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Master's Dissertation
DOI
10.11606/D.45.2007.tde-04052007-160412
Document
Author
Full name
Domingos Dellamonica Junior
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2007
Supervisor
Committee
Kohayakawa, Yoshiharu (President)
Krauskopf, Marcos Abraham Kiwi
Mandel, Arnaldo
Title in Portuguese
Extração de aleatoriedade a partir de fontes defeituosas
Keywords in Portuguese
aleatoriedade
algoritmos
combinatória
complexidade computacional
desaleatorização
pseudoaleatoriedade
teoria aditiva dos números
Abstract in Portuguese
Recentemente, Barak et al. (2004) exibiram construções de extratores e dispersores determinísticos (funções computáveis em tempo polinomial) com parâmetros melhores do que era anteriormente possível. Introduziremos os conceitos envolvidos em tal trabalho e mencionaremos suas aplicações; em particular, veremos como é possível obter cotas muito melhores para o problema Ramsey bipartido (um problema bem difícil) utilizando as construções descritas no artigo. Também apresentamos resultados originais para melhorar tais construções. Tais idéias são inspiradas no trabalho de Anup Rao (2005) e utilizam o recente êxito de Jean Bourgain (2005) em obter extratores que quebram a "barreira 1/2".
Title in English
Randomness extraction from weak random sources
Keywords in English
additive number theory
algorithms
combinatorics
computational complexity
dispersers
extractors
pseudorandomness
randomness
Abstract in English
Recently, Barak et al. (2004) constructed explicit deterministic extractors and dispersers (these are polynomial-time computable functions) with much better parameters than what was known before. We introduce the concepts involved in such a construction and mention some of its applications; in particular, we describe how it is possible to obtain much better bounds for the bipartite Ramsey problem (a very hard problem) using the machinery developed in that paper. We also present some original results that improve on these constructions. They are inspired by the work of Anup Rao (2005) and uses the recent breakthrough of Jean Bourgain (2005) in obtaining 2-source extractors that break the "1/2-barrier".
 
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diss.pdf (586.16 Kbytes)
Publishing Date
2007-06-22
 
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