This paper proposes a study of deterministic P systems with active membranes in the context of discrete time dynamical systems. First of all, we prove that, for a fixed set of objects and labels, the set of all P system configuration is countable and that the dynamical behaviors defining a chaotic system are not possible. Then, we define a notion of distance between membrane configurations encoding the intuitive concept of “dissimilarity” between configurations. We prove that all functions defined by evolution, communication, and division rules are continuous under that distance and that the resulting topological space is discrete but not complete. Furthermore, we adapt in a natural way the classical notions of sensitivity to initial conditions and topological transitivity to P systems, and we show that P systems exhibiting those new properties exist. Finally, we prove that the proposed distance is efficiently computable, i.e., its computation only requires polynomial time with respect to the size of the input configurations.

Dennunzio, A., Formenti, E., Manzoni, L., Margara, L., Menara, G. (2023). A topology for P-systems with active membranes. JOURNAL OF MEMBRANE COMPUTING, 5(4 (December 2023)), 193-204 [10.1007/s41965-023-00132-x].

A topology for P-systems with active membranes

Dennunzio, A
;
Manzoni, L;
2023

Abstract

This paper proposes a study of deterministic P systems with active membranes in the context of discrete time dynamical systems. First of all, we prove that, for a fixed set of objects and labels, the set of all P system configuration is countable and that the dynamical behaviors defining a chaotic system are not possible. Then, we define a notion of distance between membrane configurations encoding the intuitive concept of “dissimilarity” between configurations. We prove that all functions defined by evolution, communication, and division rules are continuous under that distance and that the resulting topological space is discrete but not complete. Furthermore, we adapt in a natural way the classical notions of sensitivity to initial conditions and topological transitivity to P systems, and we show that P systems exhibiting those new properties exist. Finally, we prove that the proposed distance is efficiently computable, i.e., its computation only requires polynomial time with respect to the size of the input configurations.
Articolo in rivista - Articolo scientifico
Discrete time dynamical systems; Membrane computing; P systems; Topological spaces;
English
20-dic-2023
2023
5
4 (December 2023)
193
204
reserved
Dennunzio, A., Formenti, E., Manzoni, L., Margara, L., Menara, G. (2023). A topology for P-systems with active membranes. JOURNAL OF MEMBRANE COMPUTING, 5(4 (December 2023)), 193-204 [10.1007/s41965-023-00132-x].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/456621
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