The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
A teoria dinâmica de autômatos celulares em grupos é desenvolvida. Os principais resultados são extensões não-euclidianas dos resultados de Sato e Honda sobre a dinâmica de autômatos celulares euclidianos. A noção de período de uma configuração é redefinida de uma forma mais teórica de grupo. A noção de um cofinito configuração substitui a noção de configuração periódica, onde o novo termo é dado a ela para refletir e enfatizar a importância da finitude envolvida. Com essas noções estendidas ou substituídas, são estabelecidas as relações entre preservação do período, injetividade e estabilidade de Poisson de mapas paralelos. Mostra-se que grupos residualmente finitos fornecem uma boa propriedade topológica de que configurações co-finitas são densas no espaço de configuração.
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Copiar
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
Copiar
@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},}
Copiar
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 -