Facilitation in reaction systems

Abstract

Reaction systems is a formal model of computation which originated as a model of interactions between biochemical reactions in the living cell. These interactions are based on two mechanisms, facilitation and inhibition, and this is well reflected in the formulation of reaction systems. In this paper, we investigate the facilitation aspect of reaction systems, where the products of a reaction may facilitate other reactions by providing some of their reactants. This aspect is formalized through positive dependency graphs which depict explicitly such facilitating interactions. The focus of the paper is on demonstrating how structural properties of reaction systems defined through the properties of their positive dependency graphs influence the behavioural properties of (suitable subclasses of) reaction systems, which, as usual, are defined through their transition graphs.

Pure reaction automata

“…Reaction systems have been successfully employed as a modelling tool in several areas, see for instance (Corolli et al 2012;Azimi et al 2014;Barbuti et al 2021). Concerning theoretical aspects, their properties have been studied from the point of view of the complexity of the dynamics (Formenti et al 2014a(Formenti et al , b, 2015Ehrenfeucht et al 2017;Barbuti et al 2018a;Holzer and Rauch 2021;Teh and Lim 2022;Ascone et al 2024; from the causality perspective (Brijder et al 2010;Barbuti et al 2016Barbuti et al , 2018b; by introducing in a natural way additional restrictions and extensions (Brijder et al 2011b;Salomaa 2017;Azimi 2017;Bottoni et al 2019;Manzoni et al 2020); by classifying and simulating them (Manzoni et al 2014;Atanasiu 2017, 2020); and by relating them with other computational models (Kleijn et al 2011;Păun et al 2013;Dutta et al 2019).…”