Parameterised Bisimulations: Some Applications

  • S. Arun-Kumar
  • Divyanshu Bagga
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8428)

Abstract

In [AK06] the first author had generalised the notion of bisimulation on labelled transition systems to that of a parameterised relation whose parameters were a pair of relations on the observables of a system. In this paper we present new results which show that notions of parameterised bisimilarity may be defined to capture congruences in process algebras. In particular, we show that observational congruence may be obtained as a parameterised bisimulation, thereby providing a co-inductive characterisation for the same. In another application, parameterisation is employed to prove that amortised bisimilarity is preserved under recursion in CCS by resorting to a generalisation of the so-called “upto”-technique. We then extend the framework to a name passing calculus and show that one can capture (hyper-)bisimulations in the fusion calculus [Vic98] as a parameterised (hyper-)bisimulation. However this involves giving a behaviourally equivalent alternative semantics for the fusion calculus, which is necessary for defining parameterised bisimulations in the fusion calculus and also allows for more natural definitions of bisimulations.

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References

  1. [AKH92]
    Arun-Kumar, S., Hennessy, M.: An efficiency preorder for processes. Acta Informatica 29, 737–760 (1992)CrossRefMATHMathSciNetGoogle Scholar
  2. [AKN95]
    Arun-Kumar, S., Natarajan, V.: Conformance: A precongruence close to bisimilarity. In: Structures in Concurrency Theory, pp. 55–68. Springer (1995)Google Scholar
  3. [AK06]
    Arun-Kumar, S.: On bisimilarities induced by relations on actions. In: Fourth IEEE International Conference on Software Engineering and Formal Methods, SEFM 2006, pp. 41–49. IEEE (2006)Google Scholar
  4. [Bag11]
    Bagga, D.: Parametrised bisimulations for the fusion calculus. Master’s thesis, Department of Computer Science and Engineering, IIT Delhi (2011), http://www.cse.iitd.ac.in/~bagga/bag11.html
  5. [BK85]
    Bergstra, J.A., Klop, J.W.: Algebra of communicating processes with abstraction. Theoretical Computer Science 37, 77–121 (1985)CrossRefMATHMathSciNetGoogle Scholar
  6. [KAK05]
    Kiehn, A., Arun-Kumar, S.: Amortised bisimulations. In: Wang, F. (ed.) FORTE 2005. LNCS, vol. 3731, pp. 320–334. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. [LV06]
    Lüttgen, G., Vogler, W.: Bisimulation on speed: A unified approach. Theoretical Computer Science 360, 209–227 (2006)CrossRefMATHMathSciNetGoogle Scholar
  8. [Mil89]
    Milner, R.: Communication and concurrency. Prentice-Hall, Inc. (1989)Google Scholar
  9. [MPW92a]
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, I. Information and Computation 100, 1–40 (1992)CrossRefMATHMathSciNetGoogle Scholar
  10. [MPW92b]
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, II. Information and Computation 100, 41–77 (1992)CrossRefMATHMathSciNetGoogle Scholar
  11. [PV98]
    Parrow, J., Victor, B.: The fusion calculus: Expressiveness and symmetry in mobile processes. In: Proceedings of the Thirteenth Annual IEEE Symposium on Logic in Computer Science, pp. 176–185. IEEE (1998)Google Scholar
  12. [SM92]
    Sangiorgi, D., Milner, R.: The problem of “Weak Bisimulation up to”. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 32–46. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  13. [SAK09]
    Singh, P., Arun-Kumar, S.: Axiomatization of a Class of Parametrised Bisimilarities. Perspectives in Concurrency Theory. Universities Press, India (2009)Google Scholar
  14. [Vic98]
    Victor, B.: The fusion calculus: Expressiveness and symmetry in mobile processes. PhD thesis, Uppsala University (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • S. Arun-Kumar
    • 1
  • Divyanshu Bagga
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology DelhiNew DelhiIndia

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