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- Elad Haramaty, Amir Shpilka
- Electronic Colloquium on Computational Complexity
- 2009

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 (i.e. they are not equidistributed). This result generalizes… (More)

- Elad Haramaty, Amir Shpilka, Madhu Sudan
- 2011 IEEE 52nd Annual Symposium on Foundations of…
- 2011

We consider the problem of testing if a given function $f : \F_q^n \right arrow \F_q$ 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 that every function of degree greater than $d$reveals this… (More)

- Hasan Abasi, Nader H. Bshouty, Ariel Gabizon, Elad Haramaty
- MFCS
- 2014

An r-simple k-path is a path in the graph of length k that passes through each vertex at most r times. The r-SIMPLE k-PATH 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 that there is a graph G that contains an r-simple k-path and no simple path of length… (More)

- Elad Haramaty, Madhu Sudan
- Algorithmica
- 2012

Communication in "natural" settings, e.g., between humans, is distinctly different than that in classical designed settings, in that the former is characterized by the sender and receiver not being in perfect agreement with each other. Solutions to classical communication problems thus have to overcome an extra layer of uncertainty introduced by this lack… (More)

- Elad Haramaty, Noga Ron-Zewi, Madhu Sudan
- Theory of Computing
- 2013

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 form a natural… (More)

- Elad Haramaty, Chin Ho Lee, Emanuele Viola
- Electronic Colloquium on Computational Complexity
- 2016

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 η/2. We study which tests f : {0, 1}m → [−1, 1] are ε-fooled by D + E, i.e., |E[f(D+E)]−E[f(U)]| ≤ ε where U is the uniform distribution. We show that D+E ε-fools product tests f : ({0,… (More)

- Alan Guo, Elad Haramaty, Madhu Sudan
- 2015 IEEE 56th Annual Symposium on Foundations of…
- 2015

A local tester for a code probabilistically views a small set of coordinates of a given word and based on this local view accepts code words with probability one while rejecting words far from the code with constant probability. A local tester for a code is said to be "robust" if the local views of the tester are far from acceptable views when the word… (More)

- Keren Censor-Hillel, Elad Haramaty, Zohar S. Karnin
- PODC
- 2016

Finding a maximal independent set (MIS) in a graph is a cornerstone task in distributed computing. The local nature of an MIS allows for fast solutions in a static distributed setting, which are logarithmic in the number of nodes or in their degrees. The result trivially applies for the dynamic distributed model, in which edges or nodes may be inserted or… (More)

- Ron Adany, Moran Feldman, +4 authors Tami Tamir
- IPCO
- 2013

We study a variant of the <i>generalized assignment problem</i> (<scp>gap</scp>), which we label <i>all-or-nothing</i> <scp>gap</scp> (<scp>agap</scp>). We are given a set of items, partitioned into <i>n</i> groups, and a set of <i>m</i> bins. Each item ℓ has size <i>s</i><sub>ℓ</sub> > 0, and utility <i>a</i><sub>ℓ<i>j</i></sub> ⩾ 0 if… (More)

- Mohammad Bavarian, Badih Ghazi, Elad Haramaty, Pritish Kamath, Ronald L. Rivest, Madhu Sudan
- Electronic Colloquium on Computational Complexity
- 2016

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 minimize the probability that… (More)