Amir Shpilka

In this paper we introduce a new model for computing=20

polynomials - a depth 2 circuit with a symmetric gate at the top=20

and plus gates at the bottom, i.e the circuit computes a=20

symmetric function in linear functions -

$S_{m}^{d}(\ell_1,\ell_2,...,\ell_m)$ ($S_{m}^{d}$ is the $d$'th=20

elementary symmetric polynomial in $m$ ...
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Nayantara Bhatnagar, Parikshit Gopalan, Richard J. Lipton

We study the problem of representing symmetric Boolean functions as symmetric polynomials over Z_m. We show an equivalence between such

representations and simultaneous communication protocols. Computing a function with a polynomial of degree d modulo m=pq is equivalent to a two player protocol where one player is given the first ...
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Parikshit Gopalan, Amir Yehudayoff

This paper studies the elementary symmetric polynomials $S_k(x)$ for $x \in \mathbb{R}^n$. We show that if $|S_k(x)|,|S_{k+1}(x)|$ are small for some $k>0$ then $|S_\ell(x)|$ is also small for all $\ell > k$. We use this to prove probability tail bounds for the symmetric polynomials when the inputs are only $t$-wise ... more >>>