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A deterministic extractor is a function that extracts almost perfect random bits from a weak random source. In this research monograph the author constructs deterministic extractors for several types of sources. A basic theme in this work is a methodology of recycling randomness which enables increasing the output length of deterministic extractors to near optimal length.The author's main work examines deterministic extractors for bit-fixing sources, deterministic extractors for affine sources and polynomial sources over large fields, and increasing the output length of zero-error dispersers.This work will be of interest to researchers and graduate students in combinatorics and theoretical computer science.
List of contents
IntroductionDeterministic Extractors for Bit-Fixing Sources by Obtaining an Independent SeedDeterministic Extractors for Affine Sources Over Large FieldsExtractors and Rank Extractors for Polynomial SourcesIncreasing the Output Length of Zero-Error DispersersApp. A, Sampling and PartitioningApp. B, Basic Notions from Algebraic GeometryBibliography
Summary
A deterministic extractor is a function that extracts almost perfect random bits from a weak random source. In this research monograph the author constructs deterministic extractors for several types of sources. A basic theme in this work is a methodology of recycling randomness which enables increasing the output length of deterministic extractors to near optimal length.
The author's main work examines deterministic extractors for bit-fixing sources, deterministic extractors for affine sources and polynomial sources over large fields, and increasing the output length of zero-error dispersers.
This work will be of interest to researchers and graduate students in combinatorics and theoretical computer science.
Additional text
From the reviews:
“This monograph is in the European Association for Theoretical Computer Science (EATCS) monograph series. It is an edited version of the author’s PhD thesis. … the book presents probability arguments and methods quite clearly, and in a way that readers can study them separately. Finally, the book contains two very useful appendices, one on probability methods and the other on concepts from algebraic geometry.” (Bruce Litow, ACM Computing Reviews, November, 2011)
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From the reviews:
"This monograph is in the European Association for Theoretical Computer Science (EATCS) monograph series. It is an edited version of the author's PhD thesis. ... the book presents probability arguments and methods quite clearly, and in a way that readers can study them separately. Finally, the book contains two very useful appendices, one on probability methods and the other on concepts from algebraic geometry." (Bruce Litow, ACM Computing Reviews, November, 2011)
