Solving SAT with Antimatter in Membrane Computing

Abstract

The set of NP-complete problems is split into weakly and strongly NP- complete ones. The di erence consists in the in uence of the encoding scheme of the input. In the case of weakly NP-complete problems, the intractability depends on the encoding scheme, whereas in the case of strongly NP-complete problems the problem is intractable even if all data are encoded in a unary way. The reference for strongly NP-complete problems is the Satis ability Problem (the SAT problem). In this paper, we provide a uniform family of P systems with active membranes which solves SAT { without polarizations, without dissolution, with division for elementary membranes and with matter/antimatter annihilation. To the best of our knowledge, it is the rst solution to a strongly NP-complete problem in this P system model.