On Compiling CNFs into Structured Deterministic DNNFs

  • Simone Bova
  • Florent Capelli
  • Stefan Mengel
  • Friedrich SlivovskyEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9340)


We show that the traces of recently introduced dynamic programming algorithms for #SAT can be used to construct structured deterministic DNNF (decomposable negation normal form) representations of propositional formulas in CNF (conjunctive normal form). This allows us prove new upper bounds on the complexity of compiling CNF formulas into structured deterministic DNNFs in terms of parameters such as the treewidth and the clique-width of the incidence graph.


Leaf Node Binary Tree Dynamic Programming Algorithm Computable Function Conjunctive Normal Form 
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  1. 1.
    Bova, S., Capelli, F., Mengel, S., Slivovsky, F.: Expander CNFs have exponential DNNF size. CoRR, abs/1411.1995 (2014)Google Scholar
  2. 2.
    Brault-Baron, J., Capelli, F., Mengel, S.: Understanding model counting for beta-acyclic CNF-formulas. In: Mayr, E.W., Ollinger, N. (eds.) 32nd International Symposium on Theoretical Aspects of Computer Science, STACS 2015. LIPIcs, vol. 30, pp. 143–156. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2015)Google Scholar
  3. 3.
    Chen, H.: Parameterized compilability. In: Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, IJCAI 2005, Edinburgh, Scotland, UK, July 30-August 5, 2005, pp. 412–417 (2005)Google Scholar
  4. 4.
    Darwiche, A.: Decomposable negation normal form. J. ACM 48(4), 608–647 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Darwiche, A.: On the tractable counting of theory models and its application to truth maintenance and belief revision. Journal of Applied Non-Classical Logics 11(1–2), 11–34 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Darwiche, A., Marquis, P.: A Knowledge Compilation Map. J. Artif. Intell. Res. (JAIR) 17, 229–264 (2002)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer-Verlag, New York (2006)zbMATHGoogle Scholar
  8. 8.
    Hlinený, P., Oum, S., Seese, D., Gottlob, G.: Width parameters beyond tree-width and their applications. Comput. J. 51(3), 326–362 (2008)CrossRefGoogle Scholar
  9. 9.
    Karp, R.M., Lipton, R.J.: Some connections between nonuniform and uniform complexity classes. In: Proceedings of STOC 1980, pp. 302–309. ACM (1980)Google Scholar
  10. 10.
    Ordyniak, S., Paulusma, D., Szeider, S.: Satisfiability of acyclic and almost acyclic CNF formulas. Theoretical Computer Science 481, 85–99 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Oztok, U., Darwiche, A.: CV-width: a new complexity parameter for CNFs. In: 21st European Conference on Artificial Intelligence, ECAI 2014, pp. 675–680 (2014)Google Scholar
  12. 12.
    Oztok, U., Darwiche, A.: On compiling CNF into decision-DNNF. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 42–57. Springer, Heidelberg (2014) Google Scholar
  13. 13.
    Pipatsrisawat, K., Darwiche, A.: New compilation languages based on structured decomposability. In: Proceedings of the 23rd National Conference on Artificial Intelligence, AAAI 2008, vol. 1, pp. 517–522. AAAI Press (2008)Google Scholar
  14. 14.
    Pipatsrisawat, K., Darwiche, A.: Top-down algorithms for constructing structured DNNF: theoretical and practical implications. In: Proceedings of 19th European Conference on Artificial Intelligence, ECAI 2010, Lisbon, Portugal, August 16–20, 2010. Frontiers in Artificial Intelligence and Applications, vol. 215, pp. 3–8. IOS Press (2010)Google Scholar
  15. 15.
    Razgon, I., Petke, J.: Cliquewidth and knowledge compilation. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 335–350. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  16. 16.
    Sæther, S.H., Telle, J.A., Vatshelle, M.: Solving MaxSAT and #SAT on structured CNF formulas. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 16–31. Springer, Heidelberg (2014) Google Scholar
  17. 17.
    Slivovsky, F., Szeider, S.: Model counting for formulas of bounded Clique-Width. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) Algorithms and Computation. LNCS, vol. 8283, pp. 677–687. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  18. 18.
    Vatshelle, M.: New Width Parameters of Graphs. PhD thesis, University of Bergen (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Simone Bova
    • 1
  • Florent Capelli
    • 2
  • Stefan Mengel
    • 3
  • Friedrich Slivovsky
    • 1
    Email author
  1. 1.Institute of Computer Graphics and AlgorithmsTU WienViennaAustria
  2. 2.IMJ UMR 7586 - Logique, Université Paris DiderotParisFrance
  3. 3.LIX UMR 7161, Ecole Polytechnique, Université Paris-SaclayPalaiseauFrance

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