Clause Elimination Procedures for CNF Formulas

  • Marijn Heule
  • Matti Järvisalo
  • Armin Biere
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6397)


We develop and analyze clause elimination procedures, a specific family of simplification techniques for conjunctive normal form (CNF) formulas. Extending known procedures such as tautology, subsumption, and blocked clause elimination, we introduce novel elimination procedures based on hidden and asymmetric variants of these techniques. We analyze the resulting nine (including five new) clause elimination procedures from various perspectives: size reduction, BCP-preservance, confluence, and logical equivalence. For the variants not preserving logical equivalence, we show how to reconstruct solutions to original CNFs from satisfying assignments to simplified CNFs. We also identify a clause elimination procedure that does a transitive reduction of the binary implication graph underlying any CNF formula purely on the CNF level.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marijn Heule
    • 1
  • Matti Järvisalo
    • 2
  • Armin Biere
    • 3
  1. 1.Department of Software TechnologyDelft University of TechnologyThe Netherlands
  2. 2.Department of Computer ScienceUniversity of HelsinkiFinland
  3. 3.Institute for Formal Models and VerificationJohannes Kepler UniversityLinzAustria

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