The set ${\mathbf{AC}}^0(F)$, the ${\mathbf{AC}}^0$ closure of F, is the closure with respect to substitution and concatenation recursion on notation of a set of basic functions comprehending the set F. By improving earlier work, we show that ${\mathbf{AC}}^0(F)$ is the substitution closure of a simple function set and characterize well‐known function complexity classes as the substitution closure of finite sets of simple functions.

中文翻译：

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复杂性类别的新替代基础

套装 ${\mathbf{交流电}}^0（F）$， ${\mathbf{交流电}}^0$的闭合˚F，相对于取代和级联递归一组理解该组基本功能的符号的闭合˚F。通过改进早期工作，我们表明${\mathbf{交流电}}^0（F）$ 是简单函数集的替换闭包，并将众所周知的函数复杂度类表征为简单函数有限集的替换闭包。