A Pseudo-Boolean constraint (PB-constraint) is a generalization of a clause. A PB-constraint is an inequality (equality) on a linear combination of Boolean literals \(\left(\sum_{i=1}^n a_il_i\ OP\ b\right)\) where a1, ⋯ an and b are constant integers, l1, ⋯ ,ln are literals and OP is a comparison operator. The left-hand side of a PB-constraint under assignment \(\mathcal{A}\) is equal to the sum of the coefficients whose corresponding literals are mapped to true by \(\mathcal{A}\). This kind of constraints has been widely used in expressing NP-complete problems. Several approaches have been proposed to translate a PB-constraint to CNF, [3], [2].


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  1. 1.
    Aavani, A.: Translating Pseudo-Boolean Constraints into CNF, http://arxiv.org/abs/1104.1479
  2. 2.
    Bailleux, O., Boufkhad, Y., Roussel, O.: New encodings of pseudo-boolean constraints into CNF. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 181–194. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into SAT. Journal on Satisfiability, Boolean Modeling and Computation 2(3-4), 1–25 (2006)MATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Amir Aavani
    • 1
  1. 1.Simon Fraser UniversityCanada

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