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.
Work partially funded by the French ANR projects “Curry-Howard pour la Concurrence” CHOCO ANR-07-BLAN-0324 and COMPLICE ANR-08-BLANC-0211-01.
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Hirschkoff, D., Pous, D. (2010). On Bisimilarity and Substitution in Presence of Replication. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_38
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DOI: https://doi.org/10.1007/978-3-642-14162-1_38
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