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38
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.
Local Search Strategies for Satisfiability Testing
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1995
"... It has recently been shown that local search is surprisingly good at finding satisfying assignments for certain classes of CNF formulas [24]. In this paper we demonstrate that the power of local search for satisfiability testing can be further enhanced by employinga new strategy, called "mixed rando ..."
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Cited by 269 (24 self)
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It has recently been shown that local search is surprisingly good at finding satisfying assignments for certain classes of CNF formulas [24]. In this paper we demonstrate that the power of local search for satisfiability testing can be further enhanced by employinga new strategy, called "mixed random walk", for escaping from local minima. We present experimental results showing how this strategy allows us to handle formulas that are substantially larger than those that can be solved with basic local search. We also present a detailed comparison of our random walk strategy with simulated annealing. Our results show that mixed random walk is the superior strategy on several classes of computationally difficult problem instances. Finally, we present results demonstrating the effectiveness of local search with walk for solving circuit synthesis and diagnosis problems.
Hard and Easy Distributions of SAT Problems
, 1992
"... We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to ..."
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Cited by 218 (17 self)
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We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult. Our results provide a benchmark for the evaluation of satisfiabilitytesting procedures. Introduction Many computational tasks of interest to AI, to the extent that they can be precisely characterized at all, can be shown to be NPhard in their most general form. However, there is fundamental disagreement, at least within the AI community, about the implications of this. It is claimed on the one hand that since the performance of algorithms designed to solve NPhard tasks degrades rapidly with small increases in input size, something will need to be given up to obtain acceptable behavior....
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Finding Hard Instances of the Satisfiability Problem: A Survey
, 1997
"... . Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case ..."
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Cited by 113 (1 self)
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. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.
Simplified and Improved Resolution Lower Bounds
 IN PROCEEDINGS OF THE 37TH IEEE FOCS
, 1996
"... We give simple new lower bounds on the lengths of Resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds significantly extend the range of formula sizes for which nontrivial lower bounds are known. For example, we show that with probabili ..."
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Cited by 100 (7 self)
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We give simple new lower bounds on the lengths of Resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds significantly extend the range of formula sizes for which nontrivial lower bounds are known. For example, we show that with probability approaching 1, any Resolution refutation of a randomly chosen 3CNF formula with at most n 6=5\Gammaffl clauses requires exponential size. Previous bounds applied only when the number of clauses was at most linear in the number of variables. For the pigeonhole principle our bound is a small improvement over previous bounds. Our proofs are more elementary than previous arguments, and establish a connection between Resolution proof size and maximum clause size.
Generating Hard Satisfiability Problems
 Artificial Intelligence
, 1996
"... We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible ..."
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Cited by 98 (2 self)
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We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult. Our results provide a benchmark for the evaluation of satisfiabilitytesting procedures. In Artificial Intelligence, 81 (19996) 1729. 1 Introduction Many computational tasks of interest to AI, to the extent that they can be precisely characterized at all, can be shown to be NPhard in their most general form. However, there is fundamental disagreement, at least within the AI community, about the implications of this. It is claimed on the one hand that since the performance of algorithms designed to solve NPhard tasks degrades rapidly with small increases in input size, something ...
Probabilistic Analysis Of A Generalization Of The Unit Clause Literal Selection Heuristic For The KSatisfiability Problem
 INFORMATION SCIENCE
, 1990
"... Two algorithms for the kSatisfiability problem are presented and a probabilistic analysis is performed. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithms assign values to literals appearing in a given instance of ..."
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Cited by 93 (9 self)
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Two algorithms for the kSatisfiability problem are presented and a probabilistic analysis is performed. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithms assign values to literals appearing in a given instance of kSatisfiability, one at a time, until a solution is found or it is discovered that further assignments cannot lead to finding a solution. One algorithm chooses the next literal from a unit clause if one exists and randomly from the set of remaining literals otherwise. The other algorithm uses a generalization of the UnitClause rule as a heuristic for selecting the next literal: at each step a literal is chosen randomly from a clause containing the least number of literals. The algorithms run in polynomial time and it is shown that they find a solution to a random instance of kSatisfiability with probability bounded from below by a constant greater than zero for two different ranges of...
Exploiting the deep structure of constraint problems
 Artificial Intelligence
, 1994
"... We introduce a technique for analyzing the behavior of sophisticated A.I. search programs working on realistic, largescale problems. This approach allows us to predict where, in a space of problem instances, the hardest problems are to be found and where the fluctuations in difficulty are greatest. ..."
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Cited by 72 (8 self)
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We introduce a technique for analyzing the behavior of sophisticated A.I. search programs working on realistic, largescale problems. This approach allows us to predict where, in a space of problem instances, the hardest problems are to be found and where the fluctuations in difficulty are greatest. Our key insight is to shift emphasis from modelling sophisticated algorithms directly to modelling a search space that captures their principal effects. We compare our model’s predictions with actual data on real problems obtained independently and show that the agreement is quite good. By systematically relaxing our underlying modelling assumptions we identify their relative contribution to the remaining error and then remedy it. We also discuss further applications of our model and suggest how this type of analysis can be generalized to other kinds of A.I. problems. Chapter 1
Probabilistic Analysis Of Two Heuristics For The 3Satisfiability Problem
 SIAM JOURNAL ON COMPUTING
, 1986
"... An algorithm for the 3Satisfiability problem is presented and a probabilistic analysis is performed. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithm assigns values to variables appearing in a given instance of 3 ..."
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Cited by 66 (9 self)
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An algorithm for the 3Satisfiability problem is presented and a probabilistic analysis is performed. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithm assigns values to variables appearing in a given instance of 3Satisfiability, one at a time, using the unit clause heuristic and a maximum occurring literal selection heuristic; at each step a variable is chosen randomly from a subset of variables which is usually large. The algorithm runs in polynomial time and it is shown that the algorithm finds a solution to a random instance of 3Satisfiability with probability bounded from below by a constant greater than zero for a range of parameter values. The heuristics studied here can be used to select variables in a Backtrack algorithm for 3Satisfiability. Experiments have shown that for about the same range of parameters as above the Backtrack algorithm using the heuristics finds a solution in polynom...