关于非统一细胞自动机的伊甸园定理

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-04-30 DOI:10.1088/1361-6544/ad3ffa

Xuan Kien Phung

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引用次数: 0

摘要

我们建立了众所周知的伊甸园定理的若干扩展，该定理适用于全移位和适配群宇宙上的非均匀蜂窝自动机（CA）。特别是，我们的结果定量地描述了非均匀蜂窝自动机的部分预注入性和图像大小之间的关系。对于有限类型强不可还原子移位上的多维 CA，我们还得到了一个强化的连接性结果。

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On the Garden of Eden theorem for non-uniform cellular automata

We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata (CA) over the full shifts and over amenable group universes. In particular, our results describe quantitatively the relations between the partial pre-injectivity and the size of the image of a non-uniform CA. A strengthened surjunctivity result is also obtained for multi-dimensional CA over strongly irreducible subshifts of finite type.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.