On algebraic cellular automata

被引：4

作者：

Ceccherini-Silberstein, Tullio ^{[1
]}

Coornaert, Michel ^{[2
,3
]}

机构：

[1] Univ Sannio, Dipartimento Ingn, I-82100 Benevento, Italy

[2] Univ Strasbourg, Inst Rech Math Avancee, UMR 7501, F-67000 Strasbourg, France

[3] CNRS, F-67000 Strasbourg, France

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2011年 / 84卷

关键词：

INJECTIVE ENDOMORPHISMS; FINITE-FIELDS; VARIETIES;

D O I：

10.1112/jlms/jdr016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate some general properties of algebraic cellular automata, that is, cellular automata over groups whose alphabets are affine algebraic sets and which are locally defined by regular maps. When the ground field is assumed to be uncountable and algebraically closed, we prove that such cellular automata always have a closed image with respect to the prodiscrete topology on the space of configurations and that they are reversible as soon as they are bijective.

引用

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页码：541 / 558

页数：18

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