On the pseudorandomness of automatic sequences

TL;DR

This paper investigates the pseudorandom properties of automatic sequences, analyzing their distribution and correlation measures, and identifies non-random patterns stemming from their generating functions and automata.

Contribution

It provides new insights into the pseudorandomness of automatic sequences by linking their non-random behavior to their generating functions and automata structures.

Findings

Automatic sequences can exhibit non-random behavior detectable through distribution and correlation measures.

Non-randomness is linked to functional equations of generating functions.

Automaton structure influences the pseudorandom properties of the sequences.

Abstract

We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating functions or from their generating finite automatons, respectively.