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Monographs in Theoretical Computer Science. An EATCS Series

Deterministic Extraction from Weak Random Sources

Authors: Gabizon, Ariel

  • Constructs deterministic extractors for several types of sources
  • Examines deterministic extractors for bit-fixing sources, for affine sources and polynomial sources over large fields
  • This first complete treatment of the topic introduces new results
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  • ISBN 978-3-642-14903-0
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  • ISBN 978-3-642-14902-3
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  • ISBN 978-3-642-26538-9
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About this book

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.

Reviews

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)


Table of contents (5 chapters)

  • Introduction

    Gabizon, Ariel

    Pages 1-10

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  • Deterministic Extractors for Bit-Fixing Sources by Obtaining an Independent Seed

    Gabizon, Ariel

    Pages 11-32

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  • Deterministic Extractors for Affine Sources over Large Fields

    Gabizon, Ariel

    Pages 33-53

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  • Extractors and Rank Extractors for Polynomial Sources

    Gabizon, Ariel

    Pages 55-89

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  • Increasing the Output Length of Zero-Error Dispersers

    Gabizon, Ariel

    Pages 91-122

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Buy this book

eBook n/a
  • ISBN 978-3-642-14903-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-642-14902-3
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-3-642-26538-9
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Deterministic Extraction from Weak Random Sources
Authors
Series Title
Monographs in Theoretical Computer Science. An EATCS Series
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-14903-0
DOI
10.1007/978-3-642-14903-0
Hardcover ISBN
978-3-642-14902-3
Softcover ISBN
978-3-642-26538-9
Series ISSN
1431-2654
Edition Number
1
Number of Pages
XII, 148
Topics