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 99 - 114.
Time-Varying Sequential P Systems
Artiom Alhazov 1,3 , Rudolf Freund 2 , Hilbert Heikenwälder 2 , Marion Oswald 2 ,
Yurii Rogozhin 3 , and Sergey Verlan 4
1 Università degli Studi di Milano-Bicocca
Dipartimento di Informatica, Sistemistica e Comunicazione
Viale Sarca 336, 20126 Milano, Italy
E-mail: artiom.alhazov@unimib.it
2 Faculty of Informatics, Vienna University of Technology
Favoritenstr. 9, 1040 Vienna, Austria
Email: {rudi,hilbert,marion}@emcc.at
3 Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
Str. Academiei 5, Chişinău, MD-2028, Moldova
Email: {artiom,rogozhin}@math.md
4 LACL, Département Informatique, Université Paris Est
61, av. Général de Gaulle, 94010 Créteil, France
Email: verlan@univ-paris12.fr
Abstract. In this article we introduce the regulating mechanism of control
languages for the application of rules assigned to the membranes of
a sequential P system and the variant of time-varying sets of rules available
at different transition steps. Computational completeness can only
be achieved when allowing the system to have no rules applicable for a
bounded number of steps; in this case we only need one membrane and
periodically available sets of non-cooperative rules, i.e., time-varying sequential
P systems. On the other hand, even with an arbitrary number
of membranes and regular control languages, only Parikh sets of matrix
languages can be obtained if the terminal result has to be taken as soon
as the system cannot apply any rule anymore.
1 Introduction
P systems are formal models derived from the functioning of living cells, closely
related to multiset rewriting. We refer to [13], [14], and to the web page [19] for
more details on P systems. In this article, we investigate the power of controlling
the availability of the sets of rules assigned to the membranes of a (static) P
system by a regular control language L, especially for languages L being of the
form {w} ∗ , which leads to the notion of a time-varying P system where the set
of rules available at each membrane varies periodically with time.
The notion of the time-varying controlled application of rules comes from the
area of regulated rewriting; comprehensive overviews of this area can be found in
[3], [5], and [6]); periodically time-varying grammars were already mentioned in
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