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REPORTS > KEYWORD > BOOLEAN ISOPERIMETRY:
Reports tagged with boolean isoperimetry:
TR15-011 | 22nd January 2015
Subhash Khot, Dor Minzer, Muli Safra

#### On Monotonicity Testing and Boolean Isoperimetric type Theorems

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 ... more >>>

TR17-159 | 28th October 2017

#### A $o(d) \cdot \text{polylog}~n$ Monotonicity Tester for Boolean Functions over the Hypergrid $[n]^d$

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 >>>

TR22-162 | 10th November 2022
#### Directed Isoperimetric Theorems for Boolean Functions on the Hypergrid and an $\widetilde{O}(n\sqrt{d})$ Monotonicity Tester
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 >>>