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We consider the problem of testing if a given function f : F n q → 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 ≈ d/q such that every function of degree greater than d reveals this feature on some t-dimensional affine(More)
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)
In this paper 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 in addition these codes are invariant under affine transformations of the coordinate space. Affine-invariant linear(More)
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)
A local tester for a code probabilistically views a small set of coordinates of a given word and based on this local view accepts codewords 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)
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 &ell; has size <i>s</i><sub>&ell;</sub> &gt; 0, and utility <i>a</i><sub>&ell;<i>j</i></sub> &ges; 0 if(More)
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(More)
I would like to thank my advisor, Prof. Yuval Ishai, for teaching me how research is done, for providing most of the major ideas, insights, questions and answers related to this work and for always having infinite patience and time for me. I would also like to thank Yehudayoff for their helpful input. I would like to thank Yardena Kolet for her ability to(More)