A4 Article in conference proceedings

Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations




List of Authors: Johan Kopra

Conference name: International Conference on Developments in Language Theory

Publisher: Springer

Publication year: 2020

Journal: Lecture Notes in Computer Science

Book title *: DLT 2020: Developments in Language Theory

Journal name in source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volume number: 12086

ISBN: 978-3-030-48515-3

eISBN: 978-3-030-48516-0

ISSN: 0302-9743

DOI: http://dx.doi.org/10.1007/978-3-030-48516-0_14


Abstract

We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts S β Sβ. We show that any reversible CA F:S β →S β F:Sβ→Sβ

has an almost equicontinuous direction whenever S β Sβ is not sofic. This has the corollary that non-sofic beta-shifts are topologically direct prime, i.e. they are not conjugate to direct topological factorizations X×Y X×Y

of two nontrivial subshifts X and Y. We also make some preliminary observations on direct topological factorizations of beta-shifts that are subshifts of finite type.


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Last updated on 2021-24-06 at 10:41