Exploiting Modularity of SOS Semantics to Define Quantitative Extensions of Reaction Systems

Reaction Systems (RSs) are a successful natural computing framework inspired by chemical reaction networks. A RS consists of a set of entities and a set of reactions. Entities can enable or inhibit each reaction, and are produced by reactions or provided by the environment. In a previous paper, we defined an original labelled transition system (LTS) semantics for RSs in the structural operational semantics (SOS) style. This approach has several advantages: (i) it provides a formal specification of the RS dynamics that enables the reuse of many formal analysis techniques and favors the implementation of tools, and (ii) it facilitates the definition of extensions of the RS framework by simply modifying some of the SOS rules in a modular way. In this paper, we demonstrate the extensibility of the framework by defining two quantitative variants of RSs: with reaction delays/durations, and with concentration levels. We provide a prototype logic programming implementation and apply our tool to a RS model of Th cells differentiation in the immune system