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

: Johan Kopra

: Nataša Jonoska, Dmytro Savchuk

: International Conference on Developments in Language Theory

Publisher: Springer

: 2020

Lecture Notes in Computer Science

: DLT 2020: Developments in Language Theory

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

: 12086

: 178

: 191

: 978-3-030-48515-3

: 978-3-030-48516-0

: 0302-9743

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

: 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.

BetaCA.pdf