Boolean function monotonicity testing requires (almost) $n^{1/2}$ queries

TL;DR

This paper establishes a near-tight lower bound on the number of queries needed for adaptive algorithms to test the monotonicity of Boolean functions, significantly narrowing the gap with existing upper bounds.

Contribution

It improves the lower bound for monotonicity testing to nearly match the known upper bound, advancing theoretical understanding of query complexity.

Findings

Lower bound of (n^{1/2 - c}) queries for any constant c>0

Improves previous (n^{1/3}) lower bound

Almost matches the ((\

Abstract

We show that for any constant $c>0$, any (two-sided error) adaptive algorithm for testing monotonicity of Boolean functions must have query complexity $\Omega(n^{1/2-c})$. This improves the $\tilde\Omega(n^{1/3})$ lower bound of [CWX17] and almost matches the $\tilde{O}(\sqrt{n})$ upper bound of [KMS18].