All reports by Author Elad Haramaty:

__
TR18-054
| 24th March 2018
__

Klim Efremenko, Elad Haramaty, Yael Kalai#### Interactive Coding with Constant Round and Communication Blowup

Revisions: 1

__
TR16-194
| 4th December 2016
__

Mohammad Bavarian, Badih Ghazi, Elad Haramaty, Pritish Kamath, Ronald Rivest, Madhu Sudan#### The Optimality of Correlated Sampling

__
TR16-169
| 3rd November 2016
__

Elad Haramaty, Chin Ho Lee, Emanuele Viola#### Bounded independence plus noise fools products

__
TR15-043
| 2nd April 2015
__

Alan Guo, Elad Haramaty, Madhu Sudan#### Robust testing of lifted codes with applications to low-degree testing

__
TR14-004
| 30th November 2013
__

Hasan Abasi, Nader Bshouty, Ariel Gabizon, Elad Haramaty#### On $r$-Simple $k$-Path

__
TR13-030
| 20th February 2013
__

Elad Haramaty, Noga Ron-Zewi, Madhu Sudan#### Absolutely Sound Testing of Lifted Codes

__
TR12-166
| 25th November 2012
__

Elad Haramaty, Madhu Sudan#### Deterministic Compression with Uncertain Priors

__
TR11-059
| 15th April 2011
__

Elad Haramaty, Amir Shpilka, Madhu Sudan#### Optimal testing of multivariate polynomials over small prime fields

__
TR09-080
| 19th September 2009
__

Elad Haramaty, Amir Shpilka#### On the Structure of Cubic and Quartic Polynomials

Revisions: 1

Klim Efremenko, Elad Haramaty, Yael Kalai

The problem of constructing error-resilient interactive protocols was introduced in the seminal works of Schulman (FOCS 1992, STOC 1993). These works show how to convert any two-party interactive protocol into one that is resilient to constant-fraction of error, while blowing up the communication by only a constant factor. Since ... more >>>

Mohammad Bavarian, Badih Ghazi, Elad Haramaty, Pritish Kamath, Ronald Rivest, Madhu Sudan

In the "correlated sampling" problem, two players, say Alice and Bob, are given two distributions, say $P$ and $Q$ respectively, over the same universe and access to shared randomness. The two players are required to output two elements, without any interaction, sampled according to their respective distributions, while trying to ... more >>>

Elad Haramaty, Chin Ho Lee, Emanuele Viola

Let $D$ be a $b$-wise independent distribution over

$\{0,1\}^m$. Let $E$ be the ``noise'' distribution over

$\{0,1\}^m$ where the bits are independent and each bit is 1

with probability $\eta/2$. We study which tests $f \colon

\{0,1\}^m \to [-1,1]$ are $\e$-fooled by $D+E$, i.e.,

$|\E[f(D+E)] - \E[f(U)]| \le \e$ where ...
more >>>

Alan Guo, Elad Haramaty, Madhu Sudan

A local tester for a code probabilistically looks at a given word at a small set of coordinates and based on this local view accepts codewords with probability one while rejecting words far from the code with constant probabilility. A local tester for a code is said to be ``robust'' ... more >>>

Hasan Abasi, Nader Bshouty, Ariel Gabizon, Elad Haramaty

An $r$-simple $k$-path is a {path} in the graph of length $k$ that

passes through each vertex at most $r$ times. The \simpath{r}{k}

problem, given a graph $G$ as input, asks whether there exists an

$r$-simple $k$-path in $G$. We first show that this problem is

NP-Complete. We then show ...
more >>>

Elad Haramaty, Noga Ron-Zewi, Madhu Sudan

In this work we present a strong analysis of the testability of a broad, and to date the most interesting known, class of "affine-invariant'' codes. Affine-invariant codes are codes whose coordinates are associated with a vector space and are invariant under affine transformations of the coordinate space. Affine-invariant linear codes ... more >>>

Elad Haramaty, Madhu Sudan

We consider the task of compression of information when the source of the information and the destination do not agree on the prior, i.e., the distribution from which the information is being generated. This setting was considered previously by Kalai et al. (ICS 2011) who suggested that this was a ... more >>>

Elad Haramaty, Amir Shpilka, Madhu Sudan

We consider the problem of testing if a given function $f : \F_q^n \rightarrow \F_q$ is close to a $n$-variate degree $d$ polynomial over the finite field $\F_q$ of $q$ elements. The natural, low-query, test for this property would be to pick the smallest dimension $t = t_{q,d}\approx d/q$ such ... more >>>

Elad Haramaty, Amir Shpilka

In this paper we study the structure of polynomials of degree three and four that have high bias or high Gowers norm, over arbitrary prime fields. In particular we obtain the following results. 1. We give a canonical representation for degree three or four polynomials that have a significant bias ... more >>>