Adaptive Boolean Monotonicity Testing in Total Influence Time (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 $\widetilde{O}(\sqrt{n}/\varepsilon^2)$ 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 $I(f)poly(\varepsilon^{-1}\log n)$.