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

TL;DR

This paper establishes a new lower bound on the number of queries needed for nonadaptive, one-sided error algorithms to test if Boolean functions over the hypercube are unate, improving previous bounds and advancing understanding of property testing complexity.

Contribution

It proves a tighter lower bound of / for nonadaptive, one-sided error unateness testing, surpassing earlier results and refining the theoretical limits.

Findings

Lower bound of / queries established

Improves upon previous / lower bound

Advances understanding of property testing complexity

Abstract

A Boolean function $f:\{0,1\}^d \mapsto \{0,1\}$ is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make $\Omega(\frac{d}{\log d})$ queries. This result improves upon the $\Omega(\frac{d}{\log^2 d})$ lower bound for the same class of testers due to Chen et al. (STOC, 2017).