# Seminars & Colloquia Calendar

DIMACS Theory of Computing Seminar

## Hitting Sets with Near-Optimal Error for Read-Once Branching Programs

#### Sumegha Garg, Princeton University

Location:  CoRE 301
Date & time: Wednesday, 28 March 2018 at 11:00AM - 12:00PM

Abstract:  Nisan [Nis92] constructed a pseudorandom generator for length n, width n read-once branching programs (ROBPs) with error $$\varepsilon$$ and seed length $$O(log^2(n) + log(n) · log(1/\varepsilon))$$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $$O(log(n) + log(1/\varepsilon))$$, or to construct improved hitting sets, as these would yield stronger derandomization of BPL and RL, respectively.

In this talk, we make the first improvement by constructing a hitting set with seed length $$~O?(log^2(n) + log(1/\varepsilon))$$. That is, we decouple $$\varepsilon$$ and n, and obtain near-optimal dependence on the former. The regime of parameters in which our construction strictly improves upon prior works, namely, $$log(1/\varepsilon) log n$$, is well- motivated by the work of Saks and Zhou [SZ99] who use pseudorandom generators with error $$\varepsilon = 2^{-log^2(n)}$$ in their proof for $$BPL \subseteq L^{3/2}$$.

Joint work with Mark Braverman and Gil Cohen.

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