Mixing coded systems

TL;DR

This paper characterizes mixing properties of coded systems, linking mixing to total transitivity and generator properties, and provides examples illustrating these concepts.

Contribution

It establishes a characterization of mixing coded systems and explores the existence of generators with specific properties, including counterexamples.

Findings

A coded system is mixing iff it is totally transitive.

Having a relatively prime generator implies strong property P.

An example of a mixing coded system without a relatively prime generator.

Abstract

We show that a coded system is mixing if and only if it is totally transitive and if in addition it has a relatively prime generator, then it has strong property P. We continue by showing that a mixing half-synchronized system has such a generator. Moreover, we give an example of a mixing coded system which does not have any relatively prime generator.