 
Summary: Deterministic Extractors For SmallSpace Sources
Jesse Kamp
Anup Rao
Salil Vadhan §
David Zuckerman ¶
May 11, 2010
Abstract
We give polynomialtime, 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 minentropy 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 totalentropy independent sources. This model
generalizes both the wellstudied models of independent sources and symbolfixing sources. These
sources consist of a set of r independent smaller sources over {0, 1} , where the total minentropy over
all the smaller sources is k. We give deterministic extractors for such sources when k is as small as
