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Adaptive Boolean Monotonicity Testing in Total Influence Time
Published 9 Jan 2018 in cs.DS, cs.CC, and cs.DM | (1801.02816v1)
Abstract: The problem of testing monotonicity of a Boolean function $f:{0,1}n \to {0,1}$ has received much attention recently. Denoting the proximity parameter by $\varepsilon$, the best tester is the non-adaptive $\widetilde{O}(\sqrt{n}/\varepsilon2)$ tester of Khot-Minzer-Safra (FOCS 2015). Let $I(f)$ denote the total influence of $f$. We give an adaptive tester whose running time is $I(f)poly(\varepsilon{-1}\log n)$.
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