Deterministic extractors for small-space sources

Jesse Kamp, Anup Rao, Salil Vadhan, David Zuckerman
2006 Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06  
We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on {0, 1} n as sources generated by width 2 s branching programs. Specifically, there is a constant η > 0 such that for any ζ > n −η , our algorithm extracts m = (δ−ζ)n bits that are exponentially close to uniform (in variation distance) from space s sources with min-entropy δn, where s = Ω(ζ 3 n). Previously, nothing was known for δ ≤ 1/2, even for space 0. Our
more » ... ts are obtained by a reduction to the class of total-entropy independent sources. This model generalizes both the well-studied models of independent sources and symbol-fixing sources. These sources consist of a set of r independent smaller sources over {0, 1} , where the total min-entropy over all the smaller sources is k. We give deterministic extractors for such sources when k is as small as polylog(r), for small enough .
doi:10.1145/1132516.1132613 dblp:conf/stoc/KampRVZ06 fatcat:eiozcwdvnrct5hngkee5h4moha