A Boolean function $f({\vec x})$ is sensitive to bit $x_i$ if there is at least one input vector $\vec x$ and one bit $x_i$ in $\vec x$, such that changing $x_i$ changes $f$. A function has sensitivity $s$ if among all input vectors, the largest number of bits to which $f$ is sensitive is $s$. We count the $n$-variable symmetric Boolean functions that have maximum sensitivity. We show that most such functions have the largest possible sensitivity, $n$. This suggests sensitivity is limited as a complexity measure for symmetric Boolean functions.

翻译：布尔函数 $f({\vec x})$ 对位 $x_i$ 敏感，若存在至少一个输入向量 $\vec x$ 及 $\vec x$ 中的位 $x_i$，使得改变 $x_i$ 会改变 $f$。若在所有输入向量中，$f$ 敏感的最大位数是 $s$，则该函数具有灵敏度 $s$。我们统计了具有最大灵敏度的 $n$ 元对称布尔函数。研究表明，大多数此类函数具有最大可能灵敏度 $n$。这表明对于对称布尔函数而言，灵敏度作为复杂度度量存在局限性。