. Journal of the ACM 32(1), 137–161 (1985)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Kleene, S.C.: Representation of events in nerve nets and finite automata. In: Shannon, C., McCarthy, J. (eds.) Automata Studies, pp. 3–41. Princeton University Press, Princeton (1956)Google Scholar
  19. 19.
    Larsen, K.G., Liu, X.: Compositionality through an operational semantics of contexts. Journal of Logic and Computation 1(6), 761–795 (1991)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Plotkin, G.D.: A structural approach to operational semantics. Journal of Logic and Algebraic Programming 60/61, 17–139 (2004); Originally appeared in 1981CrossRefMathSciNetGoogle Scholar
  21. 21.
    de Simone, R.: Higher-level synchronising devices in Meije–SCCS. Theoretical Computer Science 37(3), 245–267 (1985)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wan Fokkink
    • 1
    • 2
  • Rob van Glabbeek
    • 3
    • 4
  • Paulien de Wind
    • 1
  1. 1.Section Theoretical Computer ScienceVrije Universiteit AmsterdamAmsterdam
  2. 2.Department of Software EngineeringCWIAmsterdam
  3. 3.National ICT AustraliaSydney
  4. 4.School of Computer Science and EngineeringUniversity of New South WalesSydney

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