Luigi Liquori

Luigi Liquori, Michael Mendler, Claude Stolze

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.

Luigi Liquori, Michael Mendler

Building on the standard theory of process algebra with priorities, we identify a new scheduling mechanism, called "constructive reduction" which is designed to capture the essence of synchronous programming. The distinctive property of this evaluation strategy is to achieve determinacy-by-construction for multi-cast concurrent communication with shared memory. In the technical setting of CCS extended by clocks and priorities, we prove for a large class of "coherent" processes a confluence property for constructive reductions. We show that under some restrictions, called "pivotability", coherence is preserved by the operators of prefix, summation, parallel composition, restriction and hiding. Since this permits memory and sharing, we are able to cover a strictly larger class of processes compared to those in Milner's classical confluence theory for CCS without priorities.