Deterministic extractors for small-space sources

  • Authors:
  • Jesse Kamp;Anup Rao;Salil Vadhan;David Zuckerman

  • Affiliations:
  • Oracle Corporation, 500 Oracle Parkway, Redwood Shores, CA 94065, United States;Institute for Advanced Study, Princeton, NJ 08540, United States;School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, United States;Department of Computer Science, University of Texas, Austin, TX 78712, United States

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2011

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Abstract

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 @h0 such that for any @zn^-^@h, our algorithm extracts m=(@d-@z)n bits that are exponentially close to uniform (in variation distance) from space s sources with min-entropy @dn, where s=@W(@z^3n). Previously, nothing was known for @d=