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Deterministic Extractors For Small-Space Sources Jesse Kamp
 

Summary: Deterministic Extractors For Small-Space Sources
Jesse Kamp
Anup Rao
Salil Vadhan
David Zuckerman
May 11, 2010
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 2s
branching programs.
Specifically, there is a constant > 0 such that for any > n-
, our algorithm extracts m = (-)n bits
that are exponentially close to uniform (in variation distance) from space s sources with min-entropy n,
where s = (3
n). Previously, nothing was known for 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

  

Source: Anderson, Richard - Department of Computer Science and Engineering, University of Washington at Seattle
Zuckerman, David - Department of Computer Sciences, University of Texas at Austin

 

Collections: Computer Technologies and Information Sciences