We give a lower bound of $\Omega(\sqrt n)$ on the unambiguous randomised parity-query complexity of the approximate majority problem -- that is, on the lowest randomised parity-query complexity of any function over $\{0,1\}^n$ whose value is "0" if the Hamming weight of the input is at most n/3, is "1" if the weight is at least 2n/3, and may be arbitrary otherwise.
翻译:我们给出近似多数问题在无歧义随机奇偶查询复杂度上的下界$\Omega(\sqrt n)$ —— 即对于任意定义在$\{0,1\}^n$上的函数,若输入汉明重量不超过n/3时取值为"0",重量至少为2n/3时取值为"1",否则可任意取值,其最低随机奇偶查询复杂度为$\Omega(\sqrt n)$。