Membrane Computing: When Communication Is Enough

We study the computational power of P system, the math- ematical model of cellular membrane systems whose operations are mo- tivated by some principles of regulated transfer of objects (molecules) through membranes and simple mutual reactions of these objects. The original model of P system describes several possible types of oper- ations applicable to these objects, resulting in universal computational power. We show that P systems with symbol objects keep their universal computational power even if we restrict ourselves to catalyzed transport of objects through labelled membranes without their change or mutual reactions. Each transport operation is initiated by a complex of at most two objects. Moreover we do not need some other mathematical tools of P systems like priorities of operators or dissolution or creation of mem- branes to reach the universal computational power. In the second part of the paper we present a communicating P-system computing optimal parallel algorithm for finding maximum of a given set of integers. We therefore demonstrate that despite the simplicity of the model, it is (theoretically) capable to solve nontrivial computing tasks in a highly parallel and effective way.