The power of synchronizing rules in membrane computing

Abstract

Membrane computing provides computational devices inspired by living cells (called membrane systems) that are proved to be computationally universal. It is a theoretical challenge to find the minimum of resources to get the full power of a Turing machine. The major contribution of this paper is to present such a system with only ONE membrane and without ANY additional ingredient (like cooperation, division, catalysts) in which the synchronization between non-cooperative rules (of length at most three) plays an essential role. Furthermore, such a system is able to solve the SAT NP-complete problem in polynomial time.