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118
A New Method for Solving Hard Satisfiability Problems
 AAAI
, 1992
"... We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approac ..."
Abstract

Cited by 679 (20 self)
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We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the DavisPutnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, Nqueens, and Boolean induction. General application strategies and limitations of the approach are also discussed. GSAT is best viewed as a modelfinding procedure. Its good performance suggests that it may be advantageous to reformulate reasoning tasks that have traditionally been viewed as theoremproving problems as modelfinding tasks.
Planning as satisfiability
 IN ECAI92
, 1992
"... We develop a formal model of planning based on satisfiability rather than deduction. The satis ability approach not only provides a more flexible framework for stating di erent kinds of constraints on plans, but also more accurately reflects the theory behind modern constraintbased planning systems ..."
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Cited by 429 (25 self)
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We develop a formal model of planning based on satisfiability rather than deduction. The satis ability approach not only provides a more flexible framework for stating di erent kinds of constraints on plans, but also more accurately reflects the theory behind modern constraintbased planning systems. Finally, we consider the computational characteristics of the resulting formulas, by solving them with two very different satisfiability testing procedures.
Algorithms for Constraint Satisfaction Problems: A Survey
 AI MAGAZINE
, 1992
"... A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic ..."
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Cited by 368 (0 self)
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A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.
GSAT and Dynamic Backtracking
 Journal of Artificial Intelligence Research
, 1994
"... There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new te ..."
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Cited by 358 (14 self)
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There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new technique that combines these two approaches. The algorithm allows substantial freedom of movement in the search space but enough information is retained to ensure the systematicity of the resulting analysis. Bounds are given for the size of the justification database and conditions are presented that guarantee that this database will be polynomial in the size of the problem in question. 1 INTRODUCTION The past few years have seen rapid progress in the development of algorithms for solving constraintsatisfaction problems, or csps. Csps arise naturally in subfields of AI from planning to vision, and examples include propositional theorem proving, map coloring and scheduling problems. The probl...
Operations for Learning with Graphical Models
 Journal of Artificial Intelligence Research
, 1994
"... This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models ..."
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Cited by 246 (12 self)
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This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feedforward networks, and learning Gaussian and discrete Bayesian networks from data. The paper conclu...
DomainIndependent Extensions to GSAT: Solving Large Structured Satisfiability Problems
 PROC. IJCAI93
, 1993
"... GSAT is a randomized local search procedure for solving propositional satisfiability problems (Selman et al. 1992). GSAT can solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the DavisPutnam proc ..."
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Cited by 215 (11 self)
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GSAT is a randomized local search procedure for solving propositional satisfiability problems (Selman et al. 1992). GSAT can solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the DavisPutnam procedure. GSAT also efficiently solves encodings of graph coloring problems, Nqueens, and Boolean induction. However, GSAT does not perform as well on handcrafted encodings of blocksworld planning problems and formulas with a high degree of asymmetry. We present three strategies that dramatically improve GSAT's performance on such formulas. These strategies, in effect, manage to uncover hidden structure in the formula under considerations, thereby significantly extending the applicability of the GSAT algorithm.
Experimental Results on the Crossover Point in Satisfiability Problems
 In Proceedings of the Eleventh National Conference on Artificial Intelligence
, 1993
"... Determining whether a propositional theory is satisfiable is a prototypical example of an NPcomplete problem. Further, a large number of problems that occur in knowledge representation, learning, planning, and other areas of AI are essentially satisfiability problems. This paper reports on a series ..."
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Cited by 201 (3 self)
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Determining whether a propositional theory is satisfiable is a prototypical example of an NPcomplete problem. Further, a large number of problems that occur in knowledge representation, learning, planning, and other areas of AI are essentially satisfiability problems. This paper reports on a series of experiments to determine the location of the crossover point  the point at which half the randomly generated propositional theories with a given number of variables and given number of clauses are satisfiable  and to assess the relationship of the crossover point to the difficulty of determining satisfiability. We have found empirically that, for 3sat, the number of clauses at the crossover point is a linear function of the number of variables. This result is of theoretical interest since it is not clear why such a linear relationship should exist, but it is also of practical interest since recent experiments [ Mitchell et al. 92; Cheeseman et al. 91 ] indicate that the most comput...
Improvements To Propositional Satisfiability Search Algorithms
, 1995
"... ... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable ..."
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Cited by 160 (0 self)
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... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable random 3SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NPcomplete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.
SymmetryBreaking Predicates for Search Problems
, 1996
"... Many reasoning and optimization problems exhibit symmetries. Previous work has shown how special purpose algorithms can make use of these symmetries to simplify reasoning. We present a general scheme whereby symmetries are exploited by adding "symmetrybreaking" predicates to the theory. Our a ..."
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Cited by 158 (0 self)
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Many reasoning and optimization problems exhibit symmetries. Previous work has shown how special purpose algorithms can make use of these symmetries to simplify reasoning. We present a general scheme whereby symmetries are exploited by adding "symmetrybreaking" predicates to the theory. Our approach
Experimental Results on the Crossover Point in Random 3sat
 Artificial Intelligence
, 1996
"... Determining whether a propositional theory is satisfiable is a prototypical example of an NPcomplete problem. Further, a large number of problems that occur in knowledgerepresentation, learning, planning, and other ares of AI are essentially satisfiability problems. This paper reports on the most ..."
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Cited by 136 (5 self)
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Determining whether a propositional theory is satisfiable is a prototypical example of an NPcomplete problem. Further, a large number of problems that occur in knowledgerepresentation, learning, planning, and other ares of AI are essentially satisfiability problems. This paper reports on the most extensive set of experiments to date on the location and nature of the crossover point in satisfiability problems. These experiments generally confirm previous results with two notable exceptions. First, we have found that neither of the functions previously proposed accurately models the location of the crossover point. Second, we have found no evidence of any hard problems in the underconstrained region. In fact the hardest problems found in the underconstrained region were many times easier than the easiest unsatisfiable problems found in the neighborhood of the crossover point. We offer explanations for these apparent contradictions of previous results. This work has been supported ...