Extracting randomness from samplable distributions
Trevisan, L.
Vadhan, S.
Dept. of Comput. Sci., Columbia Univ., New York, NY;
This paper appears in: Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on
Publication Date: 2000
On page(s): 32-42
Meeting Date: 11/12/2000 - 11/14/2000
Location: Redondo Beach, CA, USA
ISBN: 0-7695-0850-2
References Cited: 51
INSPEC Accession Number: 6784289
Digital Object Identifier: 10.1109/SFCS.2000.892063
Current Version Published: 2002-08-06
Abstract
The standard notion of a randomness extractor is a procedure which
converts any weak source of randomness into an almost uniform
distribution. The conversion necessarily uses a small amount of pure
randomness, which can be eliminated by complete enumeration in some, but
not all, applications. We consider the problem of deterministically
converting a weak source of randomness into an almost uniform
distribution. Previously, deterministic extraction procedures were known
only for sources satisfying strong independence requirements. We look at
sources which are samplable, i.e. can be generated by an efficient
sampling algorithm. We seek an efficient deterministic procedure that,
given a sample from any samplable distribution of sufficiently large
min-entropy, gives an almost uniformly distributed output. We explore
the conditions under which such deterministic extractors exist. We
observe that no deterministic extractor exists if the sampler is allowed
to use more computational resources than the extractor. On the other
hand, if the extractor is allowed (polynomially) more resources than the
sampler, we show that deterministic extraction becomes possible. This is
true unconditionally in the nonuniform setting (i.e., when the extractor
can be computed by a small circuit), and (necessarily) relies on
complexity assumptions in the uniform setting
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