Two-Step Simulations of Reaction Systems by Minimal Ones

Reaction systems were introduced by Ehrenfeucht and Rozenberg withbiochemical applications in mind. The model is suitable for the studyof subset functions, that is, functions from the set of all subsetsof a finite set into itself. In this study the number of resourcesof a reaction system is essential for questions concerning generativecapacity. While all functions with a couple of trivial exceptionsfrom the set of subsets of a finite set S into itself can be definedif the number of resources is unrestricted, only a specific subclassof such functions is defined by minimal reaction systems, that is,the number of resources is smallest possible. On the other hand,minimal reaction systems constitute a very elegant model. In thispaper we simulate arbitrary reaction systems by minimal ones in twoderivation steps. Various techniques for doing this consist of takingnames of reactions or names of subsets as elements of the backgroundset. In this way also subset functions not at all definable by reactionsystems can be generated. We follow the original definition of reactionsystems, where both reactant and inhibitor sets are assumed to benonempty.