# Finite-state Independence and Normal Sequences

## TL;DR

This paper explores finite-state independence of normal sequences, providing characterizations via automata and an algorithm to construct independent normal words.

## Contribution

It introduces three new characterizations of finite-state independence for normal words and presents an algorithm for constructing such independent sequences.

## Key findings

- Three characterizations of finite-state independence using different automata models
- An algorithm to construct pairs of finite-state independent normal words
- Enhanced understanding of the structure of normal sequences

## Abstract

We consider the previously defined notion of finite-state independence and we focus specifically on normal words. We characterize finite-state independence of normal words in three different ways, using three different kinds of asynchronous deterministic finite automata with two input tapes containing infinite words. Based on one of the characterizations we give an algorithm to construct a pair of finite-state independent normal words.