P systems with communication based on concentration

Abstract

We consider a variant of P systems where the communication of objects is controlled by the "concentration" of these objects: after each evolution step, the objects are redistributed among the regions of the system in such a way that each region contains the same number of copies of each object (plus/minus one, when the number of objects is not divisible by the number of regions). We show that P systems of this form, with only one flip-flop catalyst but without using other control ingredients, can generate the Parikh images of all matrix languages. When an unbounded number of catalysts is available, a characterization of recursively enumerable sets of vectors of natural numbers is obtained (by systems with only one membrane).