On the directional dynamics of additive cellular automata

Authors:
A. Dennunzio;P. Di Lena;E. Formenti;L. Margara
Affiliations:
Università degli Studi di Milano-Bicocca, Dipartimento di Informatica Sistemistica e Comunicazione, viale Sarca 336/14, 20126 Milano, Italy;Università degli Studi di Bologna, Dipartimento di Scienze dellInformazione, via Mura Anteo Zamboni 7, 40127 Bologna, Italy;Université de Nice-Sophia Antipolis, Laboratoire I3S, 2000 Route des Colles, 06903 Sophia Antipolis, France;Università degli Studi di Bologna, Dipartimento di Scienze dellInformazione, via Mura Anteo Zamboni 7, 40127 Bologna, Italy
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We continue the study of cellular automata (CA) directional dynamics, i.e. , the behavior of the joint action of CA and shift maps. This notion has been investigated for general CA in the case of expansive dynamics by Boyle and Lind; and by Sablik for sensitivity and equicontinuity. In this paper we give a detailed classification for the class of additive CA providing non-trivial examples for some classes of Sablik's classification. Moreover, we extend the directional dynamics studies by considering also factor languages and attractors.