Computation of Renameable Horn Backdoors

  • Stephan Kottler
  • Michael Kaufmann
  • Carsten Sinz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4996)


Satisfiability of real-world Sat instances can be often decided by focusing on a particular subset of variables - a so-called Backdoor Set. In this paper we suggest two algorithms to compute Renameable Horn deletion backdoors. Both methods are based on the idea to transform the computation into a graph problem. This approach could be used as a preprocessing to solve hard real-world Sat instances. We also give some experimental results of the computations of Renameable Horn backdoors for several real-world instances.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
  2. 2.
    The international SAT competition (2002-2007),
  3. 3.
    Aspvall, B., Plass, M.F., Tarjan, R.E.: A linear-time algorithm for testing the truth of certain quantified boolean formulas. Inf. Proc. Lett. 8, 121–123 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Buresh-Oppenheim, J., Mitchell, D.G.: Minimum witnesses for unsatisfiable 2CNFs. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Chen, J., Liu, Y., Lu, S.: Directed feedback vertex set problem is fpt. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs (2007)Google Scholar
  6. 6.
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Demetrescu, C., Finocchi, I.: Combinatorial algorithms for feedback problems in directed graphs. Inf. Process. Lett. 86(3), 129–136 (2003)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Dilkina, B., Gomes, C.P., Sabharwal, A.: Tradeoffs in the complexity of backdoor detection. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Interian, Y.: Backdoor sets for random 3-sat. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, Springer, Heidelberg (2004)Google Scholar
  11. 11.
    Lewis, H.R.: Renaming a set of clauses as a horn set. J. ACM 25, 134–135 (1978)zbMATHCrossRefGoogle Scholar
  12. 12.
    Nishimura, N., Ragde, P., Szeider, S.: Detecting backdoor sets with respect to Horn and Binary clauses. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Nishimura, N., Ragde, P., Szeider, S.: Solving #SAT using vertex covers. Acta Informatica 44(7-8), 509–523 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)zbMATHGoogle Scholar
  15. 15.
    Paris, L., Ostrowski, R., Siegel, P., Sais, L.: Computing horn strong backdoor sets thanks to local search. In: ICTAI 2006, IEEE Computer Society, Los Alamitos (2006)Google Scholar
  16. 16.
    Ruan, Y., Kautz, H.A., Horvitz, E.: The backdoor key: A path to understanding problem hardness. In: AAAI, pp. 124–130 (2004)Google Scholar
  17. 17.
    Sinz, C.: SAT benchmarks (2003),
  18. 18.
    Szeider, S.: Backdoor sets for dll subsolvers. J. Autom. Reasoning 35, 73–88 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Szeider, S.: Matched formulas and backdoor sets. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, Springer, Heidelberg (2007)CrossRefGoogle Scholar
  20. 20.
    Williams, R., Gomes, C., Selman, B.: Backdoors to typical case complexity. In: IJCAI (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Stephan Kottler
    • 1
  • Michael Kaufmann
    • 1
  • Carsten Sinz
    • 1
  1. 1.Wilhelm–Schickard–InstituteEberhard Karls Universität TübingenTübingenGermany

Personalised recommendations