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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 131 (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...
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...
A Macro Actor/Token Implementation of Production Systems on a Dataflow Multiprocessor+
"... The importance of production systems in artificial intelligence has been repeatedly demonstrated by a number of expert systems. Much effort has therefore been expended on finding an efficient processing mechanism to process production systems. While dataflow principles of execution offer the promis ..."
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The importance of production systems in artificial intelligence has been repeatedly demonstrated by a number of expert systems. Much effort has therefore been expended on finding an efficient processing mechanism to process production systems. While dataflow principles of execution offer the promise of high programmability for numerical computations, we study here variable resolution actors, called macro actors, a processing mechanism for production systems. Characteristics of the production system paradigm are identified, based on which we introduce the concept of macro tokens as a companion to macro actors. Aset of guidelines is identified in the context of production systems to derive wellformed macro actors from primitive micro actors. Parallel pattern matching is written in macro actors/tokens to be executed on our Macro Dataflow simulator. Simulation results demonstrate that the macro approach can be an efficient implementation of production systems. 1.