Determinacy with Priorities up to Clocks

📅 2026-04-08
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🤖 AI Summary
This work addresses the core challenge in modeling the semantics of synchronous programming languages: achieving deterministic behavior in concurrent systems while supporting key features such as causality, shared-memory multithreading, and responsiveness to absent signals. To this end, the paper extends Milner’s confluence theory within the Calculus of Communicating Systems (CCS) by introducing priority-guarded actions and a clock mechanism, thereby proposing a novel notion of “consistency.” This approach compositionally and precisely encodes essential semantic characteristics of synchronous languages like Esterel. By doing so, it overcomes longstanding limitations of traditional process algebras in expressing deterministic synchronous computation and significantly enhances the ability of concurrent models to capture the rich semantics of synchronous languages.
📝 Abstract
In Milner's seminal book on communication and concurrency introducing CCS, a process algebra inherently non-deterministic, chapter 11 was completely devoted to introduce the notion of determinacy and confluence in order to identify a subcalculus of CCS in which all definable agents are confluent. At the same time, or shortly later, determinate semantics were given for programming languages that reconcile concurrency and determinacy, such as Esterel by Berry and Gonthier, or SL by Boussinot and de Simone. These dedicated semantics do not easily map to Milner's confluence theory for CCS, which is unable to express causality and shared memory multi-threading with reaction to absence in a compositional way. We present an extension of CCS with priority-guarded actions and clocks, and we exploit the added expressiveness to enrich Milner's original notion of confluence by the new concept of coherence which permits us to encode, in a compositional fashion, synchronous programming languages such as Esterel.
Problem

Research questions and friction points this paper is trying to address.

determinacy
confluence
synchronous programming
process algebra
causality
Innovation

Methods, ideas, or system contributions that make the work stand out.

priority-guarded actions
clocks
confluence
coherence
compositional encoding
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