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Electronic Colloquium on Computational Complexity

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Reports tagged with Discrete Fourier Analysis:
TR07-129 | 25th October 2007
Jeffrey C. Jackson, Homin Lee, Rocco Servedio, Andrew Wan

Learning Random Monotone DNF

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 ... more >>>

TR12-031 | 4th April 2012
Tom Gur, Omer Tamuz

Testing Booleanity and the Uncertainty Principle

Revisions: 1

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 >>>

TR19-092 | 9th July 2019
Venkatesan Guruswami, Jakub Opršal, Sai Sandeep

Revisiting Alphabet Reduction in Dinur's PCP

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 >>>

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