Affiliations: Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, University of Sevilla, 41012 Sevilla, Spain. marper@us.es | Research Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601 Opava, Czech Republic. petr.sosik@fpf.slu.cz
Note: [] Address for correspondence: Research Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601 Opava, Czech Republic
Abstract: A membrane system (P system) is a distributed computing model inspired by information processes in living cells. P systems previously provided new characterizations of a variety of complexity classes and their borderlines. Specifically, in tissue-like membrane systems, cell separation rules have been considered joint with communication rules of the form symport/antiport. On the one hand, only tractable problems can be efficiently solved by using cell separation and communication rules with length at most 2. On the other hand, an efficient and uniform solution to the SAT problem by using cell separation and communication rules with length at most 8 has been recently given. In this paper we improve the previous result by showing that the SAT problem can be solved by a family of tissue P systems with cell separation in linear time, by using communication rules with length at most 3. Thus, in the framework of tissue P systems with cell separation, we provide an optimal tractability borderline: passing from length 2 to 3 amounts to passing from non–efficiency to efficiency, assuming that P ≠ NP.
Keywords: Membrane Computing, Tissue P Systems, Cell Separation, Computational Complexity, SAT Problem
