Kamp, JesseRao, AnupVadhan, SalilZuckerman, David2014-08-192011Kamp, Jesse, Anup Rao, Salil Vadhan, and David Zuckerman. 2011. Deterministic Extractors for Small-Space Sources. Journal of Computer and System Sciences 77, no. 1: 191–220.0022-0000http://nrs.harvard.edu/urn-3:HUL.InstRepos:12724035We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on n{0,1} as sources generated by width s2 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(ζ3n). Previously, nothing was known for δ≤1/2, even for space 0. Our results 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 ℓ{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 ℓ.en-USRandomness extractorsPseudorandomnessMarkov chainsSamplable sourcesBit-fixing sourcesIndependent sourcesJournal Article2014-08-1910.1016/j.jcss.2010.06.014