We extend the Ting--Yao randomized maximum-finding algorithm [TY94] to inputs that need not be pairwise distinct: each parity test $P(i,B)=\prod_{a\in B}(x_i-x_a):0$ on $B\subseteq[n]\setminus\{i\}$ is simulated by $O(\log |B|)$ ordinary polynomial tests, raising depth from $O((\log n)^2)$ to $O((\log n)^3)$ while preserving the $O(n^{-c})$ failure probability for every fixed $c>0$.

翻译：我们将Ting-Yao随机化最大值查找算法[TY94]扩展至输入元素不必两两互异的情形：每个奇偶检验$P(i,B)=\prod_{a\in B}(x_i-x_a):0$（其中$B\subseteq[n]\setminus\{i\}$）可通过$O(\log |B|)$个普通多项式检验模拟实现，使得深度从$O((\log n)^2)$提升至$O((\log n)^3)$，同时对于任意固定$c>0$保持$O(n^{-c})$的失败概率。