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

2025-01-15

AI Summary

This paper addresses the verification of deadlock and resource contention in parallel processes within the π-calculus. We propose a novel logical characterization method: recursive- and race-free π-processes are modeled as sequent calculus derivations, yielding the first purely logical characterization of deadlock-freedom. By establishing a precise correspondence between process semantics and logical derivations, we obtain a concise, decidable logical criterion for deadlock-freedom. Moreover, we prove that all such processes admit faithful encodings into choreographic programs, thereby establishing strong completeness of choreography languages for concurrent behavior. These results extend the “computation-as-deduction” paradigm to concurrency verification, broadening its theoretical scope. Our approach provides a new foundation for logic-based verification of concurrent programs, bridging process calculi and proof theory in a principled manner.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance

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.

Problem

• Pi-calculus
• Deadlock-freedom
• Resource-competition

Innovation

• π-calculus
• deadlock-free processes
• choreography languages