Ranks of compositionally closed minimal reaction systems

reaction system is a computational model motivated by the functioning of living cells. In previous studies, Ehrenfeucht et al. have classified the functions specified by minimal reaction systems. Several studies have focused on the reaction system ranks of functions specified by minimal reaction systems, where the rank pertains to the minimum size of a specifying reaction system. This paper focuses on reaction system rank for a class of union-additive functions specified by minimal reaction systems introduced by Salomaa, which are closed under composition. More precisely, we establish a sufficient condition for the equality of reaction system ranks for functions belonging to the class. Then we study the reaction system ranks of such functions with signature sizes one and two, as well as those with one-to-one signatures, specifically over ternary and quaternary alphabets. Lastly, we establish a lower upper bound of reaction system ranks of such functions with one-to-one signatures for |S| ≥ 5.