Weak Bisimulation Up to Elaboration

  • Damien Pous
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)


We study the use of the elaboration preorder (due to Arun-Kumar and Natarajan) in the framework of up-to techniques for weak bisimulation. We show that elaboration yields a correct technique that encompasses the commonly used up to expansion technique. We also define a theory of up-to techniques for elaboration that in particular validates an elaboration up to elaboration technique, while it is known that weak bisimulation up to weak bisimilarity is unsound. In this sense, the resulting setting improves over previous works in terms of modularity.

Our results are obtained using nontrivial proofs that exploit termination arguments. In particular, we need the termination of internal computations for the up-to techniques to be correct. We show how this condition can be relaxed to some extent in order to handle processes exhibiting infinite internal behaviour.


Visible Action Label Transition System Elaboration Relation Symmetric Relation Safe Function 
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  1. 1.
    Arun-Kumar, S., Hennessy, M.: An Efficiency Preorder for Processes. Acta Informatica 29(9), 737–760 (1992)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Arun-Kumar, S., Natarajan, V.: Conformance: A Precongruence Close to Bisimilarity. In: Proc. Struct. in Concurrency Theory, pp. 55–68. Springer, Heidelberg (1995)Google Scholar
  3. 3.
    Fournet, C.: The Join-Calculus: a Calculus for Distributed Mobile Programming. PhD thesis, Ecole Polytechnique (1998)Google Scholar
  4. 4.
    Groote, J., Reniers, M.: Algebraic Process Verification. In: Handbook of Process Algebra, pp. 1151–1208. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  5. 5.
    Hirschkoff, D., Pous, D., Sangiorgi, D.: A Correct Abstract Machine for Safe Ambients. In: Jacquet, J.-M., Picco, G.P. (eds.) COORDINATION 2005. LNCS, vol. 3454, pp. 17–32. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Montanari, U., Sassone, V.: Dynamic Congruence vs. Progressing Bisimulation for CCS. Fundamenta Informaticae 16(1), 171–199 (1992)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Pous, D.: Up-to Techniques for Weak Bisimulation. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 730–741. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Pous, D.: Weak Bisimulation up to Elaboration. In: Long version of this paper, with full proofs (2006), Available from:
  9. 9.
    Sangiorgi, D.: On the Bisimulation Proof Method. Journal of Mathematical Structures in Computer Science 8, 447–479 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    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
  11. 11.
    Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Damien Pous
    • 1
  1. 1.ENS Lyon 

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