Parity Tests with Ties

Ron Kupfer

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arXiv · 2604.19158

Parity Tests with Ties

Ron Kupfer

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Abstract

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 $c>0$.

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Ron Kupfer. 2026-04-21. Parity Tests with Ties. https://arxiv.org/abs/2604.19158

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