Tissue P systems with evolutional communication rules with two objects in the left-hand side

Abstract

In the framework of Membrane Computing, several efficient solutions to computationally hard problems have been given. To find new borderlines between families of P systems that can solve them and the ones that cannot is an important task to tackle the P versus NP problem. Adding syntactic and/or semantic ingredients can mean passing from non-efficiency to presumed efficiency. Here, we try to get narrow frontiers, setting the stage to adapt efficient solutions from a family of P systems to another one. In order to do that, a solution to the SAT problem is given by means of a family of tissue P systems with evolutional symport/antiport rules and cell separation with the restriction that both the left-hand side and the right-hand side of the rules have at most two objects; that is, with recognizer P systems from {mathcal {TSEC}}(2, 2). This result improves a previous one, when 3 objects could be used in the left-hand side of the evolutional communication rules