Cobham-Semenov theorem and $\NN^d$-subshifts

TL;DR

This paper presents new proofs of the Cobham's first theorem and the Cobham-Semenov theorem in the context of symbolic and tiling dynamics, respectively, offering fresh perspectives on these classical results.

Contribution

It introduces novel proof techniques for the Cobham and Cobham-Semenov theorems using symbolic and tiling dynamics approaches.

Findings

New proof of Cobham's first theorem using symbolic dynamics

New proof of Cobham-Semenov theorem in the primitive case using tiling dynamics

Enhanced understanding of the connection between automata theory and dynamical systems

Abstract

We give a new proof of the Cobham's first theorem using ideas from symbolic dynamics and of the Cobham-Semenov theorem (in the primitive case) using ideas from tiling dynamics.