# On Almost Periodicity Criteria for Morphic Sequences in Some Particular Cases

## TL;DR

This paper provides polynomial-time criteria for determining almost periodicity in morphic sequences, specifically fixed points of non-erasing morphisms and automatic sequences, supporting the conjecture of decidability in this area.

## Contribution

It introduces efficient algorithms for almost periodicity in specific morphic sequences and offers evidence towards the general decidability conjecture.

## Key findings

- Polynomial-time algorithms for fixed points of non-erasing morphisms.
- Criteria for automatic sequences to be almost periodic.
- Supporting evidence for the decidability conjecture.

## Abstract

In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm solving the problem is found. A result more or less supporting the conjecture of decidability of the general problem is given.