Upper and lower bounds for the computational power of P systems with mobile membranes

Abstract

We continue the study of P systems with mobile membranes introduced in [7], which is a variant of P systems with active membranes, but having none of the features like polarizations, label change and division of non-elementary membranes. This variant was shown to be computationally universal (RE) using only the simple operations of endocytosis and exocytosis; moreover, if elementary membrane division is allowed, it is capable of solving NP-complete problems. It was shown in [5] that 4 membranes are sufficient for universality while using only endo/exo operations. In this paper, we study the computational power of these systems more systematically: we examine not only the power due to the number of membranes, but also with respect to the kind of rules used, thereby trying to find out the border line between universality and non-universality. We show that 3 membranes are sufficient for computational universality, whereas two membranes are not, if λ-free rules are used. © Springer-Verlag Berlin Heidelberg 2006.