Testing Unateness Nearly Optimally [article]

Xi Chen, Erik Waingarten
2019 arXiv   pre-print
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.
arXiv:1904.05309v1 fatcat:6diyyuqjivepldgreedum3dlcy