A4 Refereed article in a conference publication
Dynamics of Cellular Automata on Beta-Shifts and Direct Topological Factorizations
Authors: Johan Kopra
Editors: Nataša Jonoska, Dmytro Savchuk
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: 12086
First page : 178
Last page: 191
ISBN: 978-3-030-48515-3
eISBN: 978-3-030-48516-0
ISSN: 0302-9743
DOI: https://doi.org/10.1007/978-3-030-48516-0_14
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/48728747
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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