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On Bisimilarity and Substitution in Presence of Replication

  • Daniel Hirschkoff
  • Damien Pous
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6199)

Abstract

We prove a new congruence result for the π-calculus: bisimilarity is a congruence in the sub-calculus that does not include restriction nor sum, and features top-level replications. Our proof relies on algebraic properties of replication, and on a new syntactic characterisation of bisimilarity. We obtain this characterisation using a rewriting system rather than a purely equational axiomatisation. We then deduce substitution closure, and hence, congruence. Whether bisimilarity is a congruence when replications are unrestricted remains open.

Keywords

Parallel Composition Label Transition System Replication Operator Substitution Closure Process Calculus 
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.

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References

  1. 1.
    Aceto, L., Fokkink, W.J., Ingolfsdottir, A., Luttik, B.: Finite equational bases in process algebra: Results and open questions. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 338–367. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Boreale, M., Sangiorgi, D.: Some congruence properties for π-calculus bisimilarities. Theoretical Computer Science 198, 159–176 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Christensen, S., Hirshfeld, Y., Moller, F.: Decidable subsets of CCS. Computer Journal 37(4), 233–242 (1994)CrossRefGoogle Scholar
  4. 4.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. Journal of ACM 32(1), 137–161 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hirschkoff, D., Pous, D.: Extended version of this abstract, http://hal.archives-ouvertes.fr/hal-00375604/
  6. 6.
    Hirschkoff, D., Pous, D.: A distribution law for CCS and a new congruence result for the pi-calculus. Logial Methods in Computer Science 4(2) (2008)Google Scholar
  7. 7.
    Hirshfeld, Y., Jerrum, M.: Bisimulation equivalence is decidable for normed process algebra. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 412–421. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Lanese, I., Pérez, J.A., Sangiorgi, D., Schmitt, A.: On the expressiveness and decidability of higher-order process calculi. In: LICS, pp. 145–155. IEEE, Los Alamitos (2008)Google Scholar
  9. 9.
    Milner, R.: Functions as Processes. J. of Mathematical Structures in Computer Science 2(2), 119–141 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Nestmann, U., Pierce, B.C.: Decoding choice encodings. Information and Computation 163, 1–59 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Pous, D.: Complete lattices and up-to techniques. In: Shao, Z. (ed.) APLAS 2007. LNCS, vol. 4807, pp. 351–366. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Pous, D.: Techniques modulo pour les bisimulations. PhD thesis, ENS Lyon (2008)Google Scholar
  13. 13.
    Sangiorgi, D.: On the bisimulation proof method. J. of Mathematical Structures in Computer Science 8, 447–479 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Daniel Hirschkoff
    • 1
  • Damien Pous
    • 2
  1. 1.ENS Lyon, Université de Lyon, CNRS, INRIA 
  2. 2.CNRS, Laboratoire d’Informatique de Grenoble 

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