Decidability of uniform recurrence of morphic sequences

TL;DR

This paper proves that determining whether a morphic sequence is uniformly recurrent is a decidable problem, establishing bounds on derived sequences and linking uniformly recurrent morphic sequences to primitive substitutive sequences.

Contribution

It introduces a decision procedure for uniform recurrence in morphic sequences and shows that such sequences are primitive substitutive sequences.

Findings

Uniform recurrence of morphic sequences is decidable.

The number of derived sequences of uniformly recurrent morphic sequences is bounded.

Uniformly recurrent morphic sequences are primitive substitutive sequences.

Abstract

We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic sequences are primitive substitutive sequences.