# Asymptotic Analysis of Regular Sequences

@article{Heuberger2018AsymptoticAO, title={Asymptotic Analysis of Regular Sequences}, author={Clemens Heuberger and Daniel Krenn}, journal={Algorithmica}, year={2018}, volume={82}, pages={429 - 508} }

In this article, q -regular sequences in the sense of Allouche and Shallit are analysed asymptotically. It is shown that the summatory function of a regular sequence can asymptotically be decomposed as a finite sum of periodic fluctuations multiplied by a scaling factor. Each of these terms corresponds to an eigenvalue of the sum of matrices of a linear representation of the sequence; only the eigenvalues of absolute value larger than the joint spectral radius of the matrices contribute terms…

## 3 Citations

### The periodic complexity function of the Thue-Morse word, the Rudin-Shapiro word, and the period-doubling word

- Computer Science
- 2021

A different method is given than that of Mignosi and Restivo for computing the asymptotics of the periodic complexity function of the Thue–Morse word and how to apply the method to other automatic sequences, like the Rudin–Shapiro word and the period-doubling word.

### The periodic complexity function of the Thue-Morse word and the Rudin-Shapiro word

- Computer ScienceArXiv
- 2021

A different method is given than that of Mignosi and Restivo for computing the asymptotics of the periodic complexity function of the Thue–Morse word and how to apply the method to other automatic sequences, like the Rudin–Shapiro word.

### Asymptotic Analysis of q-Recursive Sequences

- MathematicsAlgorithmica
- 2022

For an integer q≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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