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
그룹에 따른 세포 오토마타의 역학 이론이 개발되었습니다. 주요 결과는 유클리드 셀룰러 오토마타의 역학에 대한 Sato와 Honda의 결과를 비유클리드 확장한 것입니다. 구성 기간의 개념은 보다 그룹적인 이론적 방식으로 재정의됩니다. 의 개념 공동 유한 구성은 관련된 유한성의 중요성을 반영하고 강조하기 위해 새로운 용어가 제공되는 주기적인 구성의 개념을 대체합니다. 이러한 확장되거나 대체된 개념을 통해 평행 지도의 기간 보존성, 주입성 및 포아송 안정성 간의 관계가 확립됩니다. 잔여 유한 그룹은 동일 유한 구성이 구성 공간에서 조밀하다는 멋진 토폴로지 속성을 제공하는 것으로 표시됩니다.
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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},}
부
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 -