Simulation of reaction systems by the strictly minimal ones

Abstract

Reaction systems, introduced by Ehrenfeucht and Rozenberg, are elementary computational models based on biochemical reactions transpiring within the living cells. Numerous studies focus on mathematical aspects of minimal reaction systems due to their simplicity and rich generative power. Manzoni et al. (Int J Found Comput Sci 25(4):441-457, 2014) showed that every reaction system can be simulated by some minimal reaction system over an extended background set. Motivated by their work, we introduce the concepts of strictly minimal and hybrid reaction systems. Using our new concepts, the result of Manzoni et al. is revisited and strengthened. We also show that extension of the background set by a polynomially bounded number of elements is not sufficient to guarantee the aforementioned simulation. Finally, an analogous result for strong simulation is obtained.

Controllability of reaction systems

“…Since their introduction in 2007, two major research directions on reaction systems have been established. The first direction focuses on their formal properties as a dynamical system: sequences of states [31,32], power of small systems for various size measures [17,[34][35][36]38], cycles and attractors [5,14,16], connections to propositional logic [33], etc. The second major direction of research on reaction systems consists in exploring their potential as a modelling framework, in particular for biological applications [3,4,10].…”