二维线性CA的不可逆性与伊甸园

Doston Jumaniyozov, B. Omirov, Shovkat Redjepov, S. Uguz
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摘要

本文考虑一个五边形格,研究了具有域[公式:见文]的二维元胞自动机(整模集合[公式:见文])具有零边界条件的规则矩阵,并分析了它们的特性。在此基础上,提出了一种von Neumann邻域零边界条件下规则矩阵秩的计算算法。最后,给出了二维元胞自动机伊甸园构型存在的充分必要条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Irreversibility of 2D Linear CA and Garden of Eden
In this paper, we consider a pentagonal lattice and we investigate the rule matrix with null boundary condition for two-dimensional cellular automata with the field [Formula: see text] (the set of integers modulo [Formula: see text]) and analyze their characteristics. Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained.
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