Strictly Temporally Periodic Points in Cellular Automata

Alberto Dennunzio
(Universitá degli Studi di Milano-Bicocca, Dipartimento di Informatica Sistemistica e Comunicazione,Italy)
Pietro Di Lena
(Universitá degli Studi di Bologna, Dipartimento di Scienze dell'Informazione, Italy)
Luciano Margara
(Universitá degli Studi di Bologna, Dipartimento di Scienze dell'Informazione, Italy)

We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic. This set turns out to be dense for almost equicontinuous surjective cellular automata while it is empty for the positively expansive ones. In the class of additive cellular automata, the set of strictly periodic points can be either dense or empty. The latter happens if and only if the cellular automaton is topologically transitive.

In Enrico Formenti: Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires (AUTOMATA&JAC 2012), La Marana, Corsica, September 19-21, 2012, Electronic Proceedings in Theoretical Computer Science 90, pp. 225–235.
Published: 13th August 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.90.18 bibtex PDF
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