Towards Bridging Two Cell-Inspired Models: P Systems and R Systems GheorgheP˘aun 1,2 , Mario J. P´ erez-Jim´ enez 2 1 Institute of Mathematics of the Romanian Academy PO Box 1-764, 014700 Bucure¸ sti, Romania 2 Department of Computer Science and Artificial Intelligence University of Sevilla Avda. Reina Mercedes s/n, 41012 Sevilla, Spain gpaun@us.es, marper@us.es Summary. We examine, from the point of view of membrane computing, the two basic assumptions of reaction systems, the “threshold” and “no permanence” ones. In certain circumstances (e.g., defining the successful computations by local halting), the second assumption can be incorporated in a transition P system or in a symport/antiport P system without losing the universality. The case of the first postulate remains open: the reaction systems deal, deterministically, with finite sets of symbols, which is not of much interest for computing; three ways to introduce nondeterminism are suggested and left as research topics. 1 Introduction The aim of this note is to bridge two branches of natural computing inspired from the biochemistry of a living cell, membrane computing (see, e.g., [11], [12], [13], and the domain website from [15]) and the recently introduced reaction systems area – see [2], [3], [4], [5], [6]. Both areas deals with populations of reactants (molecules) which evolve by means of reactions, with several basic differences. Most of these differences are not mentioned here (e.g., the compartmental structure of models – P systems – in membrane computing versus the missing of membranes in reaction systems – we also call them R systems –, the focus on evolution, not on computation, in reaction systems, the unique form of rules in reaction systems and so on), and we recall the two basic ones in the formulation from [2]: The way that we define the result of a set of reactions on a set of elements formalizes the following two assumptions that we made about the chemistry of a cell: (i) We assume that we have the “threshold” supply of elements (molecules) – either an element is present and then we have “enough” of it, or an element is