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

We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text]. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] is not sofic. This has the corollary that non-sofic beta-shifts ar...

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Autor principal: Kopra, Johan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7247874/
http://dx.doi.org/10.1007/978-3-030-48516-0_14
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author Kopra, Johan
author_facet Kopra, Johan
author_sort Kopra, Johan
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description We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text]. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] 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 [Formula: see text] 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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spelling pubmed-72478742020-05-26 Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations Kopra, Johan Developments in Language Theory Article We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text]. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] 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 [Formula: see text] 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. 2020-05-26 /pmc/articles/PMC7247874/ http://dx.doi.org/10.1007/978-3-030-48516-0_14 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Kopra, Johan
Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations
title Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations
title_full Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations
title_fullStr Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations
title_full_unstemmed Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations
title_short Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations
title_sort dynamics of cellular automata on beta-shifts and direct topological factorizations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7247874/
http://dx.doi.org/10.1007/978-3-030-48516-0_14
work_keys_str_mv AT koprajohan dynamicsofcellularautomataonbetashiftsanddirecttopologicalfactorizations

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