Search results for "Unit propagation"

showing 2 items of 2 documents

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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Efficient CNF Encoding of Boolean Cardinality Constraints

2003

In this paper, we address the encoding into CNF clauses of Boolean cardinality constraints that arise in many practical applications. The proposed encoding is efficient with respect to unit propagation, which is implemented in almost all complete CNF satisfiability solvers. We prove the practical efficiency of this encoding on some problems arising in discrete tomography that involve many cardinality constraints. This encoding is also used together with a trivial variable elimination in order to re-encode parity learning benchmarks so that a simple Davis and Putnam procedure can solve them.

Discrete mathematicsTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESCardinalityUnit propagationComputer scienceConstrained optimizationData_CODINGANDINFORMATIONTHEORYVariable eliminationComputer Science::Computational ComplexityConjunctive normal formBoolean data typeSatisfiability
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