Minimal Reaction Systems Defining Subset Functions

Abstract

In reaction systems introduced by Ehrenfeucht and Rozenberg the number of resources is essential when various questions concerning generative capacity are investigated. While almost all functions from the set of subsets of a finite set $S$ into itself can be defined by unrestricted reaction systems, only a specific subclass of such functions is defined by minimal reaction systems. In this paper we show that also minimal reaction systems suffice for defining all such functions, provided repetitive use is allowed. Specifically, everything generated by an arbitrary reaction system is generated by a minimal one in three steps. In this way also some functions not at all definable by reaction systems can be generated by minimal reaction systems. All subsets of $S$, in any prechosen order, appear in the sequence of a minimal reaction system.