2D Linear CA with Mixing Boundary Conditions and Reversibility

Doston Jumaniyozov, J. Casas, M. González, B. Omirov, Shovkat Redjepov
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Abstract

In this paper, we consider two-dimensional cellular automata (CA) with the von Neumann neighborhood. We study the characterization of 2D linear cellular automata defined by the von Neumann neighborhood with new type of boundary conditions over the field [Formula: see text]. Furthermore, we investigate the rule matrices of 2D von Neumann CA by applying the group of permutations [Formula: see text]. Moreover, the algorithm for computing the rank of rule matrices is given. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for considered two-dimensional cellular automata are obtained.
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具有混合边界条件和可逆性的二维线性CA
本文考虑具有von Neumann邻域的二维元胞自动机(CA)。我们研究了由von Neumann邻域定义的二维线性元胞自动机在场上具有新型边界条件的表征[公式:见文本]。此外,我们利用置换群研究了二维von Neumann CA的规则矩阵[公式:见文本]。并给出了规则矩阵秩的计算算法。最后,得到了所考虑的二维元胞自动机存在伊甸园构型的充分必要条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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