Functions and sequences generated by reaction systems

The paper investigates formal properties of reaction systems introduced by Ehrenfeucht and Rozenberg. A reaction system defines a function from the set 2S of subsets of a finite set S into 2S itself. We investigate properties of such functions, and characterize situations when the function is total. We also introduce and characterize the property of functional completeness. Function classes defined by different types of reaction systems are compared. Comparisons are carried out also between different methods of generating long sequences and cycles.