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292
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 374 (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...
Efficient Conflict Driven Learning in a Boolean Satisfiability Solver
 In ICCAD
, 2001
"... One of the most important features of current stateoftheart SAT solvers is the use of conflict based backtracking and learning techniques. In this paper, we generalize various conflict driven learning strategies in terms of different partitioning schemes of the implication graph. We reexamine th ..."
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Cited by 305 (8 self)
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One of the most important features of current stateoftheart SAT solvers is the use of conflict based backtracking and learning techniques. In this paper, we generalize various conflict driven learning strategies in terms of different partitioning schemes of the implication graph. We reexamine the learning techniques used in various SAT solvers and propose an array of new learning schemes. Extensive experiments with real world examples show that the best performing new learning scheme has at least a 2X speedup compared with learning schemes employed in stateoftheart SAT solvers.
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 168 (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.
Encoding Plans in Propositional Logic
, 1996
"... In recent work we showed that planning problems can be efficiently solved by general propositional satisfiability algorithms (Kautz and Selman 1996). A key issue in this approach is the development of practical reductions of planning to SAT. We introduce a series of different SAT encodings for STRIP ..."
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Cited by 158 (8 self)
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In recent work we showed that planning problems can be efficiently solved by general propositional satisfiability algorithms (Kautz and Selman 1996). A key issue in this approach is the development of practical reductions of planning to SAT. We introduce a series of different SAT encodings for STRIPSstyle planning, which are sound and complete representations of the original STRIPS specification, and relate our encodings to the Graphplan system of Blum and Furst (1995). We analyze the size complexity of the various encodings, both in terms of number of variables and total length of the resulting formulas. This paper complements the empirical evaluation of several of the encodings reported in Kautz and Selman (1996). We also introduce a novel encoding based on the theory of causal planning, that exploits the notionof "lifting" from the theoremproving community. This new encoding strictly dominates the others in terms of asymptotic complexity. Finally, we consider further reductions i...
HeavyTailed Phenomena in Satisfiability and Constraint Satisfaction Problems
 J. of Autom. Reasoning
, 2000
"... Abstract. We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by ver ..."
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Cited by 153 (26 self)
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Abstract. We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or “heavy tails”. We will show that these distributions are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We also show how random restarts can effectively eliminate heavytailed behavior. Furthermore, for harder problem instances, we observe long tails on the lefthand side of the distribution, which is indicative of a nonnegligible fraction of relatively short, successful runs. A rapid restart strategy eliminates heavytailed behavior and takes advantage of short runs, significantly reducing expected solution time. We demonstrate speedups of up to two orders of magnitude on SAT and CSP encodings of hard problems in planning, scheduling, and circuit synthesis. Key words: satisfiability, constraint satisfaction, heavy tails, backtracking 1.
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 134 (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.
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...
Automatic SATCompilation of Planning Problems
 IJCAI97
, 1997
"... Recent work by Kautz et al. provides tantalizing evidence that large, classical planning problems may be efficiently solved by translating them into propositional satisfiability problems, using stochastic search techniques, and translating the resulting truth assignments back into plans for the ..."
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Cited by 129 (10 self)
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Recent work by Kautz et al. provides tantalizing evidence that large, classical planning problems may be efficiently solved by translating them into propositional satisfiability problems, using stochastic search techniques, and translating the resulting truth assignments back into plans for the original problems. We explore the space of such transformations, providing a simple framework that generates eight major encodings (generated by selecting one of four action representations and one of two frame axioms) and a number of subsidiary ones. We describe a fullyimplemented compiler that can generate each of these encodings, and we test the compiler on a suite of STRIPS planning problems in order to determine which encodings have the best properties.
Sound and efficient inference with probabilistic and deterministic dependencies
, 2006
"... Reasoning with both probabilistic and deterministic dependencies is important for many realworld problems, and in particular for the emerging field of statistical relational learning. However, probabilistic inference methods like MCMC or belief propagation tend to give poor results when determin ..."
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Cited by 101 (17 self)
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Reasoning with both probabilistic and deterministic dependencies is important for many realworld problems, and in particular for the emerging field of statistical relational learning. However, probabilistic inference methods like MCMC or belief propagation tend to give poor results when deterministic or neardeterministic dependencies are present, and logical ones like satisfiability testing are inapplicable to probabilistic ones. In this paper we propose MCSAT, an inference algorithm that combines ideas from MCMC and satisfiability. MCSAT is based on Markov logic, which defines Markov networks using weighted clauses in firstorder logic. From the point of view of MCMC,MCSAT is a slice sampler with an auxiliary variable per clause, and with a satisfiabilitybased method for sampling the original variables given the auxiliary ones. From the point of view of satisfiability, MCSAT wraps a procedure around the SampleSAT uniform sampler that enables it to sample from highly nonuniform distributions over satisfying assignments. Experiments on entity resolution and collective classification problems show that MCSAT greatly outperforms Gibbs sampling and simulated tempering over a broad range of problem sizes and degrees of determinism.
Effective Use of Boolean Satisfiability Procedures in the Formal Verification of Superscalar and VLIW Microprocessors
 Journal of Symbolic Computation
, 2001
"... We compare SATcheckers and decision diagrams on the evaluation of Boolean formulas produced in the formal verification of both correct and buggy versions of superscalar and VLIW microprocessors. We identify one SATchecker that significantly outperforms the rest. We evaluate ways to enhance its per ..."
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Cited by 89 (13 self)
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We compare SATcheckers and decision diagrams on the evaluation of Boolean formulas produced in the formal verification of both correct and buggy versions of superscalar and VLIW microprocessors. We identify one SATchecker that significantly outperforms the rest. We evaluate ways to enhance its performance by variations in the generation of the Boolean correctness formulas. We reassess optimizations previously used to speed up the formal verification and probe future challenges.