Boolean function monotonicity testing requires (almost) $n^{1/2}$ queries
By: Mark Chen , Xi Chen , Hao Cui and more
Potential Business Impact:
Finds if a computer program is always fair.
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].
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