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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 311 - 322.<br />

<strong>Membrane</strong>s with Local Envir<strong>on</strong>ments<br />

Tamás Mihálydeák 1 and Zoltán Csajbók 2<br />

1 Department of Computer Science, Faculty of Informatics, University of Debrecen<br />

Egyetem tér 1, H-4010 Debrecen, Hungary<br />

mihalydeak.tamas@inf.unideb.hu<br />

2 Department of Health Informatics, Faculty of Health, University of Debrecen,<br />

Sóstói út 2-4, H-4400 Nyíregyháza, Hungary<br />

csajbok.zoltan@foh.unideb.hu<br />

Abstract. Active cell comp<strong>on</strong>ents involved in real biological processes<br />

have to be close enough to a membrane in order to be able to pass through<br />

it. Rough set theory gives a plausible opportunity to model a border z<strong>on</strong>e<br />

around a cell-like formati<strong>on</strong>. However, this theory works within c<strong>on</strong>venti<strong>on</strong>al<br />

set theory, and so to apply its ideas to membrane computing, first,<br />

we have worked out an adequate approximati<strong>on</strong> framework for multisets.<br />

Next, we propose a two-comp<strong>on</strong>ent structure c<strong>on</strong>sisting of a P system<br />

and a partial approximati<strong>on</strong> space for multisets. Using the approximati<strong>on</strong><br />

technique, we specify the closeness around membranes, even from<br />

inside and outside, via border z<strong>on</strong>es. Then, we define communicati<strong>on</strong><br />

rules within the P system in such a way that they operate in the border<br />

z<strong>on</strong>es solely. The two comp<strong>on</strong>ents mutually cooperate.<br />

Keywords: Approximati<strong>on</strong> of sets, rough multisets, membrane computing<br />

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

As it is well known P systems (membrane systems) were introduced by Păun<br />

([9]). P systems can be c<strong>on</strong>sidered as distributed computing devices which were<br />

motivated by the structure and functi<strong>on</strong>ing of a living cell. <strong>Membrane</strong>s delimit<br />

compartments (regi<strong>on</strong>s), which are arranged in a cell-like (hence hierarchical)<br />

structure. A set of rules is given for every regi<strong>on</strong>. These rules can model reacti<strong>on</strong>s<br />

inside a regi<strong>on</strong> (like chemical reacti<strong>on</strong>s work), or processes of passing objects<br />

through membranes (like biological processes work). In the general model,<br />

regi<strong>on</strong>s are represented by multisets and two types of rules are given: rewriting<br />

rules for the first type and communicati<strong>on</strong> rules (either symport or antiport fashi<strong>on</strong>)<br />

for the sec<strong>on</strong>d type. There are some generalizati<strong>on</strong>s of P systems in which<br />

n<strong>on</strong>hierarchical arrangements of compartments are also c<strong>on</strong>sidered.<br />

In the case of communicati<strong>on</strong> rules objects pass through membranes. If we<br />

pay our attenti<strong>on</strong> to biological processes we can say that an object has to be<br />

close enough to a membrane in order to be able to pass through it. In different<br />

versi<strong>on</strong>s of P systems <strong>on</strong>e can find some variants which embody the c<strong>on</strong>cept of<br />

space and positi<strong>on</strong> inside a regi<strong>on</strong> (see for example [2], [3]), and so these systems<br />

311

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