Testing Unateness Nearly Optimally

04/10/2019

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by   Xi Chen, et al.

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We present an Õ(n^2/3/ϵ^2)-query algorithm that tests whether an unknown Boolean function f{0,1}^n→{0,1} is unate (i.e., every variable is either non-decreasing or non-increasing) or ϵ-far from unate. The upper bound is nearly optimal given the Ω̃(n^2/3) lower bound of [CWX17a]. The algorithm builds on a novel use of the binary search procedure and its analysis over long random paths.