[Colloquium] Theory Seminars at Computer Science

[Donna Brooms via Colloquium]

Department of Computer Science & Mathematics

Combinatorics & Theoretical Seminar

 Rocco Served (Columbia University)

Tuesday, November 14, 2017

Ryerson 251 @ 3:30 pm

Title: Fooling Intersections of low-weight halfspaces

Abstract:

A weight-$t$ halfspace is a Boolean function $f(x)=\mathrm{sign}(w_1 x_1 + \cdots + w_n x_n - \theta)$ where each $w_i$ is an integer in $\{-t,\dots,t\}.$  We give an explicit pseudorandom generator that $\delta$-fools any intersection of $k$ weight-$t$ halfspaces with seed length poly$(\log n, \log k,t,1/\delta)$. In particular, our result gives an explicit PRG that fools any intersection of any quasipoly$(n)$ number of halfspaces of any polylog$(n)$ weight to any $1/$polylog$(n)$ accuracy using seed length polylog$(n).$

Prior to this work no explicit PRG with seed length $o(n)$ was known even for fooling intersections of $n$ weight-1 halfspaces to constant accuracy.

Our analysis introduces new coupling-based ingredients into the standard Lindeberg method for establishing quantitative central limit theorems and associated pseudorandomness results.

Joint work with Li-Yang Tan. 

Host: Prof. Li-Yang Tan

(Refreshments will be served prior to the talk in Ry. 255 @ 3pm)

 
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