Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla
Abstract
The search for effcient solutions of computationally hard problems by means
of families of membrane systems has lead to a wide and prosperous eld of research. The
study of computational complexity theory in Membrane Computing is mainly based on
the look for frontiers of effciency between different classes of membrane systems. Every
frontier provides a powerful tool for tackling the P versus NP problem in the following
way. Given two classes of recognizer membrane systems R1 and R2, being systems from
R1 non-effcient (that is, capable of solving only problems from the class P) and systems
from R2 presumably e cient (that is, capable of solving NP-complete problems), and
R2 the same class that R1 with some ingredients added, passing from R1 to R2 is
comparable to passing from the non effciency to the presumed effciency. In order to
prove that P = NP, it would be enough to, given a solution of an NP-complete problem
by means of a family of recognizer membrane systems from R2, try to remove the added
ingredients to R2 from R1. In this paper, we study if it is possible to solve SAT by
means of a family of recognizer P systems from AM0(�����d;+n), whose non-effciency was
demonstrated already
