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Towards an understanding of hillclimbing procedures for SAT
 In Proceedings of AAAI93
, 1993
"... Recently several local hillclimbing procedures for propositional satisability havebeen proposed, which are able to solve large and di cult problems beyond the reach ofconventional algorithms like DavisPutnam. By the introduction of some new variants of these procedures, we provide strong experimen ..."
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Cited by 138 (6 self)
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Recently several local hillclimbing procedures for propositional satisability havebeen proposed, which are able to solve large and di cult problems beyond the reach ofconventional algorithms like DavisPutnam. By the introduction of some new variants of these procedures, we provide strong experimental evidence to support the conjecture that neither greediness nor randomness is important in these procedures. One of the variants introduced seems to o er signi cant improvements over earlier procedures. In addition, we investigate experimentally how their performance depends on their parameters. Our results suggest that runtime scales less than simply exponentially in the problem size. 1
Satisfiability Testing with More Reasoning and Less Guessing
, 1995
"... A new algorithm for testing satisfiability of propositional formulas in conjunctive normal form (CNF) is described. It applies reasoning in the form of certain resolution operations, and identification of equivalent literals. Resolution produces growth in the size of the formula, but within a global ..."
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Cited by 56 (10 self)
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A new algorithm for testing satisfiability of propositional formulas in conjunctive normal form (CNF) is described. It applies reasoning in the form of certain resolution operations, and identification of equivalent literals. Resolution produces growth in the size of the formula, but within a global quadratic bound; most previous methods avoid operations that produce any growth, and generally do not identify equivalent literals. Computational experience indicates that the method does substantially less "guessing" than previously reported algorithms, while keeping a polynomial time bound on the work done between guesses. Experiments indicate that, for larger problems, the time investment in reasoning returns a profit in reduced searching, and the profit increases with increasing problem size. Experimental data compares six branching strategies of the proposed algorithm on a variety of problems, including several Dimacs benchmarks. These branching strategies were shown to perform differently with statistical signi cance. A new scheme based on Johnson's maximum satisfiability approximation algorithm was found to be the best overall. Both satisfiable and unsatifi able random 3CNF formulas with 50283 variables and 4.27 ratio of clauses to variables have been tested; this class is generally acknowledged to be relatively "hard" and
Lemma and Cut Strategies for Propositional Model Elimination
 Annals of Mathematics and Artificial Intelligence
, 1999
"... This paper describes new "lemma" and "cut" strategies that are efficient to apply in the setting of propositional Model Elimination. It builds upon the Cliteral strategy proposed by Shostak, and studied further by Letz, Mayr and Goller. Previous strategies for managing lemmas an ..."
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Cited by 9 (6 self)
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This paper describes new "lemma" and "cut" strategies that are efficient to apply in the setting of propositional Model Elimination. It builds upon the Cliteral strategy proposed by Shostak, and studied further by Letz, Mayr and Goller. Previous strategies for managing lemmas and Cliterals in Model Elimination were oriented toward firstorder theorem proving. The original "cumulative" strategy remembers lemmas forever, and was found to be too inefficient. The previously reported Cliteral and unit lemma strategies, such as "strong regularity", forget them unnecessarily soon in the propositional domain. An intermediate strategy, called "quasipersistent" lemmas, is introduced. Supplementing this strategy, methods for "eager" lemmas, and two forms of controlled cut provide further efficiencies. The techniques have been incorporated into Modoc, which is an implementation of Model Elimination, extended with a new pruning method that is designed to eliminate certain refutation attempts th...
Incomplete thoughts about incomplete satisfiability procedures
 Proceedings of the 2nd DIMACS Challenge
, 1993
"... Recent successes with incomplete satis ability procedures raise numerous issues about their uses and evaluation. Most such procedures search for \yes " answers, and give up if they do not nd one. The need for \no " answers as well is addressed. It is shown that a recent approximati ..."
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Cited by 7 (2 self)
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Recent successes with incomplete satis ability procedures raise numerous issues about their uses and evaluation. Most such procedures search for \yes &quot; answers, and give up if they do not nd one. The need for \no &quot; answers as well is addressed. It is shown that a recent approximation algorithm of Yannakakis can produce \no &quot; answers only in somewhat trivial cases. The possibility of salvaging information from a\yes &quot; program that is giving up, and using it to nd a \no &quot; answer is discussed. Two incomplete procedures were studied experimentally. One (based on \easy &quot; resolutions) produces \no &quot; answers. The other (based on Johnson's maximum satis ability approximation algorithm) produces \yes &quot; answers. Both are deterministic, polynomial time algorithms, quadratic with careful implementation. Combined, they solved 83 % of the formulas generated from a circuitbased application, ranging from 400 to over 10000 variables.