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

TL;DR

This paper introduces an efficient adaptive testing algorithm for unateness of Boolean functions, requiring nearly linear queries in the input size, with high probability of correct rejection for non-unate functions.

Contribution

It provides the first adaptive unateness tester with query complexity close to linear in n, improving over previous methods.

Findings

Queries are $O(n \, \log(n)/\epsilon)$ for the tester.

Tester always accepts unate functions.

Rejects functions that are $\epsilon$-far from unate with probability at least 0.9.

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.