利用多项式cnn求二维二元元胞自动机的复杂度阈值

2010 12th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA 2010) Pub Date : 2010-03-29 DOI:10.1109/CNNA.2010.5430277

G. E. Pazienza, E. Gómez-Ramírez

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引用次数: 2

摘要

关于细胞非线性网络(cnn)和细胞自动机(CA)之间关系的理论研究导致了一维细胞自动机的复杂性指数和复杂性阈值等新概念的定义，但它们在二维细胞自动机中的解释尚未得到研究。在本文中，我们证明多项式cnn可以提供对二维二进制CA的深入了解，并允许我们引入复杂性指数的严格定义。在其他结果中，我们证明了二维CA的复杂性阈值与一维CA相同，并且众所周知的生命游戏是最简单的通用二维二进制元胞自动机。

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Threshold of complexity in 2D binary Cellular Automata found through Polynomial CNNs

The theoretical studies about the relationship between Cellular Nonlinear Networks (CNNs) and Cellular Automata (CA) have led to the definition of new concepts, such as the complexity index and the threshold of complexity, for 1D CA. However, their interpretation in 2D CA has not been investigated yet. In this paper, we show that Polynomial CNNs can provide a deep insight into 2D binary CA and allow us to introduce a rigorous definition of complexity index. Among other results, we prove that the threshold of complexity in 2D CA is the same as in 1D CA and that the well-known Game of Life is the simplest universal 2D binary Cellular Automaton.

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2010 12th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA 2010)

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