Narrowing Frontiers of Efficiency with Evolutional Communication Rules and Cell Separation

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 way to tackle the P versus NP problem. Adding syntactic and/or semantic ingredients can mean passing from non-efficiency to presumably 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.