All reports by Author Aaron Potechin:

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TR21-091
| 29th June 2021
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Gil Cohen, Dor Minzer, Shir Peleg, Aaron Potechin, Amnon Ta-Shma#### Expander Random Walks: The General Case and Limitations

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TR16-058
| 12th April 2016
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Boaz Barak, Samuel Hopkins, Jonathan Kelner, Pravesh Kothari, Ankur Moitra, Aaron Potechin#### A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem

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TR12-185
| 29th December 2012
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Siu Man Chan, Aaron Potechin#### Tight Bounds for Monotone Switching Networks via Fourier Analysis

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TR09-142
| 17th December 2009
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Aaron Potechin#### Bounds on Monotone Switching Networks for Directed Connectivity

Revisions: 1

Gil Cohen, Dor Minzer, Shir Peleg, Aaron Potechin, Amnon Ta-Shma

Cohen, Peri and Ta-Shma (STOC'21) considered the following question: Assume the vertices of an expander graph are labelled by $\pm 1$. What "test" functions $f : \{\pm 1\}^t \to \{\pm1 \}$ can or cannot distinguish $t$ independent samples from those obtained by a random walk? [CPTS'21] considered only balanced labelling, ... more >>>

Boaz Barak, Samuel Hopkins, Jonathan Kelner, Pravesh Kothari, Ankur Moitra, Aaron Potechin

We prove that with high probability over the choice of a random graph $G$ from the Erd\H{o}s-R\'enyi distribution $G(n,1/2)$, the $n^{O(d)}$-time degree $d$ Sum-of-Squares semidefinite programming relaxation for the clique problem will give a value of at least $n^{1/2-c(d/\log n)^{1/2}}$ for some constant $c>0$.

This yields a nearly tight ...
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Siu Man Chan, Aaron Potechin

We prove tight size bounds on monotone switching networks for the NP-complete problem of

$k$-clique, and for an explicit monotone problem by analyzing a pyramid structure of height $h$ for

the P-complete problem of generation. This gives alternative proofs of the separations of m-NC

from m-P and of m-NC$^i$ from ...
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Aaron Potechin

We prove that any monotone switching network solving directed connectivity on $N$ vertices must have size $N^{\Omega(\log N)}$

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