On asymptotically automatic sequences

Jakub Konieczny

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arXiv · 2305.09885

On asymptotically automatic sequences

Jakub Konieczny

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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.

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Jakub Konieczny. 2023-05-17. On asymptotically automatic sequences. https://arxiv.org/abs/2305.09885

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