All reports by Author Michael Whitmeyer:

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TR23-154
| 12th October 2023
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Vishnu Iyer, Siddhartha Jain, Matt Kovacs-Deak, Vinayak Kumar, Luke Schaeffer, Daochen Wang, Michael Whitmeyer#### On the Rational Degree of Boolean Functions and Applications

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TR22-109
| 27th July 2022
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Siddharth Iyer, Michael Whitmeyer#### Searching for Regularity in Bounded Functions

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TR21-004
| 10th January 2021
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Vishnu Iyer, Avishay Tal, Michael Whitmeyer#### Junta Distance Approximation with Sub-Exponential Queries

Vishnu Iyer, Siddhartha Jain, Matt Kovacs-Deak, Vinayak Kumar, Luke Schaeffer, Daochen Wang, Michael Whitmeyer

We study a natural complexity measure of Boolean functions known as the (exact) rational degree. For total functions $f$, it is conjectured that $\mathrm{rdeg}(f)$ is polynomially related to $\mathrm{deg}(f)$, where $\mathrm{deg}(f)$ is the Fourier degree. Towards this conjecture, we show that symmetric functions have rational degree at least $\mathrm{deg}(f)/2$ and ... more >>>

Siddharth Iyer, Michael Whitmeyer

Given a function $f:\mathbb F_2^n \to [-1,1]$, this work seeks to find a large affine subspace $\mathcal U$ such that $f$, when restricted to $\mathcal U$, has small nontrivial Fourier coefficients.

We show that for any function $f:\mathbb F_2^n \to [-1,1]$ with Fourier degree $d$, there exists an affine subspace ... more >>>

Vishnu Iyer, Avishay Tal, Michael Whitmeyer

Leveraging tools of De, Mossel, and Neeman [FOCS, 2019], we show two different results pertaining to the tolerant testing of juntas. Given black-box access to a Boolean function $f:\{\pm1\}^{n} \to \{\pm1\}$ we give a poly$(k, \frac{1}{\varepsilon})$ query algorithm that distinguishes between functions that are $\gamma$-close to $k$-juntas and $(\gamma+\varepsilon)$-far from ... more >>>