分类密度的元胞自动机装配线的噪声敏感性和遍历性
Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density
摘要：
我们研究了复合元胞自动机对H. [Phys.Rev.E55，R2081（1997）]对噪声进行分析，并在数值上评估所得概率元胞自动机（PCA）的密度分类性能。我们的结论是，复合PCA可靠地执行密度分类任务，只有非常小的噪声水平。特别是，它不能优于嘈杂的Gacs-Kurdyumov-Levin自动机，一个不完美的分类器，任何级别的噪音。虽然原来的复合CA是nonergodic的，松弛时间的分析表明，其嘈杂的版本是一个遍历自动机，与松弛时间代数衰减的扩展范围内的参数与指数非常接近（可能等于）的平均场值。
英文摘要：
We investigate the sensitivity of the composite cellular automaton of H. Fukś [Phys. Rev. E 55, R2081 (1997)] to noise and assess the density classification performance of the resulting probabilistic cellular automaton (PCA) numerically. We conclude that the composite PCA performs the density classification task reliably only up to very small levels of noise. In particular, it cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an imperfect classifier, for any level of noise. While the original composite CA is nonergodic, analyses of relaxation times indicate that its noisy version is an ergodic automaton, with the relaxation times decaying algebraically over an extended range of parameters with an exponent very close (possibly equal) to the mean-field value.
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