On Subsumption Removal and On-the-Fly CNF Simplification

  • Lintao Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3569)


CNF Boolean formulas generated from resolution or solution enumeration often have much redundancy. Efficient algorithms are needed to simplify and compact such CNF formulas. In this paper, we present a novel algorithm to maintain a subsumption-free CNF clause database by efficiently detecting and removing subsumption as the clauses are being added. We then present an algorithm that compact CNF formula further by applying resolutions to make it Decremental Resolution Free. Our experimental evaluations show that these algorithms are efficient and effective in practice.


Boolean Function Variable Elimination Subsumption Check Clause Database Boolean Constraint Propagation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Marques-Silva, J.P., Sakallah, K.A.: GRASP: A Search Algorithm for Propositional Satisfiability. IEEE Tran. on Computers 48, 506–521 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Zhang, L., Malik, S.: Towards Symmetric Treatment of Conflicts And Satisfaction in Quantified Boolean Satisfiability Solver. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, p. 200. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Biere, A.: Resolve and Expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Subbarayan, S., Pradhan, D.K.: NiVER: Non Increasing Variable Elimination Resolution for Preprocessing SAT instances. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 276–291. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Chauhan, P., Clarke, E.M., Kroening, D.: Using SAT Based Image Computation for Reachability Analysis. Technical Report CMU-CS-03-151, Carnegie Mellon University (July 2003)Google Scholar
  7. 7.
    de Kleer, J.: An Improved Incremental Algorithm for Generating Prime Implicates. In: Proc. of the 10th National Conference on Artificial Intelligence, AAAI 1992 (1992)Google Scholar
  8. 8.
    Chatalic, P., Simon, L.: Multi-Resolution on Compressed Sets of Clauses. In: Twelfth International Conference on Tools with Artificial Intelligence, ICTAI 2000 (2000)Google Scholar
  9. 9.
    Minato, S.: Zero-Suppressed BDDs for Set Manipula-tion in Combinatorial Problems. In: Proc. of the Design Automation Conference (DAC 1993), pp. 272–277 (1993)Google Scholar
  10. 10.
    Hachtel, G., Somenzi, F.: Logic Sysntheiss and Verification Algorithms. Kluwer Academic Publishers, Dordrecht (1996)Google Scholar
  11. 11.
    Kang, H.J., Park, I.-C.: SAT-Based Unbounded Symbolic Model Checking. In: Proc. 40th Design Automation Conference, DAC 2003 (2003)Google Scholar
  12. 12.
    Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Engineering an efficient SAT Solver. In: Proceedings of the Design Automation Conference (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Lintao Zhang
    • 1
  1. 1.Microsoft Research Silicon Valley LabSunnyvaleUSA

Personalised recommendations