@misc {IOPORT.00018525,
author = {Allouche, Jean-Paul and Shallit, Jeffrey},
title = {The ring of $k$-regular sequences.},
howpublished = {Theoretical aspects of computer science, Proc. 7th Annu. Symp., STACS '90, Rouen/Fr. 1990, Lect. Notes Comput. Sci. 415, 12-23 (1990).},
year = {1990},
abstract = {[For the entire collection see Zbl 0728.00020.] This is an extended abstract of a forthcoming paper which generalizes the well-known concept of automatic sequences. Let $k$ be an integer $\ge 2$. A sequence $S$ is called $k$-regular if it takes its values in a ring $R$ and if there exists a subring $R'$ of $R$ such that the $R'$-module generated by all subsequences of the form $(S(k\sp en+a))\sb{n\ge 0}$, where $e\ge 0$ and $0\le a