On normality in shifts of finite type

TL;DR

This paper explores the concept of normality in sequences within shifts of finite type, characterizing it through incompressibility via lossless transducers, extending known results from full shifts to more general cases.

Contribution

It provides a new characterization of normality in shifts of finite type using incompressibility and lossless transducers, generalizing previous results from full shifts.

Findings

Normality characterized by incompressibility in shifts of finite type

Extension of known results from full shifts to finite type shifts

Provides a new perspective on sequence normality in symbolic dynamics

Abstract

In this paper we consider the notion of normality of sequences in shifts of finite type. A sequence is normal if the frequency of each block exists and is equal to the Parry measure of the block. We give a characterization of normality in terms of incompressibility by lossless transducers. The result was already known in the case of the full shift.