Deterministic Extraction from Weak Random Sources

ISBN-13: 9783642265389 / Angielski / Miękka / 2012 / 148 str.

Ariel Gabizon

Opis

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.

Recenzje

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)

Spis treści

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

Blurb

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.