Complexité et automates cellulaires linéaires

Issue		RAIRO-Theor. Inf. Appl. Volume 34, Number 5, September-October 2000


Page(s)		403 - 423
DOI		10.1051/ita:2000124

DOI: 10.1051/ita:2000124
Theoret. Informatics Appl. 34 (2000) 403-423

Complexité et automates cellulaires linéaires

Valérie Berthé
IML, UPR 9016, Case 907, 163 avenue de Luminy, 13288 Marseille Cedex 09, France; (berthe@iml.univ-mrs.fr)

Reçu le 2 mars 2000. Accepté le 18 octobre 2000.

Abstract: The aim of this paper is to evaluate the growth order of the complexity function (in rectangles) for two-dimensional sequences generated by a linear cellular automaton with coefficients in $\mathbb{Z}/l \mathbb{Z}$ , and polynomial initial condition. We prove that the complexity function is quadratic when l is a prime and that it increases with respect to the number of distinct prime factors of l.

Résumé: Le but de cet article est d'évaluer l'ordre de croissance de la fonction de complexité rectangulaire de suites doubles engendrées par un automate cellulaire linéaire à coefficients dans $\mathbb{Z}/l \mathbb{Z}$ et à condition initiale polynomiale. On montre que la fonction de complexité est quadratique quand l est un nombre premier et qu'elle croît en proportion du nombre de facteurs premiers distincts de l.

AMS Subject Classification: 68R15, 11B85, 68Q80, 05A10.

Communicated by: J. Berstel.

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