A real number x is absolutely normal if, for every base $b\ge 2$, every two equally long strings of digits appear with equal asymptotic frequency in the base-b expansion of x. This paper presents an explicit algorithm that generates the binary expansion of an absolutely normal number x, with the nth bit of x appearing after $n\mathrm{polylog}(n)$ computation steps. This speed is achieved by simultaneously computing and diagonalizing against a martingale that incorporates Lempel-Ziv parsing algorithms in all bases.

中文翻译：

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在近乎线性的时间内计算绝对正态数

一个实数x是绝对正规的，如果对于每个基数$乙\ge 2$，每两个同样长的数字串在x的基数b展开中以相等的渐近频率出现。本文提出一种显式算法生成一个绝对正常数量的二进制展开X，与Ñ的第i位X之后出现$n\mathrm{多对数}(n)$计算步骤。这个速度是通过同时计算和对角化在所有碱基中结合 Lempel-Ziv 解析算法的鞅来实现的。