Deriving weak bisimulation congruences from reduction systems

Bruni, R, Gadducci, F, Montanari, U and Sobocinski, P (2005) Deriving weak bisimulation congruences from reduction systems. Abadi, M and de Alfaro, L (eds.) Concur, San Francisco, United States. 22 - 25 Aug 2005. pp. 293-307 .

Abstract

The focus of process calculi is interaction rather than computation, and for this very reason: (i) their operational semantics is conveniently expressed by LTSs whose labels model the possible interactions with the environment; (ii) their abstract semantics is conveniently expressed by observational congruences. However, many current-day process calculi are more easily equipped with reduction semantics, which focus on their internal dynamics but where the notion of observable action is missing. Recent techniques attempted to bridge this gap by synthesizing LTSs whose labels are process contexts that catalyze reactions and for which bisimulation is a congruence. Starting from Sewell's set-theoretic construction, category theoretic techniques were developed to define minimal LTS based on Leifer and Milner's relative pushouts, later refined by Sassone and the fourth author to deal with structural congruences given as groupoidal 2-categories. The paper aims at proving that double categories provide an even more suitable formalism for the synthesis of LTSs, as well as for congruence proofs. Albeit the framework is more sophisticated, constructions hard to phrase in set-theoretic settings become more general and intuitive, and in the end simpler. Moreover, the formalism allows for a straightforward definition of weak bisimulation congruence, not available in previous approaches.

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