一维约束密度分类
Restricted density classification in one dimension
摘要：
密度分类任务是确定出现在数组中的哪个符号占多数。解决这个任务的元胞自动机需要收敛到一个统一的配置，在每个站点的多数符号。目前还不知道一个一维元胞自动机与二进制字母表是否可以分类所有的伯努利随机配置几乎肯定根据其密度。我们表明，任何细胞自动机，洗出有限的岛屿在线性时间分类所有伯努利随机配置的参数接近0或1几乎肯定正确。证明是一个直接应用的“渗透”的论点，可以追溯到Gacs（1986）。
英文摘要：
The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uniform configuration with the majority symbol at each site. It is not known whether a one-dimensional cellular automaton with binary alphabet can classify all Bernoulli random configurations almost surely according to their densities. We show that any cellular automaton that washes out finite islands in linear time classifies all Bernoulli random configurations with parameters close to 0 or 1 almost surely correctly. The proof is a direct application of a "percolation" argument which goes back to Gacs (1986).
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