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A Lightweight Formalization of the Metatheory of Bisimulation-Up-To

Kaustuv Chaudhuri 1 Matteo Cimini 2 Dale Miller 1
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : Bisimilarity of two processes is formally established by producing a bisimulation relation that contains those two processes and obeys certain closure properties. In many situations, particularly when the under-lying labeled transition system is unbounded, these bisimulation relations can be large and even infinite. The bisimulation-up-to technique has been developed to reduce the size of the relations being computed while retaining soundness, that is, the guarantee of the existence of a bisimulation. Such techniques are increasingly becoming a critical ingredient in the automated checking of bisimilarity. This paper is devoted to the formalization of the meta theory of several major bisimulation-up-to techniques for the process calculi CCS and the π-calculus (with replication). Our formalization is based on recent work on the proof theory of least and greatest fixpoints, particularly the use of relations defined (co-)inductively, and of co-inductive proofs about such relations, as implemented in the Abella theorem prover. An important feature of our formalization is that our definitions of the bisimulation-up-to relations are, in most cases, straightforward translations of published informal definitions, and our proofs clarify several technical details of the informal descriptions. Since the logic behind Abella also supports λ-tree syntax and generic reasoning using the ∇-quantifier, our treatment of the π-calculus is both direct and natural.
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Kaustuv Chaudhuri, Matteo Cimini, Dale Miller. A Lightweight Formalization of the Metatheory of Bisimulation-Up-To. 4th ACM-SIGPLAN Conference on Certified Programs and Proofs (CPP), ACM-SIGPLAN, Jan 2015, Mumbai, India. ⟨10.1145/2676724.2693170⟩. ⟨hal-01091524⟩

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