Concurrency, Causality and Conflict via Independence in Reversible Calculi

2026-09-16

AI Summary

该论文通过引入独立性概念，利用可逆性研究进程演算中的并发、因果和冲突关系，并通过Beluga证明助手验证了相关理论。

Abstract

Among the different ways of approaching the semantics of process calculi, true-concurrency models stand out for their ability to highlight subtle interplays between events. At their heart lie three crucial relations: concurrency, causality and conflict. This paper shows that reversibility, when endowed with a notion of independence, provides a rich tooling to study and characterise these true-concurrency relations. First, we prove that systems admitting pre-reversibility (i.e., that can be extended with an independence relation satisfying some basic axioms) have a unique notion of independence, events, concurrency, causality and conflict. We then analyse the relationship between independence and the true-concurrency relations, establishing novel independence-based characterisations of causality and conflict. Our second series of contributions revolves around two concrete process calculi and two syntactic notions defined on their transition labels, namely independence and dependence; we prove that they partition connected transitions and characterise elegantly concurrency on adjacent transitions. This part of our development was machine-checked using the proof assistant Beluga. Last, we study how the key mechanism commonly used in reversible process algebra can be used as a proxy to retrieve causality and core independence on past events. We conclude by discussing how our results extend beyond reversible systems.

Problem

• Concurrency
• Causality
• Conflict
• Independence
• Reversible Calculi

Innovation

• reversibility
• independence
• true-concurrency
• causality
• conflict