%0 Generic
%D 2012
%T An Optimal Frontier of the Efficiency of Tissue P Systems with Cell Division
%A Antonio E. Porreca
%A Niall Murphy
%A Mario J. Pérez-Jiménez
%C Seville, Spain
%I Fénix Editora
%P 141-166
%S Proceedings of the Tenth Brainstorming Week on Membrane Computing
%U http://www.gcn.us.es/10BWMC/10BWMCvolII/papers/mario-enrico-niall-revised.pdf
%V II
%X In the framework of tissue P systems with cell division, the length of communication rules provides a frontier for the tractability of decision problems. On the one hand, the limitation on the eﬃciency of tissue P systems with cell division and communication rules of length 1 has been established. On the other hand, polynomial time solutions to NP–complete problems by using families of tissue P systems with cell division and communication rules of length at most 3 has been provided. In this paper, we improve the previous result by showing that the HAM-CYCLE problem can be solved in polynomial time by a family of tissue P systems with cell division by using communication rules with length at most 2. Hence, a new tractability boundary is given: passing from 1 to 2 amounts to passing from non–eﬃciency to eﬃciency, assuming that P is different from NP.
%8 02/2012