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- W2952208743 abstract "We consider the problem of testing whether an unknown Boolean function $f$ is monotone versus $epsilon$-far from every monotone function. The two main results of this paper are a new lower bound and a new algorithm for this well-studied problem. Lower bound: We prove an $tilde{Omega}(n^{1/5})$ lower bound on the query complexity of any non-adaptive two-sided error algorithm for testing whether an unknown Boolean function $f$ is monotone versus constant-far from monotone. This gives an exponential improvement on the previous lower bound of $Omega(log n)$ due to Fischer et al. [FLN+02]. We show that the same lower bound holds for monotonicity testing of Boolean-valued functions over hypergrid domains ${1,ldots,m}^n$ for all $mge 2$. Upper bound: We give an $tilde{O}(n^{5/6})text{poly}(1/epsilon)$-query algorithm that tests whether an unknown Boolean function $f$ is monotone versus $epsilon$-far from monotone. Our algorithm, which is non-adaptive and makes one-sided error, is a modified version of the algorithm of Chakrabarty and Seshadhri [CS13a], which makes $tilde{O}(n^{7/8})text{poly}(1/epsilon)$ queries." @default.
- W2952208743 created "2019-06-27" @default.
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- W2952208743 date "2014-12-17" @default.
- W2952208743 modified "2023-10-05" @default.
- W2952208743 title "New algorithms and lower bounds for monotonicity testing" @default.
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- W2952208743 doi "https://doi.org/10.48550/arxiv.1412.5655" @default.
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