English

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

Computational Complexity 2025-11-10 v2 Discrete Mathematics Data Structures and Algorithms

Abstract

We show that for any constant c>0c>0, any (two-sided error) adaptive algorithm for testing monotonicity of Boolean functions must have query complexity Ω(n1/2c)\Omega(n^{1/2-c}). This improves the Ω~(n1/3)\tilde\Omega(n^{1/3}) lower bound of [CWX17] and almost matches the O~(n)\tilde{O}(\sqrt{n}) upper bound of [KMS18].

Keywords

Cite

@article{arxiv.2511.04558,
  title  = {Boolean function monotonicity testing requires (almost) $n^{1/2}$ queries},
  author = {Mark Chen and Xi Chen and Hao Cui and William Pires and Jonah Stockwell},
  journal= {arXiv preprint arXiv:2511.04558},
  year   = {2025}
}