A process algebraic approach to reaction systems

In the area of Natural Computing, Reaction Systems (RSs) are a qualitative abstraction inspired by the functioning of living cells, suitable to model the main mechanisms of biochemical reactions. RSs interact with a context, and pose challenges for modularity, compositionality, extendibility and behavioural equivalence. In this paper we define a modular encoding of RSs as processes in the chained Core Network Algebra (cCNA), which is a new variant of the link-calculus. The encoding represents the behaviour of each entity separately and preserves faithfully their features, and we prove its correctness and completeness. Our encoding provides a Labelled Transition System (LTS) semantics for RSs. Based on the LTS semantics, we adapt the classical notion of bisimulation to define a novel equivalence, called bio-similarity, for studying properties of RSs. In particular, we define a new assertion language based on regular expressions, which allows us to specify the properties of interest, and use it to extend Hennessy-Milner logic to our setting. We prove that our bio-similarity relation and the logical equivalence, that are defined parametrically on some assertion of interest, coincide. Finally, we claim that our encoding contributes to increase the expressiveness of RSs, by exploiting the interaction among different RSs.