On uniform recurrence of HD0l systems

TL;DR

This paper proves that it is decidable to determine whether a morphic sequence is uniformly recurrent, leveraging recent results on the decidability of the HD0L periodicity problem.

Contribution

It establishes the decidability of uniform recurrence for morphic sequences by connecting it to the HD0L periodicity problem.

Findings

Decidability of uniform recurrence for morphic sequences.

Utilizes recent proofs of HD0L periodicity.

Provides a method to determine uniform recurrence.

Abstract

We prove that the problem of deciding whether a given morphic sequence is uniformly recurrent is decidable. The proof uses decidability of HD0L periodicity problem, which was recently proved in papers of F.Durand and I.Mitrofanov.