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Deterministic Extraction from Weak Random Sources

By Ariel Gabizon

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In this research monograph, the author constructs deterministic extractors for several types of sources, using a methodology of recycling randomness which enables increasing the output length of deterministic extractors to near optimal length.

Full Description

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  • ISBN13: 978-3-6421-4902-3
  • 160 Pages
  • User Level: Science
  • Publication Date: October 7, 2010
  • Available eBook Formats: PDF

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Full Description
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.
Table of Contents

Table of Contents

  1. Introduction Deterministic Extractors for Bit
  2. Fixing Sources by Obtaining an Independent Seed Deterministic Extractors for Affine Sources Over Large Fields Extractors and Rank Extractors for Polynomial Sources Increasing the Output Length of Zero
  3. Error Dispersers App. A, Sampling and Partitioning App. B, Basic Notions from Algebraic Geometry Bibliography
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