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

Abstract

We prove a lower bound of $\Omega (n^{1/2-c})$, for all $c>0$, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an $n$-variable Boolean function is monotone versus constant-far from monotone. This improves a $\tilde{\Omega }(n^{1/5})$ lower bound for the same problem that was recently given in [CST14] and is very close to $\Omega (n^{1/2})$, which we conjecture is the optimal lower bound for this model.

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