<?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%">Mónica Cardona</style></author><author><style face="normal" font="default" size="100%">M. Angels Colomer</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%">Characterizing the aperiodicity of irreducible markov chains by using P Systems </style></title><secondary-title><style face="normal" font="default" size="100%">7th Brainstorming Week on Membrane Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/02/2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.gcn.us.es/?q=node/414</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%">Sevilla, España</style></pub-location><volume><style face="normal" font="default" size="100%">I</style></volume><pages><style face="normal" font="default" size="100%">81-96</style></pages><isbn><style face="normal" font="default" size="100%">978-84-613-2837-6</style></isbn><abstract><style face="normal" font="default" size="100%">It is well known that any irreducible and aperiodic Markov chain has exactly
one stationary distribution, and for any arbitrary initial distribution, the sequence of
distributions at time n converges to the stationary distribution, that is, the Markov
chain is approaching equilibrium as n → ∞.
    In this paper, a characterization of the aperiodicity in existential terms of some state
is given. At the same time, a P system with external output is associated with any
irreducible Markov chain. The designed system provides the aperiodicity of that Markov
chain and spends a polynomial amount of resources with respect to the size of the input.
A formal verification of this solution is presented and a comparative analysis with respect
to another known solution is described.
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