An asymptotic version of Cobham's theorem

TL;DR

This paper introduces asymptotically automatic sequences as a generalization of automatic sequences and proves a Cobham's theorem variant for this broader class, expanding understanding of sequence automata.

Contribution

It extends Cobham's theorem to asymptotically automatic sequences, a new class that generalizes automatic sequences.

Findings

Proves a Cobham's theorem variant for asymptotically automatic sequences.

Defines the concept of asymptotically automatic sequences.

Establishes properties and implications of the new sequence class.

Abstract

We introduce the notion of an asymptotically automatic sequence, which generalises the notion of an automatic sequence, and we prove a variant of Cobham's theorem for the newly introduced class of sequences.