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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.
Contents
Introduction
Deterministic Extractors for Bit-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-Error Dispersers
App. A, Sampling and Partitioning
App. B, Basic Notions from Algebraic Geometry
Bibliography
