Search results for "Local consistency"

showing 3 items of 3 documents

Counting by Statistics on Search Trees: Application to Constraint Satisfaction Problems

1997

In 1975, Knuth proposed a simple statistical method for investigating search trees. We use this technique for estimating the number of solutions of constraint satisfaction problem CSP and boolean satisfiability problem SAT instances. We show that, depending on domain reductions, tree-based estimates have a lower variance than estimates based on uniform sampling from the search space. Nevertheless, because the variance remains extremely high in the general case, a confidence interval cannot be derived, but a lower bound of the number of solutions. These results are confirmed by many experiments.

Complexity of constraint satisfactionBacktrackingConstraint graphArtificial IntelligenceStatisticsConstraint satisfaction dual problemHybrid algorithm (constraint satisfaction)Local consistencyComputer Vision and Pattern RecognitionConstraint satisfactionConstraint satisfaction problemMathematicsTheoretical Computer ScienceIntelligent Data Analysis
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New Encodings of Pseudo-Boolean Constraints into CNF

2009

International audience; This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.

Discrete mathematics[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]Polynomial021103 operations researchUnit propagation[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]0211 other engineering and technologies[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]02 engineering and technologyComputer Science::Computational ComplexityExpressive powerExponential functionCombinatorics[ INFO.INFO-CC ] Computer Science [cs]/Computational Complexity [cs.CC]Encoding (memory)0202 electrical engineering electronic engineering information engineeringLocal consistency020201 artificial intelligence & image processingPoint (geometry)[INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC][ INFO.INFO-DS ] Computer Science [cs]/Data Structures and Algorithms [cs.DS]Mathematics
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Integration of an LP Solver into Interval Constraint Propagation

2011

This paper describes the integration of an LP solver into iSAT, a Satisfiability Modulo Theories solver that can solve Boolean combinations of linear and nonlinear constraints. iSAT is a tight integration of the well-known DPLL algorithm and interval constraint propagation allowing it to reason about linear and nonlinear constraints. As interval arithmetic is known to be less efficient on solving linear programs, we will demonstrate how the integration of an LP solver can improve the overall solving performance of iSAT.

Nonlinear systemSatisfiability modulo theoriesDPLL algorithmLocal consistencyBoolean combinationInterval (mathematics)SolverAlgorithmMathematicsInterval arithmetic
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