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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > ELAD HARAMATY:
All reports by Author Elad Haramaty:

TR16-194 | 4th December 2016
Mohammad Bavarian, Badih Ghazi, Elad Haramaty, Pritish Kamath, Ronald Rivest, Madhu Sudan

The Optimality of Correlated Sampling

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 >>>


TR16-169 | 3rd November 2016
Elad Haramaty, Chin Ho Lee, Emanuele Viola

Bounded independence plus noise fools products

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 >>>


TR15-043 | 2nd April 2015
Alan Guo, Elad Haramaty, Madhu Sudan

Robust testing of lifted codes with applications to low-degree testing

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 >>>


TR14-004 | 30th November 2013
Hasan Abasi, Nader Bshouty, Ariel Gabizon, Elad Haramaty

On $r$-Simple $k$-Path

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 >>>


TR13-030 | 20th February 2013
Elad Haramaty, Noga Ron-Zewi, Madhu Sudan

Absolutely Sound Testing of Lifted Codes

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 >>>


TR12-166 | 25th November 2012
Elad Haramaty, Madhu Sudan

Deterministic Compression with Uncertain Priors

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 >>>


TR11-059 | 15th April 2011
Elad Haramaty, Amir Shpilka, Madhu Sudan

Optimal testing of multivariate polynomials over small prime fields

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 >>>


TR09-080 | 19th September 2009
Elad Haramaty, Amir Shpilka

On the Structure of Cubic and Quartic Polynomials

Revisions: 1

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 >>>




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