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Master's Dissertation
DOI
10.11606/D.45.2011.tde-02062011-181639
Document
Author
Full name
Glauber de Bona
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Finger, Marcelo (President)
Aragão, Marcus Vinicius Soledade Poggi de
Cozman, Fabio Gagliardi
Title in Portuguese
Satisfazibilidade probabilística
Keywords in Portuguese
lógica probabilística
redução de Turing
redução polinomial
satisfazibilidade (SAT)
satisfazibilidade probabilística (PSAT)
transição de fase
Abstract in Portuguese
Este trabalho estuda o problema da Satisfazibilidade Probabilística (PSAT), revendo a sua solução via programação linear, além de propor novos algoritmos para resolvê-lo através da redução ao SAT. Construímos uma redução polinomial do PSAT para o SAT, chamada de Redução Canônica, codificando operações da aritmética racional em bits, como variáveis lógicas. Analisamos a complexidade computacional dessa redução e propomos uma Redução Canônica de Precisão Limitada para contornar tal complexidade. Apresentamos uma Redução de Turing do PSAT ao SAT, baseada no algoritmo Simplex e na Forma Normal Atômica que introduzimos. Sugerimos modificações em tal redução em busca de eficiência computacional. Por fim, implementamos essas reduções a m de investigar o perl de complexidade do PSAT, observamos o fenômeno de transição de fase e discutimos as condições para sua detecção.
Title in English
Probabilistic satisfiability
Keywords in English
phase transition
polynomial reduction
probabilistic logic
probabilistic satisfiability (PSAT)
satisfiability (SAT)
Turing reduction
Abstract in English
This work studies the Probabilistic Satisfiability problem (PSAT), reviewing its solution through linear programming, and proposing new algorithms to solve it. We construct a polynomial many-to-one reduction from PSAT to SAT, called Canonical Reduction, codifying rational arithmetic operations into bits, as logical variables. We analyze the computational complexity of this reduction and we propose a Limited Precision Canonical Reduction to reduce such complexity. We present a Turing Reduction from PSAT to SAT, based on the Simplex algorithm and the Atomic Normal Form we introduced. We suggest modifications in such reduction looking for computational eficiency. Finally, we implement these reductions in order to investigate the complexity profile of PSAT, the phase transition phenomenom is observed and the conditions for its detection are discussed.
 
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tese.pdf (1.06 Mbytes)
Publishing Date
2011-07-20
 
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