<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Antonio E. Porreca</style></author><author><style face="normal" font="default" size="100%">Niall Murphy</style></author><author><style face="normal" font="default" size="100%">Mario J. Pérez-Jiménez</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">An Optimal Frontier of the Efficiency of Tissue P Systems with Cell Division</style></title><secondary-title><style face="normal" font="default" size="100%">Tenth Brainstorming Week on Membrane Computing</style></secondary-title><tertiary-title><style face="normal" font="default" size="100%">Proceedings of the Tenth Brainstorming Week on Membrane Computing</style></tertiary-title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/2012</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.gcn.us.es/10BWMC/10BWMCvolII/papers/mario-enrico-niall-revised.pdf</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Fénix Editora</style></publisher><pub-location><style face="normal" font="default" size="100%">Seville, Spain</style></pub-location><volume><style face="normal" font="default" size="100%">II</style></volume><pages><style face="normal" font="default" size="100%">141-166</style></pages><abstract><style face="normal" font="default" size="100%">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.</style></abstract></record></records></xml>