论文标题
使用基本规则14评估本地结构近似的质量
Evaluating the Quality of Local Structure Approximation Using Elementary Rule 14
论文作者
论文摘要
蜂窝自动机（CA）可以看作是概率度量空间中的地图。这样的地图通常是无限维度的，为了促进其特性的研究，尤其是在应用程序的背景下，已经提出了有限维近似值。最常用的一种被称为局部结构理论，由H. Gutowitz等人开发。在1987年。尽管这种近似值在CA研究中的普及，但缺乏严格评估其准确性的示例。为了填补这一空白，我们为规则14构建了局部结构近似，并以严格的方式研究其动态，而无需依赖数值实验。然后，我们将结果与已知的确切结果进行比较。
Cellular automata (CA) can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their properties, especially in the context of applications, finite-dimensional approximations have been proposed. The most commonly used one is known as the local structure theory, developed by H. Gutowitz et al. in 1987. In spite of the popularity of this approximation in CA research, examples of rigorous evaluations of its accuracy are lacking. In an attempt to fill this gap, we construct a local structure approximation for rule 14, and study its dynamics in a rigorous fashion, without relying on numerical experiments. We then compare the outcome with known exact results.
