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On Compiling CNFs into Structured Deterministic DNNFs

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Theory and Applications of Satisfiability Testing -- SAT 2015 (SAT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9340))

Abstract

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.

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References

  1. Bova, S., Capelli, F., Mengel, S., Slivovsky, F.: Expander CNFs have exponential DNNF size. CoRR, abs/1411.1995 (2014)

    Google Scholar 

  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. 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. Darwiche, A.: Decomposable negation normal form. J. ACM 48(4), 608–647 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  6. Darwiche, A., Marquis, P.: A Knowledge Compilation Map. J. Artif. Intell. Res. (JAIR) 17, 229–264 (2002)

    MathSciNet  MATH  Google Scholar 

  7. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer-Verlag, New York (2006)

    MATH  Google Scholar 

  8. Hlinený, P., Oum, S., Seese, D., Gottlob, G.: Width parameters beyond tree-width and their applications. Comput. J. 51(3), 326–362 (2008)

    Article  Google Scholar 

  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. Ordyniak, S., Paulusma, D., Szeider, S.: Satisfiability of acyclic and almost acyclic CNF formulas. Theoretical Computer Science 481, 85–99 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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. 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. 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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  18. Vatshelle, M.: New Width Parameters of Graphs. PhD thesis, University of Bergen (2012)

    Google Scholar 

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Correspondence to Friedrich Slivovsky .

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Bova, S., Capelli, F., Mengel, S., Slivovsky, F. (2015). On Compiling CNFs into Structured Deterministic DNNFs. In: Heule, M., Weaver, S. (eds) Theory and Applications of Satisfiability Testing -- SAT 2015. SAT 2015. Lecture Notes in Computer Science(), vol 9340. Springer, Cham. https://doi.org/10.1007/978-3-319-24318-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-24318-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24317-7

  • Online ISBN: 978-3-319-24318-4

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