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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 199 - 210.<br />

A Formal Framework for P Systems with<br />

Dynamic Structure<br />

Rudolf Freund 1 , Ignacio Pérez-Hurtado 2 , Agustín Riscos-Núñez 2 , and Sergey<br />

Verlan 3<br />

1 Faculty of Informatics, Vienna University of Technology<br />

Favoritenstr. 9, 1040 Vienna, Austria<br />

Email: rudi@emcc.at<br />

2 Research Group <strong>on</strong> Natural <strong>Computing</strong>,<br />

Department of Computer Science and Artificial Intelligence,<br />

University of Sevilla,<br />

Avda. Reina Mercedes s/n, 41012, Sevilla, Spain<br />

Email: {perezh,ariscosn}@us.es<br />

3 LACL, Département Informatique, Université Paris Est,<br />

61, av. Général de Gaulle, 94010 Créteil, France<br />

Email: verlan@univ-paris12.fr<br />

Abstract. This article introduces a general formalism/framework flexible<br />

enough to cover descripti<strong>on</strong>s of different variants of P systems having<br />

a dynamic membrane structure. This framework can be useful for the<br />

precise definiti<strong>on</strong> of new variants of P systems with dynamic structure,<br />

for the comparis<strong>on</strong> of existing definiti<strong>on</strong>s as well as for their extensi<strong>on</strong>.<br />

We give a detailed definiti<strong>on</strong> of the formalism and show how existing<br />

variants of P systems with dynamic structure can be translated to it.<br />

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

This article is an attempt to fulfill the goal of defining a formal framework<br />

that captures the essential properties of P systems with dynamic structure. This<br />

framework can be seen as a kind of meta-language that permits to describe<br />

a P system and its evoluti<strong>on</strong>. Our main goal is to provide a simple tool for<br />

the analysis of different models of P systems with dynamic structure. There<br />

are numerous possible applicati<strong>on</strong>s of the results of such an analysis, as, for<br />

example, the comparis<strong>on</strong> and the extensi<strong>on</strong> of existing models and the creati<strong>on</strong><br />

of new models of P systems with a dynamic structure.<br />

The article extends the approach used in [3] for P systems with static structure.<br />

We recall that the framework for the static P systems is mainly composed of<br />

five ingredients: the definiti<strong>on</strong> of the c<strong>on</strong>figurati<strong>on</strong> of the system, the definiti<strong>on</strong> of<br />

rules, the definiti<strong>on</strong> of the applicability and of the applicati<strong>on</strong> of a rule/multiset<br />

of rules, transiti<strong>on</strong> mode and halting c<strong>on</strong>diti<strong>on</strong>. The c<strong>on</strong>figurati<strong>on</strong> is a list of multisets<br />

corresp<strong>on</strong>ding to the c<strong>on</strong>tents of membranes of a P system and the rules<br />

generalize most kind of rules used in the P systems area. Based <strong>on</strong> this general<br />

199

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