On Bisimilarity and Substitution in Presence of Replication

Daniel Hirschkoff (1, 2) , Damien Pous (2, 1, 3)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages
3 SARDES - System architecture for reflective distributed computing environments

We prove a new congruence result for the pi-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.

Mots clés: axiomatisation; bisimilarity; replication; congruence; process algebra

Domaines: Langage de programmation [cs.PL]

Daniel Hirschkoff, Damien Pous. On Bisimilarity and Substitution in Presence of Replication. ICALP, Jul 2010, Bordeaux, France. pp.454-465, ⟨10.1007/978-3-642-14162-1_38⟩. ⟨hal-00375604v4⟩