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A New Look at Survey Propagation and its Generalizations
"... We study the survey propagation algorithm [19, 5, 4], which is an iterative technique that appears to be very effective in solving random kSAT problems even with densities close to threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), ..."
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Cited by 49 (13 self)
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We study the survey propagation algorithm [19, 5, 4], which is an iterative technique that appears to be very effective in solving random kSAT problems even with densities close to threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), parameterized by a real number ρ. We then show that applying belief propagation— a wellknown “messagepassing” technique—to this family of MRFs recovers various algorithms, ranging from pure survey propagation at one extreme (ρ = 1) to standard belief propagation on the uniform distribution over SAT assignments at the other extreme (ρ = 0). Configurations in these MRFs have a natural interpretation as generalized satisfiability assignments, on which a partial order can be defined. We isolate cores as minimal elements in this partial
Pruning processes and a new characterization of convex geometries
, 2007
"... We provide a new characterization of convex geometries via a multivariate version of an identity that was originally proved by Maneva, Mossel and Wainwright for particular combinatorial objects defined in the context of the kSAT problem. We thus highlight the connection between various characteriz ..."
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Cited by 2 (1 self)
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We provide a new characterization of convex geometries via a multivariate version of an identity that was originally proved by Maneva, Mossel and Wainwright for particular combinatorial objects defined in the context of the kSAT problem. We thus highlight the connection between various characterizations of convex geometries and a family of removal processes studied in the literature on random structures. 1
Convex geometries in ksat problems
, 2007
"... In analyzing the survey propagation algorithm, Maneva, Mossel, and Wainwright discovered a polynomial identity that holds for a Boolean formula F and a satisfying assignment a. We show that F and a give rise to a convex geometry, and that convex geometries are precisely the combinatorial objects sat ..."
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Cited by 2 (1 self)
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In analyzing the survey propagation algorithm, Maneva, Mossel, and Wainwright discovered a polynomial identity that holds for a Boolean formula F and a satisfying assignment a. We show that F and a give rise to a convex geometry, and that convex geometries are precisely the combinatorial objects satisfying (the multivariate analog of) that polynomial identity. 1
Pruning Processes and a New Characterization of Convex Geometries
, 2008
"... We provide a new characterization of convex geometries via a multivariate version of an identity that was originally proved by Maneva, Mossel and Wainwright for certain combinatorial objects arising in the context of the kSAT problem. We thus highlight the connection between various characterizatio ..."
Abstract
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We provide a new characterization of convex geometries via a multivariate version of an identity that was originally proved by Maneva, Mossel and Wainwright for certain combinatorial objects arising in the context of the kSAT problem. We thus highlight the connection between various characterizations of convex geometries and a family of removal processes studied in the literature on random structures.
Probabilistic Analysis of Satisfiability Algorithms
, 2008
"... Probabilistic and averagecase analysis can give useful insight into the question of what algorithms for testing satisfiability might be effective and why. Under certain circumstances, one or more structural properties shared by each of a family or class of expressions may be exploited to solve such ..."
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Probabilistic and averagecase analysis can give useful insight into the question of what algorithms for testing satisfiability might be effective and why. Under certain circumstances, one or more structural properties shared by each of a family or class of expressions may be exploited to solve such expressions efficiently;