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Unsatisfied variables in local search
 HYBRID PROBLEMS, HYBRID SOLUTIONS, TENTH BIENNIAL CONFERENCE ON AI AND COGNITIVE SCIENCE, IOS
, 1995
"... Several local search algorithms for propositional satis ability havebeen proposed which can solve hard random problems beyond the range of conventional backtracking procedures. In this paper, we explore the impact of focusing search in these procedures on the "unsatisfied variables"; that is, those ..."
Abstract

Cited by 45 (2 self)
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Several local search algorithms for propositional satis ability havebeen proposed which can solve hard random problems beyond the range of conventional backtracking procedures. In this paper, we explore the impact of focusing search in these procedures on the "unsatisfied variables"; that is, those variables which appear in clauses which are not yet satisfied. For random problems, we show that such a focus reduces the sensitivity to input parameters. We also observe a simple scaling law in performance. For nonrandom problems, we showthat whilst this focus can improve performance, many problems remain difficult. We speculate that such problems will remain hard for local search unless constraint propagation techniques can be combined with hillclimbing.
Formal Theory Building Using Automated Reasoning Tools
 In
, 1998
"... The merits of representing scientific theories in formal logic are wellknown. Expressing a scientific theory in formal logic explicates the theory as a whole, and the logic provides formal criteria for evaluating the theory, such as soundness and consistency. On the one hand, these criteria corresp ..."
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Cited by 6 (6 self)
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The merits of representing scientific theories in formal logic are wellknown. Expressing a scientific theory in formal logic explicates the theory as a whole, and the logic provides formal criteria for evaluating the theory, such as soundness and consistency. On the one hand, these criteria correspond to natural questions to be asked about the theory: is the theory contradictionfree? (is the theory logically consistent?) is the theoretical argumentation valid? (can a theorem be soundly derived from the premises?) and other such questions. On the other hand, testing for these criteria amounts to making many specific proof attempts or model searches: respectively, does the theory have a model? can we find a proof of a particular theorem? As a result, testing for these criteria quickly defies manual processing. Fortunately, automated reasoning provides some valuable tools for this endeavor. This paper discusses the use of firstorder logic and existing automated rea...
The Partial Rehabilitation of Propositional Resolution
, 1996
"... Resolution has not been an effective tool for deciding satisfiability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satisfiable. A new pruning method is described, which is designed to eliminate certain refutation attempts that cannot succeed. ..."
Abstract

Cited by 6 (3 self)
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Resolution has not been an effective tool for deciding satisfiability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satisfiable. A new pruning method is described, which is designed to eliminate certain refutation attempts that cannot succeed. The method exploits the concept of "autarky", which was introduced by Monien and Speckenmeyer. New forms of lemma creation are also introduced, which eliminate the need to carry out refutation attempts that must succeed. The resulting algorithm, called "Modoc", is a modification of propositional model elimination. Informally, an autarky is a "selfsufficient" model for some clauses, but which does not affect the remaining clauses of the formula. Whereas Monien and Speckenmeyer's work was oriented toward finding a model, our method has as its primary goal to find a refutation in the style of model elimination. However, Modoc finds a model if it fails to find a refutation, essentially by combi...
Lemma and Cut Strategies for TwoSided Propositional Resolution (Extended Abstract)
, 1996
"... Resolution has not been an effective tool for deciding satisfiability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satisfiable. However, a new pruning method, which is designed to eliminate certain refutation attempts that cannot succeed, has ..."
Abstract
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Resolution has not been an effective tool for deciding satisfiability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satisfiable. However, a new pruning method, which is designed to eliminate certain refutation attempts that cannot succeed, has been shown to eliminate much of the redundancy of propositional model elimination. The pruning method exploits the concept of "autarky", which was introduced by Monien and Speckenmeyer. Informally, an autarky is a "selfsufficient" model for some clauses, but which does not affect the remaining clauses of the formula. Autarky pruning permits the algorithm, called "Modoc", to be "twosided" in the sense that it constructs a model if the formula is satisfiable and constructs a refutation proof if it is not. This talk describes new "lemma" and "cut" strategies that are efficient to apply in the setting of propositional resolution. It builds upon the Cliteral strategy proposed by Shostak, and s...