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13th International Conference on Membrane Computing - MTA Sztaki

13th International Conference on Membrane Computing - MTA Sztaki

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<str<strong>on</strong>g>13th</str<strong>on</strong>g> <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> <strong>Membrane</strong> <strong>Computing</strong>, CMC13,<br />

Budapest, Hungary, August 28 - 31, 2012. Proceedings, pages 277 - 290.<br />

The Eciency of Tissue P Systems with Cell<br />

Separati<strong>on</strong> Relies <strong>on</strong> the Envir<strong>on</strong>ment<br />

Luis F. Macías-Ramos 1 , Mario J. Pérez-Jiménez 1 , Agustín Riscos-Núñez 1 ,<br />

Miquel Rius-F<strong>on</strong>t 2 , and Luis Valencia-Cabrera 1<br />

1 Research Group <strong>on</strong> Natural <strong>Computing</strong><br />

Department of Computer Science and Articial Intelligence<br />

University of Sevilla, Spain<br />

{lfmaciasr, marper, ariscosn, lvalencia}@us.es<br />

2 Department of Applied Mathematics IV<br />

Universitat Politècnica de Catalunya, Spain<br />

mrius@ma4.upc.edu<br />

Abstract. The classical deniti<strong>on</strong> of tissue P systems includes a distinguished<br />

alphabet with the special assumpti<strong>on</strong> that its elements are<br />

available in an arbitrarily large amount of copies. These objects are<br />

shared in a distinguished place of the system, called the envir<strong>on</strong>ment.<br />

This ability of having innitely many copies of some objects has been<br />

widely exploited in the design of ecient soluti<strong>on</strong>s to computati<strong>on</strong>ally<br />

hard problems by means of tissue P systems.<br />

This paper deals with computati<strong>on</strong>al aspects of tissue P systems with<br />

cell separati<strong>on</strong> where there is no such envir<strong>on</strong>ment as described above.<br />

The main result is that <strong>on</strong>ly tractable problems can be eciently solved<br />

by using this kind of P systems. Bearing in mind that NPcomplete<br />

problems can be eciently solved by using tissue P systems without<br />

envir<strong>on</strong>ment and with cell divisi<strong>on</strong>, we deduce that in the framework<br />

of tissue P systems without envir<strong>on</strong>ment, the kind of rules (separati<strong>on</strong><br />

versus divisi<strong>on</strong>) provides a new fr<strong>on</strong>tier of the tractability of decisi<strong>on</strong><br />

problems.<br />

Keywords: <strong>Membrane</strong> <strong>Computing</strong>, Tissue P System, Cell Separati<strong>on</strong>,<br />

Envir<strong>on</strong>ment of a Tissue, Computati<strong>on</strong>al Complexity, Borderline of<br />

Tractability<br />

1 Introducti<strong>on</strong><br />

<strong>Membrane</strong> <strong>Computing</strong> is a young branch of Natural <strong>Computing</strong> initiated by<br />

Gh. P un in the end of 1998 [15]. The computati<strong>on</strong>al devices of this paradigm,<br />

called P systems, operate in a distributed, parallel and n<strong>on</strong>-deterministic manner,<br />

getting inspirati<strong>on</strong> from living cells (their structure and functi<strong>on</strong>ing), as well as<br />

from the way cells are organized in tissues, organs, etc.<br />

Several dierent models of cell-like P systems have been successfully used<br />

to solve computati<strong>on</strong>ally hard problems eciently, by trading space for time,<br />

usually following a brute force approach: an exp<strong>on</strong>ential workspace is created<br />

277

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