Enhancing Reaction Systems: A Process Algebraic Approach

Abstract

In the area of Natural Computing, reaction systems are a qualitative abstraction inspired by the functioning of living cells, suitable to model the main mechanisms of biochemical reactions. This model has already been applied and extended successfully to various areas of research. Reaction systems interact with the environment represented by the context, and pose problems of implementation, as it is a new computation model. In this paper we consider the link-calculus, which allows to model multiparty interaction in concurrent systems, and show that it allows to embed reaction systems, by representing the behaviour of each entity and preserving faithfully their features. We show the correctness and completeness of our embedding. We illustrate our framework by showing how to embed a lac operon regulatory network. Finally, our framework can contribute to increase the expressiveness of reaction systems, by exploiting the interaction among different reaction systems.

SOS Rules for Equivalences of Reaction Systems

“…In Brodo et al [9,10] we derived similar results to those presented here by encoding RSs into cCNA, a multi-party process algebra (a variant of the linkcalculus [5,6]). In comparison with the encoding of RS in cCNA, we get here a much simpler computational model, closer to the syntax of RSs, preserving the expressiveness at the level of transition labels.…”

“…In Bodei et al [9] and Brodo et al [10] we have presented the encoding of RS into (Lnk) Fig. 2: SOS semantics rule for the connector operator the link-calculus and we have already discussed how to connect two encoded RS such that some of the entities produced by one RS are provided to the second one, similarly to what has been done in Bottoni et al [7].…”

“…For contexts we exploit some classic process algebraic operators (action prefix, sum and recursion). This way we can recursively define contexts that possibly exhibit nondeterministic behaviour, as sometimes have already appeared in the literature [18,9]. Even though we enrich the expressiveness of contexts, the overall LTS still remains finite.…”

Quantitative extensions of reaction systems based on SOS semantics

“…Inspired by process algebras such as CCS [26], in [18,19,27] the authors introduced an algebraic syntax for RSs and equipped it with SOS inference rules defining the behaviour of each operator. This made it possible to consider a LTS semantics for RSs, where states are terms of the algebra, each transition corresponds to a step of the RS and transition labels retain some information on the entities needed to perform each step.…”