Feasibility of Organizations – A Refinement of Chemical Organization Theory with Application to P Systems

Abstract

In membrane computing, a relatively simple set of reaction rules usually implies a complex “constructive” dynamics, in which novel molecular species appear and present species vanish. Chemical organization theory is a new approach that deals with such systems by describing chemical computing as a transition between organizations, which are closed and self-maintaining sets of molecular species. In this paper we show that for the case of mass-action kinetics some organizations are not feasible in the space of concentrations and thus need not to be considered in the analysis. We present a theorem providing criteria for an unfeasible organization. This is a refinement of organization theory making its statements more precise. In particular it follows for the design of a membrane computing system that the desired resulting organization of a chemical computing process should be a feasible organization. Nevertheless we show that due to the membranes in a P system unfeasible organizations can be observed, suggesting a strong link between the two approaches.