Irreducible reaction systems and reaction system rank.

Reaction systems, introduced by Ehrenfeucht and Rozenberg, are a simple yet versatile model of computation inspired by biochemical reactions in living cells. This contribution falls under one of the active research lines that studies the mathematical nature of subset functions specified by reaction systems, also called rs functions. We introduce the concept of irreducibility for reaction systems and also reaction system rank for rs functions. Apart from some elementary results and basic analysis, the paper focuses on the bounds of reaction system rank. It is found that for every background set, the upper limit of reaction system rank (for all corresponding rs functions, as well as for those that are bijective) is attainable.