NDLI: Deterministic Extractors for Small-Space Sources

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Deterministic Extractors for Small-Space Sources

Content Provider	Semantic Scholar
Author	Rao, Anup Vadhan, Salil P. Kamp, Jesse Zuckerman, David
Copyright Year	2010
Abstract	We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on {0, 1} as sources generated by width 2 branching programs. Specifically, there is a constant η > 0 such that for any ζ > n−η , our algorithm extractsm = (δ−ζ)n bits that are exponentially close to uniform (in variation distance) from space s sources with min-entropy δn, where s = Ω(ζn). 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 {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 `. ∗A preliminary version of this paper appeared in the Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pages 691–700, 2006. †Oracle Corporation, 500 Oracle Parkway, Redwood Shores, CA 94065, (jesse.kamp@oracle.com). Supported in part by NSF Grant CCR-0310960. ‡Institute for Advanced Study, Princeton, NJ 08540, (arao@ias.edu). Supported in part by NSF Grants CCR-0310960, CCF-0832797, and DMS-0835373. §School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, (salil@eecs.harvard.edu). Supported by NSF grant CCF-0133096, ONR grant N00014-04-1-0478, and US-Israel BSF grant 2002246. ¶Department of Computer Science, University of Texas, Austin, TX 78712, (diz@cs.utexas.edu). Supported in part by a David and Lucile Packard Fellowship for Science and Engineering, NSF Grants CCR-0310960 and CCF-0634811, a Radcliffe Institute Fellowship, and a Guggenheim Fellowship.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://dash.harvard.edu/bitstream/handle/1/12724035/small-space.pdf?isAllowed=y&sequence=1
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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