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Chapitre D'ouvrage Année : 2021

Pseudo-Boolean and Cardinality Constraints

Résumé

Pseudo-Boolean and cardinality constraints are a natural generalization of clauses. While a clause expresses that at least one literal must be true, a cardinality constraint expresses that at least n literals must be true and a pseudo-Boolean constraint states that a weighted sum of literals must be greater than a constant. These contraints have a high expressive power, have been intensively studied in 0/1 programming and are close enough to the satisfiability problem to benefit from the recents advances in this field. Besides, optimization problems are naturally expressed in the pseudo-Boolean context. This chapter presents the inference rules on pseudo-Boolean constraints and demonstrates their increased inference power in comparison with resolution. It also shows how the modern satisfiability algorithms can be extended to deal with pseudo-Boolean constraints.
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Dates et versions

hal-04461963 , version 1 (16-02-2024)

Identifiants

Citer

Olivier Roussel, Vasco Manquinho. Pseudo-Boolean and Cardinality Constraints. Armin Biere; Marijn Heule; Hans van Maaren; Toby Walsh. Handbook of Satisfiability, second edition, 336, IOS Press, pp.1087-1129, 2021, Frontiers in Artificial Intelligence and Applications, 978-1-64368-160-3. ⟨10.3233/FAIA201012⟩. ⟨hal-04461963⟩
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