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Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 127 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Algorithms for Combinatorial Optimization in Real Time and their Automated Refinement by Genetic Programming
 University of Illinois at UrbanaChampaign
, 1994
"... The goal of this research is to develop a systematic, integrated method of designing efficient search algorithms that solve optimization problems in real time. Search algorithms studied in this thesis comprise metacontrol and primitive search. The class of optimization problems addressed are called ..."
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Cited by 7 (1 self)
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The goal of this research is to develop a systematic, integrated method of designing efficient search algorithms that solve optimization problems in real time. Search algorithms studied in this thesis comprise metacontrol and primitive search. The class of optimization problems addressed are called combinatorial optimization problems, examples of which include many NPhard scheduling and planning problems, and problems in operations research and artificialintelligence applications. The problems we have addressed have a welldefined problem objective and a finite set of welldefined problem constraints. In this research, we use statespace trees as problem representations. The approach we have undertaken in designing efficient search algorithms is an engineering approach and consists of two phases: (a) designing generic search algorithms, and (b) improving by geneticsbased machine learning methods parametric heuristics used in the search algorithms designed. Our approach is a systematic method that integrates domain knowledge, search techniques, and automated learning techniques for designing better search algorithms. Knowledge captured in designing one search algorithm can be carried over for designing new ones. iv ACKNOWLEDGEMENTS I express my sincere gratitude to all the people who have helped me in the course of my graduate study. My thesis advisor, Professor Benjamin W. Wah, was always available for discussions and encouraged me to explore new ideas. I am deeply grateful to the committee
Convergence Properties of Optimization Algorithms for the Satisfiability (SAT) Problem
 IEEE Trans. on Computers
, 1996
"... : The satisfiability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms t ..."
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Cited by 2 (1 self)
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: The satisfiability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real space has been developed [31, 35, 34, 32]. Many optimization techniques, such as the steepest descent method, Newton's method, and the coordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution is sufficiently close to the optimal solution, the steepest descent method has a linear convergence ratio fi ! 1, Newton's method has a convergence ratio of order two, and the convergence ratio of the steepest descent method is approximately (1 \Gamma fi=m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the...