On asymptotically automatic sequences
Volume 215 / 2024
Acta Arithmetica 215 (2024), 249-287
MSC: Primary 11B85; Secondary 68Q45
DOI: 10.4064/aa230619-26-4
Published online: 12 August 2024
Abstract
We study the notion of an asymptotically automatic sequence, which generalises the notion of an automatic sequence. While $k$-automatic sequences are characterised by finiteness of $k$-kernels, the $k$-kernels of asymptotically $k$-automatic sequences are only required to be finite up to equality almost everywhere. We prove basic closure properties and a linear bound on asymptotic subword complexity, show that results concerning frequencies of symbols are no longer true for the asymptotic analogue, and discuss some classification problems. Published in Open Access (under CC-BY license).
