SOS Rules for Equivalences of Reaction Systems

Abstract

Reaction Systems (RSs) are a successful computational framework inspired by biological systems. A RS combines a set of entities with a set of reactions over them. Entities can be provided by an external context, used to enable or inhibit each reaction, and also produced by reactions. RS semantics is defined in terms of an (unlabelled) rewrite system: given the current set of entities, a rewrite step consists of the application of all and only the enabled reactions. In this paper we define, for the first time, a compositional labelled transition system for RSs with recursive and nondeterministic contexts, in the structural operational semantics (SOS) style. This is achieved by distilling a signature whose operators directly correspond to the ingredients of RSs and by defining some simple SOS inference rules for any such operator. The rich information recorded in the labels allows us to define an assertion language to tailor behavioural equivalences on some specific properties or entities. The SOS approach is suited to drive additional enhancements of RSs along features such as quantitative measurements of entities and communication between RSs. The SOS rules have been also exploited to design a prototype implementation in logic programming.