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arXiv · 2501.08928

Formulas as Processes, Deadlock-Freedom as Choreographies (Extended Version)

Matteo Acclavio·Giulia Manara·Fabrizio Montesi
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Abstract

We introduce a novel approach to studying properties of processes in the {\pi}-calculus based on a processes-as-formulas interpretation, by establishing a correspondence between specific sequent calculus derivations and computation trees in the reduction semantics of the recursion-free {\pi}-calculus. Our method provides a simple logical characterisation of deadlock-freedom for the recursion- and race-free fragment of the {\pi}-calculus, supporting key features such as cyclic dependencies and an independence of the name restriction and parallel operators. Based on this technique, we establish a strong completeness result for a nontrivial choreographic language: all deadlock-free and race-free finite {\pi}-calculus processes composed in parallel at the top level can be faithfully represented by a choreography. With these results, we show how the paradigm of computation-as-derivation extends the reach of logical methods for the study of concurrency, by bridging important gaps between logic, the expressiveness of the {\pi}-calculus, and the expressiveness of choreographic languages.

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Matteo Acclavio, Giulia Manara, Fabrizio Montesi. 2025-01-15. Formulas as Processes, Deadlock-Freedom as Choreographies (Extended Version). https://doi.org/10.1007/978-3-031-91118-7_2

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