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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
La théorie dynamique des automates cellulaires sur les groupes est développée. Les principaux résultats sont des extensions non euclidiennes des résultats de Sato et Honda sur la dynamique des automates cellulaires euclidiens. La notion de période d'une configuration est redéfinie de manière plus théorique groupale. La notion de co-fini La configuration remplace la notion de configuration périodique, où le nouveau terme lui est donné pour refléter et souligner l'importance de la finitude impliquée. Avec ces notions étendues ou substituées, les relations entre la préservabilité de période, l'injectivité et la stabilité de Poisson des cartes parallèles sont établies. Il est démontré que les groupes résiduellement finis donnent une propriété topologique intéressante selon laquelle les configurations co-finies sont denses dans l'espace de configuration.
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Shuichi YUKITA, "Dynamics of Cellular Automata on Groups" in IEICE TRANSACTIONS on Information,
vol. E82-D, no. 10, pp. 1316-1323, October 1999, doi: .
Abstract: Dynamical theory of cellular automata on groups is developed. Main results are non-Euclidean extensions of Sato and Honda's results on the dynamics of Euclidean cellular automata. The notion of the period of a configuration is redefined in a more group theoretical way. The notion of a co-finite configuration substitutes the notion of a periodic configuration, where the new term is given to it to reflect and emphasize the importance of finiteness involved. With these extended or substituted notions, the relations among period preservablity, injectivity, and Poisson stability of parallel maps are established. Residually finite groups are shown to give a nice topological property that co-finite configurations are dense in the configuration space.
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_10_1316/_p
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@ARTICLE{e82-d_10_1316,
author={Shuichi YUKITA, },
journal={IEICE TRANSACTIONS on Information},
title={Dynamics of Cellular Automata on Groups},
year={1999},
volume={E82-D},
number={10},
pages={1316-1323},
abstract={Dynamical theory of cellular automata on groups is developed. Main results are non-Euclidean extensions of Sato and Honda's results on the dynamics of Euclidean cellular automata. The notion of the period of a configuration is redefined in a more group theoretical way. The notion of a co-finite configuration substitutes the notion of a periodic configuration, where the new term is given to it to reflect and emphasize the importance of finiteness involved. With these extended or substituted notions, the relations among period preservablity, injectivity, and Poisson stability of parallel maps are established. Residually finite groups are shown to give a nice topological property that co-finite configurations are dense in the configuration space.},
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - Dynamics of Cellular Automata on Groups
T2 - IEICE TRANSACTIONS on Information
SP - 1316
EP - 1323
AU - Shuichi YUKITA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 1999
AB - Dynamical theory of cellular automata on groups is developed. Main results are non-Euclidean extensions of Sato and Honda's results on the dynamics of Euclidean cellular automata. The notion of the period of a configuration is redefined in a more group theoretical way. The notion of a co-finite configuration substitutes the notion of a periodic configuration, where the new term is given to it to reflect and emphasize the importance of finiteness involved. With these extended or substituted notions, the relations among period preservablity, injectivity, and Poisson stability of parallel maps are established. Residually finite groups are shown to give a nice topological property that co-finite configurations are dense in the configuration space.
ER -