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DIMACS Theory of Computing Seminar

On polynomial approximations to AC0

Location:  Other - CoRE 301
Date & time: Wednesday, 14 September 2016 at 11:00AM - 11:11AM

Prahladh Harsha, TIFR (long term visitor at RU/DIMACS): In this talk, we will discuss some questions related to polynomial approximations of AC0. A classic result due to Tarui (1991) and Beigel, Reingold, and Spielman (1991), states that any AC0 circuit of size s and depth d has an ?-error probabilistic polynomial over the reals of degree at most (log(s~?))^{O(d)}. We will have a re-look at this construction and show how to improve the bound to (log s)^{O(d)}?log(1~?), which is much better for small values of ?.

As an application of this result, we show that (log s)^{O(d)}?log(1~?)-wise independence fools AC0, improving on Tal's strengthening of Braverman's theorem that (log(s~?))^{O(d)}-wise independence fools AC0. Time permitting, we will also discuss some lower bounds on the best polynomial approximations to AC0.

Joint work with Srikanth Srinivasan

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