Subhash Khot, Dor Minzer, Muli Safra

We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, we

give a monotonicity testing algorithm that makes $\tilde{O}(\sqrt{n}/\epsilon^2)$ non-adaptive queries to a function

$f:\{0,1\}^n \mapsto \{0,1\}$, always accepts a monotone function and rejects a function that is $\epsilon$-far from

being monotone ...
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Hadley Black, Deeparnab Chakrabarty, C. Seshadhri

We study monotonicity testing of Boolean functions over the hypergrid $[n]^d$ and design a non-adaptive tester with $1$-sided error whose query complexity is $\tilde{O}(d^{5/6})\cdot \text{poly}(\log n,1/\epsilon)$. Previous to our work, the best known testers had query complexity linear in $d$ but independent of $n$. We improve upon these testers as ... more >>>

Hadley Black, Deeparnab Chakrabarty, C. Seshadhri

The problem of testing monotonicity for Boolean functions on the hypergrid, $f:[n]^d \to \{0,1\}$ is a classic topic in property testing. When $n=2$, the domain is the hypercube. For the hypercube case, a breakthrough result of Khot-Minzer-Safra (FOCS 2015) gave a non-adaptive, one-sided tester making $\widetilde{O}(\varepsilon^{-2}\sqrt{d})$ queries. Up to polylog ... more >>>