P systems with active membranes: attacking NP-complete problems

TLDR: It is proved that a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects, is not only computationally universal, but also able to solve NP complete problems in polynomial time.

Abstract: P systems are parallel Molecular Computing models based on processing multisets of objects in cell-like membrane structures. Various variants were already shown to be computationally universal, equal in power to Turing machines. In this paper one proposes a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects. Moreover, the membranes can multiply themselves by division. We prove that this variant is not only computationally universal, but also able to solve NP complete problems in polynomial (actually, linear) time. We exemplify this assertion with the well-known SAT problem.