All reports by Author Ryan O'Donnell:

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TR16-147
| 19th September 2016
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Ryan O'Donnell, A. C. Cem Say#### The weakness of CTC qubits and the power of approximate counting

Revisions: 1

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TR16-142
| 11th September 2016
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Jason Li, Ryan O'Donnell#### Bounding laconic proof systems by solving CSPs in parallel

Revisions: 1

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TR16-141
| 11th September 2016
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Ryan O'Donnell#### SOS is not obviously automatizable, even approximately

Revisions: 1

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TR15-082
| 13th May 2015
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Boaz Barak, Ankur Moitra, Ryan O'Donnell, Prasad Raghavendra, Oded Regev, David Steurer, Luca Trevisan, Aravindan Vijayaraghavan, David Witmer, John Wright#### Beating the random assignment on constraint satisfaction problems of bounded degree

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TR14-091
| 22nd July 2014
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Ryan O'Donnell, A. C. Cem Say#### One time-travelling bit is as good as logarithmically many

Revisions: 1

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TR10-006
| 11th January 2010
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YI WU, Ryan O'Donnell, David Zuckerman, Parikshit Gopalan#### Fooling functions of halfspaces under product distributions

Revisions: 2

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TR09-130
| 1st December 2009
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Ryan O'Donnell, YI WU, Yuan Zhou#### Optimal lower bounds for locality sensitive hashing (except when $q$ is tiny)

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TR08-055
| 19th May 2008
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Ryan O'Donnell#### Some Topics in Analysis of Boolean Functions

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TR07-128
| 10th November 2007
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Kevin Matulef, Ryan O'Donnell, Ronitt Rubinfeld, Rocco Servedio#### Testing Halfspaces

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TR07-043
| 7th May 2007
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Uriel Feige, Guy Kindler, Ryan O'Donnell#### Understanding Parallel Repetition Requires Understanding Foams

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TR05-101
| 20th September 2005
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Guy Kindler, Ryan O'Donnell, Subhash Khot, Elchanan Mossel#### Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?

Ryan O'Donnell, A. C. Cem Say

We present two results in structural complexity theory concerned with the following interrelated

topics: computation with postselection/restarting, closed timelike curves (CTCs), and

approximate counting. The first result is a new characterization of the lesser known complexity

class BPP_path in terms of more familiar concepts. Precisely, BPP_path is the class of ...
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Jason Li, Ryan O'Donnell

We show that the basic semidefinite programming relaxation value of any constraint satisfaction problem can be computed in NC; that is, in parallel polylogarithmic time and polynomial work. As a complexity-theoretic consequence we get that MIP1$[k,c,s] \subseteq $ PSPACE provided $s/c \leq (.62-o(1))k/2^k$, resolving a question of Austrin, HÃ¥stad, and ... more >>>

Ryan O'Donnell

Suppose we want to minimize a polynomial $p(x) = p(x_1, \dots, x_n)$, subject to some polynomial constraints $q_1(x), \dots, q_m(x) \geq 0$, using the Sum-of-Squares (SOS) SDP hierarachy. Assume we are in the "explicitly bounded" ("Archimedean") case where the constraints include $x_i^2 \leq 1$ for all $1 \leq i \leq ... more >>>

Boaz Barak, Ankur Moitra, Ryan O'Donnell, Prasad Raghavendra, Oded Regev, David Steurer, Luca Trevisan, Aravindan Vijayaraghavan, David Witmer, John Wright

We show that for any odd $k$ and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $\frac{1}{2} + \Omega(1/\sqrt{D})$ fraction of constraints, where $D$ is a bound on the number of constraints that each variable occurs in. ... more >>>

Ryan O'Donnell, A. C. Cem Say

We consider computation in the presence of closed timelike curves (CTCs), as proposed by Deutsch. We focus on the case in which the CTCs carry classical bits (as opposed to qubits). Previously, Aaronson and Watrous showed that computation with polynomially many CTC bits is equivalent in power to PSPACE. On ... more >>>

YI WU, Ryan O'Donnell, David Zuckerman, Parikshit Gopalan

We construct pseudorandom generators that fool functions of halfspaces (threshold functions) under a very broad class of product distributions. This class includes not only familiar cases such as the uniform distribution on the discrete cube, the uniform distribution on the solid cube, and the multivariate Gaussian distribution, but also includes ... more >>>

Ryan O'Donnell, YI WU, Yuan Zhou

We study lower bounds for Locality Sensitive Hashing (LSH) in the strongest setting: point sets in $\{0,1\}^d$ under the Hamming distance. Recall that $\mathcal{H}$ is said to be an $(r, cr, p, q)$-sensitive hash family if all pairs $x,y \in \{0,1\}^d$ with dist$(x,y) \leq r$ have probability at least $p$ ... more >>>

Ryan O'Donnell

This article accompanies a tutorial talk given at the 40th ACM STOC conference. In it, we give a brief introduction to Fourier analysis of boolean functions and then discuss some applications: Arrow?s Theorem and other ideas from the theory of Social Choice; the Bonami-Beckner Inequality as an extension of Chernoff/Hoeffding ... more >>>

Kevin Matulef, Ryan O'Donnell, Ronitt Rubinfeld, Rocco Servedio

This paper addresses the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x)=sgn(w ⋅ x - θ). We consider halfspaces over the continuous domain R^n (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean cube {-1,1}^n ... more >>>

Uriel Feige, Guy Kindler, Ryan O'Donnell

Motivated by the study of Parallel Repetition and also by the Unique

Games Conjecture, we investigate the value of the ``Odd Cycle Games''

under parallel repetition. Using tools from discrete harmonic

analysis, we show that after $d$ rounds on the cycle of length $m$,

the value of the game is ...
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Guy Kindler, Ryan O'Donnell, Subhash Khot, Elchanan Mossel

In this paper we show a reduction from the Unique Games problem to the problem of approximating MAX-CUT to within a factor of $\GW + \eps$, for all $\eps > 0$; here $\GW \approx .878567$ denotes the approximation ratio achieved by the Goemans-Williamson algorithm~\cite{GW95}. This implies that if the Unique ... more >>>