13th International Conference on Membrane Computing - MTA Sztaki

<strong>13th</strong> <strong>International</strong> <strong>Conference</strong> on Membrane Computing, CMC13,
Budapest, Hungary, August 28 - 31, 2012. Proceedings, pages 311 - 322.
Membranes with Local Environments
Tamás Mihálydeák 1 and Zoltán Csajbók 2
1 Department of Computer Science, Faculty of Informatics, University of Debrecen
Egyetem tér 1, H-4010 Debrecen, Hungary
mihalydeak.tamas@inf.unideb.hu
2 Department of Health Informatics, Faculty of Health, University of Debrecen,
Sóstói út 2-4, H-4400 Nyíregyháza, Hungary
csajbok.zoltan@foh.unideb.hu
Abstract. Active cell components involved in real biological processes
have to be close enough to a membrane in order to be able to pass through
it. Rough set theory gives a plausible opportunity to model a border zone
around a cell-like formation. However, this theory works within conventional
set theory, and so to apply its ideas to membrane computing, first,
we have worked out an adequate approximation framework for multisets.
Next, we propose a two-component structure consisting of a P system
and a partial approximation space for multisets. Using the approximation
technique, we specify the closeness around membranes, even from
inside and outside, via border zones. Then, we define communication
rules within the P system in such a way that they operate in the border
zones solely. The two components mutually cooperate.
Keywords: Approximation of sets, rough multisets, membrane computing
1 Introduction
As it is well known P systems (membrane systems) were introduced by Păun
([9]). P systems can be considered as distributed computing devices which were
motivated by the structure and functioning of a living cell. Membranes delimit
compartments (regions), which are arranged in a cell-like (hence hierarchical)
structure. A set of rules is given for every region. These rules can model reactions
inside a region (like chemical reactions work), or processes of passing objects
through membranes (like biological processes work). In the general model,
regions are represented by multisets and two types of rules are given: rewriting
rules for the first type and communication rules (either symport or antiport fashion)
for the second type. There are some generalizations of P systems in which
nonhierarchical arrangements of compartments are also considered.
In the case of communication rules objects pass through membranes. If we
pay our attention to biological processes we can say that an object has to be
close enough to a membrane in order to be able to pass through it. In different
versions of P systems one can find some variants which embody the concept of
space and position inside a region (see for example [2], [3]), and so these systems
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