Affiliations: Key Laboratory of Image Processing and Intelligent Control, Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China. niuyunyun1003@163.com, lqpan@mail.hust.edu.cn | Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, University of Sevilla, 41012 Seville, Spain. marper@us.es | Department of Applied Mathematics IV, Universitat Politécnica de Catalunya, Edifici C3, Despatx 016, Av. del Canal Olimpic s/n, 08860 Casteldefels, Spain. mrius@ma4.upc.edu
Note: [] Address for correspondence: Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: A tissue P system with cell division is a computing model which has two basic features: intercellular communication and the ability of cell division. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to computationally hard problems in polynomial time. In this work we present an efficient solution to the tripartite matching problem by a family of such devices. This solution leads to an interesting open problem whether tissue P systems with cell division and communication rules of length 2 can solve NP-complete problems. An answer to this open problem will provide a borderline between efficiency and non-efficiency in terms of the lengths of communication rules.
Keywords: Membrane Computing, Tissue P System, Cell Division, Tripartite Matching Problem
