Shallit and Wang showed that the automatic complexity $A(x)\ge n/13$ for almost all $x\in\{0,1\}^n$. They also stated that Holger Petersen had informed them that the constant 13 can be reduced to 7. Here we show that it can be reduced to $2+\epsilon$ for any $\epsilon>0$.

中文翻译：

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自动复杂度的不可压缩定理

Shallit 和 Wang 证明了几乎所有 $x\in\{0,1\}^n$ 的自动复杂度 $A(x)\ge n/13$。他们还表示 Holger Petersen 已经通知他们常数 13 可以减少到 7。这​​里我们表明，对于任何 $\epsilon>0$，它都可以减少到 $2+\epsilon$。