Note on Simulation by Strictly Minimal Reaction Systems with Limited Resources

Abstract

Reaction systems, introduced by Ehrenfeucht and Rozenberg, are computational models inspired by biochemical reactions transpiring  within the living cells and is often compared with membrane computing which is inspired by the functioning of the cellular membranes. This relatively young research area has since evolved into diverse research directions on various extensions of the original framework. One particular direction focuses on mathematical properties of functions specified by minimal reaction systems, due to their simplicity and richness.Some notion of simulation of reaction systems was introduced by Manzoni, Pocas, and Porreca and they showed that every reaction system can be simulated by some strictly minimal reaction system (each reaction involves only one resource) over an extended background set. This short exposition contains some additional result extending the author's recent collaborative work on simulation of reaction systems [W.C. Teh, A. Atanasiu, Simulation of reaction systems by the strictly minimal ones, J. Membr. Comput., 2020. doi: 10.1007/s41965-020-00042-2]. In particular, the non-simulation of certain functions specified by strictly minimal reaction systems is shown when the number of extra resource is limited to one.