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)


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.


Parallel Composition Label Transition System Replication Operator Substitution Closure Process Calculus 
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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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