Jeffrey C. Jackson, Homin Lee, Rocco Servedio, Andrew Wan

We give an algorithm that with high probability properly learns random monotone t(n)-term

DNF under the uniform distribution on the Boolean cube {0, 1}^n. For any polynomially bounded function t(n) <= poly(n) the algorithm runs in time poly(n, 1/eps) and with high probability outputs an eps accurate monotone DNF ...
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Tom Gur, Omer Tamuz

Let $f:\{-1,1\}^n \to \mathbb{R}$ be a real function on the hypercube, given

by its discrete Fourier expansion, or, equivalently, represented as

a multilinear polynomial. We say that it is Boolean if its image is

in $\{-1,1\}$.

We show that every function on the hypercube with a ... more >>>

Venkatesan Guruswami, Jakub OprÅ¡al, Sai Sandeep

Dinur's celebrated proof of the PCP theorem alternates two main steps in several iterations: gap amplification to increase the soundness gap by a large constant factor (at the expense of much larger alphabet size), and a composition step that brings back the alphabet size to an absolute constant (at the ... more >>>