A more reasonable proof of Cobham's theorem

TL;DR

This paper offers a concise new proof of Cobham's theorem that avoids Kronecker's approximation theorem, enabling potential generalizations beyond automatic sequences.

Contribution

It introduces a simplified proof of Cobham's theorem that can be extended to broader contexts beyond automatic sequences.

Findings

Proof avoids Kronecker's approximation theorem

Facilitates generalization beyond automatic sequences

Simplifies understanding of Cobham's theorem

Abstract

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.