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

Xi Chen; Anindya De; Rocco A. Servedio; Li-Yang Tan

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arXiv · 1412.5657

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

Xi Chen·Anindya De·Rocco A. Servedio·Li-Yang Tan

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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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BibTeX RIS

Xi Chen, Anindya De, Rocco A. Servedio, Li-Yang Tan. 2014-12-17. Boolean function monotonicity testing requires (almost) $n^{1/2}$ non-adaptive queries. https://arxiv.org/abs/1412.5657

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