An $\widetilde{O}(n)$ Queries Adaptive Tester for Unateness

Abstract

We present an adaptive tester for the unateness property of Boolean functions. Given a function $f:\{0,1\}^n \to \{0,1\}$ the tester makes $O(n \log(n)/\epsilon)$ adaptive queries to the function. The tester always accepts a unate function, and rejects with probability at least 0.9 if a function is $\epsilon$-far from being unate.