Surjective multidimensional cellular automata are non-wandering: A combinatorial proof

Authors:
Luigi Acerbi;Alberto Dennunzio;Enrico Formenti
Affiliations:
University of Edinburgh, DTC in Neuroinformatics and Computational Neuroscience, School of Informatics, Edinburgh EH8 9AB, UK;Universití degli studi di Milano-Bicocca, Dipartimento di Informatica Sistemistica e Comunicazione, viale Sarca 336, 20126 Milano, Italy;Université Nice-Sophia Antipolis, Laboratoire I3S, 2000 Route des Colles, 06903 Sophia Antipolis, France
Venue:
Information Processing Letters
Year:
2013

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Abstract

A combinatorial proof that surjective D-dimensional CA are non-wandering is given. This answers an old open question stated in Blanchard and Tisseur (2000) [3]. Moreover, an explicit upper bound for the return time is given.