A1 Refereed original research article in a scientific journal
Direct prime subshifts and canonical covers
Authors: Kopra Johan
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2023
Journal: Ergodic Theory and Dynamical Systems
Journal name in source: ERGODIC THEORY AND DYNAMICAL SYSTEMS
Journal acronym: ERGOD THEOR DYN SYST
Article number: PII S0143385722000335
Number of pages: 20
ISSN: 0143-3857
eISSN: 1469-4417
DOI: https://doi.org/10.1017/etds.2022.33
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/175399025
Abstract
We present a new sufficient criterion to prove that a non-sofic half-synchronized subshift is direct prime. The criterion is based on conjugacy invariant properties of Fischer graphs of half-synchronized shifts. We use this criterion to show as a new result that all n-Dyck shifts are direct prime, and we also give new proofs of direct primeness of non-sofic beta-shifts and non-sofic S-gap shifts. We also construct a class of non-sofic synchronized direct prime subshifts which additionally admit reversible cellular automata with all directions sensitive.
We present a new sufficient criterion to prove that a non-sofic half-synchronized subshift is direct prime. The criterion is based on conjugacy invariant properties of Fischer graphs of half-synchronized shifts. We use this criterion to show as a new result that all n-Dyck shifts are direct prime, and we also give new proofs of direct primeness of non-sofic beta-shifts and non-sofic S-gap shifts. We also construct a class of non-sofic synchronized direct prime subshifts which additionally admit reversible cellular automata with all directions sensitive.
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