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209
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 386 (15 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...
Limited Discrepancy Search
 In Proceedings IJCAI’95
, 1995
"... Many problems of practical interest can be solved using tree search methods because carefully tuned successor ordering heuristics guide the search toward regions of the space that are likely to contain solutions. For some problems, the heuristics often lead directly to a solution— but not always. Li ..."
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Cited by 304 (5 self)
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Many problems of practical interest can be solved using tree search methods because carefully tuned successor ordering heuristics guide the search toward regions of the space that are likely to contain solutions. For some problems, the heuristics often lead directly to a solution— but not always. Limited discrepancy search addresses the problem of what to do when the heuristics fail. Our intuition is that a failing heuristic might well have succeeded if it were not for a small number of "wrong turns " along the way. For a binary tree of height d, there are only d ways the heuristic could make a single wrong turn, and only d(di)/2 ways it could make two. A small number of wrong turns can be overcome by systematically searching all paths that differ from the heuristic path in at most a small number of decision points, or "discrepancies." Limited discrepancy search is a backtracking algorithm that searches the nodes of the tree in increasing order of such discrepancies. We show formally and experimentally that limited discrepancy search can be expected to outperform existing approaches. 1
Sato: An efficient propositional prover.
 In Proceedings of the International Conference on Automated Deduction. Lecture Notes in Artificial Intelligence
, 1997
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Knowledge compilation and theory approximation
 Journal of the ACM
, 1996
"... Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often t ..."
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Cited by 185 (5 self)
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Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often too restrictive for practical applications, whereas the latter leads to uncertainty about exactly what can and cannot be inferred from the knowledge base. We present a third alternative, in which knowledge given in a general representation language is translated (compiled) into a tractable form — allowing for efficient subsequent query answering. We show how propositional logical theories can be compiled into Horn theories that approximate the original information. The approximations bound the original theory from below and above in terms of logical strength. The procedures are extended to other tractable languages (for example, binary clauses) and to the firstorder case. Finally, we demonstrate the generality of our approach by compiling concept descriptions in a general framebased language into a tractable form.
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 174 (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.
An Algorithm to Evaluate Quantified Boolean Formulae and its Experimental Evaluation
 Journal of Automated Reasoning
, 1999
"... The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that ..."
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Cited by 155 (5 self)
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The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that extends propositional logic in a way such that many advanced forms of propositional reasoning, e.g., circumscription, can be easily formulated as evaluation of a QBF. Algorithms for evaluation of QBFs are suitable for the experimental analysis on a wide range of complexity classes, a property not easily found in other formalisms. Evaluate is based on a generalization of the DavisPutnam procedure for SAT, and is guaranteed to work in polynomial space. Before presenting the algorithm, we discuss several abstract properties of QBFs that we singled out to make it more efficient. We also discuss various options that were investigated about heuristics and data structures, and report the main res...
The Quest for Efficient Boolean Satisfiability Solvers
, 2002
"... has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL ..."
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Cited by 149 (3 self)
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has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL) about forty years ago, this area has seen active research effort with many interesting contributions that have culminated in stateoftheart SAT solvers today being able to handle problem instances with thousands, and in same cases even millions, of variables. In this paper we examine some of the main ideas along this passage that have led to our current capabilities. Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. For the most part, we focus on techniques within the basic DPLL search framework, but also briefly describe other approaches and look at some possible future research directions. 1.
Testing Heuristics: We Have It All Wrong
 Journal of Heuristics
, 1995
"... The competitive nature of most algorithmic experimentation is a source of problems that are all too familiar to the research community. It is hard to make fair comparisons between algorithms and to assemble realistic test problems. Competitive testing tells us which algorithm is faster but not w ..."
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Cited by 147 (2 self)
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The competitive nature of most algorithmic experimentation is a source of problems that are all too familiar to the research community. It is hard to make fair comparisons between algorithms and to assemble realistic test problems. Competitive testing tells us which algorithm is faster but not why. Because it requires polished code, it consumes time and energy that could be spent doing more experiments. This paper argues that a more scientific approach of controlled experimentation, similar to that used in other empirical sciences, avoids or alleviates these problems. We have confused research and development; competitive testing is suited only for the latter. Most experimental studies of heuristic algorithms resemble track meets more than scientific endeavors. Typically an investigator has a bright idea for a new algorithm and wants to show that it works better, in some sense, than known algorithms. This requires computational tests, perhaps on a standard set of benchmark p...
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 145 (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...
Locating the Phase Transition in Binary Constraint Satisfaction Problems
 Artificial Intelligence
, 1994
"... The phase transition in binary constraint satisfaction problems, i.e. the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solutions, as the constraints become tighter, is investigated by examining the behaviour of samples of ..."
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Cited by 135 (4 self)
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The phase transition in binary constraint satisfaction problems, i.e. the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solutions, as the constraints become tighter, is investigated by examining the behaviour of samples of randomlygenerated problems. In contrast to theoretical work, which is concerned with the asymptotic behaviour of problems as the number of variables becomes larger, this paper is concerned with the location of the phase transition in finite problems. The accuracy of a prediction based on the expected number of solutions is discussed; it is shown that the variance of the number of solutions can be used to set bounds on the phase transition and to indicate the accuracy of the prediction. A class of sparse problems, for which the prediction is known to be inaccurate, is considered in detail; it is shown that, for these problems, the phase transition depends on the topology of the constraint gr...