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- W2234555324 abstract "We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions. Given oracle access to an unknown Boolean function $f:{0,1}^n rightarrow {0,1}$ and sampling oracle access to an unknown distribution $mathcal{D}$ over ${0,1}^n$, we present an $tilde{O}(n^{1/3}/epsilon^5)$-query algorithm that tests whether $f$ is a monotone conjunction versus $epsilon$-far from any monotone conjunction with respect to $mathcal{D}$. This improves the previous best upper bound of $tilde{O}(n^{1/2}/epsilon)$ by Dolev and Ron when $1/epsilon$ is small compared to $n$. For some constant $epsilon_0>0$, we also prove a lower bound of $tilde{Omega}(n^{1/3})$ for the query complexity, improving the previous best lower bound of $tilde{Omega}(n^{1/5})$ by Glasner and Servedio. Our upper and lower bounds are tight, up to a poly-logarithmic factor, when the distance parameter $epsilon$ is a constant. Furthermore, the same upper and lower bounds can be extended to the distribution-free testing of general conjunctions, and the lower bound can be extended to that of decision lists and linear threshold functions." @default.
- W2234555324 created "2016-06-24" @default.
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- W2234555324 date "2015-12-21" @default.
- W2234555324 modified "2023-09-27" @default.
- W2234555324 title "Tight Bounds for the Distribution-Free Testing of Monotone Conjunctions" @default.
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- W2234555324 doi "https://doi.org/10.1137/1.9781611974331.ch5" @default.
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