Additive cellular automata and algebraic series
type: Item
instance of: scholarly article
title: Additive cellular automata and algebraic series
zbMATH Open document ID: 0787.68074
DOI: 10.1016/0304-3975(93)90165-P
author: Philippe Dumas
author: Bruce Litow
published in: Theoretical Computer Science
publication date: 1993-12-01T00:00:00Z
review text: A class of one-dimensional cellular automata in which the value of each cell depends in additive manner of its neighbours is studied. Generating series are used to describe the behavior of a cell in time and their basic properties are proved. Also it is shown that proper generating functions can be computed directly in the cases where the values of a cell are elements of a finite field or are complex numbers. In the second part of the paper a number of examples is given relating additive cellular automata and some ``automatic sequences'' like paper folding sequences, or Catalan or Motzkin numbers.
Mathematics Subject Classification ID: 68Q80
Mathematics Subject Classification ID: 11B85
zbMATH DE Number: 440337
zbMATH Keywords: algebraic series
zbMATH Keywords: Catalan numbers
zbMATH Keywords: automatic sequences
zbMATH Keywords: cellular automata
zbMATH Keywords: generating functions
zbMATH Keywords: paper folding sequences
zbMATH Keywords: Motzkin numbers
reviewed by: Jozef Vyskoč
MaRDI profile type: Publication
cites work: Finite automata in number theory
cites work: Suites algébriques, automates et substitutions
cites work: Calcul pratique des coefficients de Taylor d'une fonction algébrique
cites work: Algebraic functions over finite fields
cites work: Q3669422
cites work: Folds! III: More morphisms
cites work: Algebraic properties of cellular automata
cites work: Q3750126
full work available at URL: 0304-3975(93)90165-p
OpenAlex ID: W1970313887
description: scientific article; zbMATH DE number 440337