Translating Pseudo-Boolean Constraints into CNF

  • Amir Aavani
Conference paper

DOI: 10.1007/978-3-642-21581-0_28

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6695)
Cite this paper as:
Aavani A. (2011) Translating Pseudo-Boolean Constraints into CNF. In: Sakallah K.A., Simon L. (eds) Theory and Applications of Satisfiability Testing - SAT 2011. SAT 2011. Lecture Notes in Computer Science, vol 6695. Springer, Berlin, Heidelberg


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

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

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