Testing Unateness Nearly Optimally

Abstract

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

References in corpus (2)

• Testing Unateness of Real-Valued Functions
• A Lower Bound for Nonadaptive, One-Sided Error Testing of Unateness of Boolean Functions over the Hypercube