Almost periodicity, finite automata mappings, and related effectiveness issues

Abstract

The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic sequences includes the class of eventually strongly almost periodic sequences, and we prove this inclusion to be strict. We prove that the class of eventually strongly almost periodic sequences is closed under finite automata mappings and finite transducers. Moreover, an effective form of this result is presented. Finally we consider some algorithmic questions concerning almost periodicity.

Uniformly recurrent sequences and minimal Cantor omega-limit sets

“…Connections are made to kneading sequences of unimodal maps, and it is shown that a sequence A B is uniformly recurrent if and only if B is uniformly recurrent. The definitions and techniques used in this section are motivated by computer science results in [8] and [9]. Definition 4.1.…”