Skip to main content
SpringerLink
Log in

Lower Bounds for Width-Restricted Clause Learning on Small Width Formulas

  • Conference paper
Theory and Applications of Satisfiability Testing – SAT 2010 (SAT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6175))

Abstract

It has been observed empirically that clause learning does not significantly improve the performance of a SAT solver when restricted to learning clauses of small width only. This experience is supported by lower bound theorems. It is shown that lower bounds on the runtime of width-restricted clause learning follow from resolution width lower bounds. This yields the first lower bounds on width-restricted clause learning for formulas in 3-CNF.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alekhnovich, M., Johannsen, J., Pitassi, T., Urquhart, A.: An exponential separation between regular and general resolution. Theory of Computing 3, 81–102 (2007); Preliminary Version in Proc. 34th ACM Symposium on Theory of Computing (2002)

    Google Scholar 

  2. Alon, N., Spencer, J.: The Probabilistic Method. John Wiley and Sons, Chichester (2002)

    MATH  Google Scholar 

  3. Atserias, A., Dalmau, V.: A combinatorial characterization of resolution width. Journal of Computer and System Sciences 74, 323–334 (2008); Preliminary version in Proc. 18th IEEE Conference on Computational Complexity (2003)

    Google Scholar 

  4. Atserias, A., Fichte, J.K., Thurley, M.: Clause learning algorithms with many restarts and bounded-width resolution. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 114–127. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Bayardo Jr., R.J., Schrag, R.C.: Using CSP look-back techniques to solver real-world SAT instances. In: Proc. 14th Natl. Conference on Artificial Intelligence, pp. 203–208 (1997)

    Google Scholar 

  6. Beame, P., Kautz, H.A., Sabharwal, A.: Towards understanding and harnessing the potential of clause learning. Journal of Artificial Intelligence Research 22, 319–351 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Ben-Sasson, E., Wigderson, A.: Short proofs are narrow — resolution made simple. Journal of the ACM 48 (2001); Preliminary Version in Proc. 31st ACM Symposium on Theory of Computing (1999)

    Google Scholar 

  8. Bonet, M.L., Galesi, N.: Optimality of size-width tradeoffs for resolution. Computational Complexity 10(4), 261–276 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Buss, S.R., Hoffmann, J., Johannsen, J.: Resolution trees with lemmas: Resolution refinements that characterize DLL algorithms with clause learning. Logical Methods in Computer Science 4(4) (2008)

    Google Scholar 

  10. Davis, M., Logemann, G., Loveland, D.W.: A machine program for theorem-proving. Communications of the ACM 5(7), 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gomes, C.P., Selman, B., Crato, N.: Heavy-tailed distributions in combinatorial search. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330. Springer, Heidelberg (1997)

    Google Scholar 

  12. Hertel, P., Bacchus, F., Pitassi, T., van Gelder, A.: Clause learning can effectively p-simulate general propositional resolution. In: Fox, D., Gomes, C.P. (eds.) Proceedings of the 23rd AAAI Conference on Artificial Intelligence, AAAI 2008, pp. 283–290. AAAI Press, Menlo Park (2008)

    Google Scholar 

  13. Hoffmann, J.: Resolution proofs and DLL-algorithms with clause learning. Diploma Thesis, LMU München (2007)

    Google Scholar 

  14. Iwama, K., Miyazaki, S.: Tree-like resolution is superpolynomially slower than dag-like resolution for the pigeonhole principle. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, p. 133. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Johannsen, J.: An exponential lower bound for width-restricted clause learning. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 128–140. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  16. Kolaitis, P.G., Vardi, M.Y.: On the expressive power of Datalog: Tools and a case study. Journal of Computer and System Sciences 51(1), 110–134 (1990); Preliminary version in Proc. 9th ACM Symposium on Principles of Database Systems (1990)

    Google Scholar 

  17. Krishnamurthy, B.: Short proofs for tricky formulas. Acta Informatica 22, 253–274 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lubotzky, A., Phillips, R., Sarnak, P.: Ramanujan graphs. Combinatorica 8(3), 261–277 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  19. Margulis, G.A.: Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators. Problems of Information Transmission 24, 39–46 (1988)

    MathSciNet  MATH  Google Scholar 

  20. Pipatsrisawat, K., Darwiche, A.: On the power of clause-learning SAT solvers with restarts. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 654–668. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Segerlind, N., Buss, S.R., Impagliazzo, R.: A switching lemma for small restrictions and lower bounds for k-DNF resolution. SIAM Journal on Computing 33(5), 1171–1200 (2004); Preliminary version in Proc. 43rd IEEE Symposium on Foundations of Computer Science (2002)

    Google Scholar 

  22. Silva, J.P.M., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: Proc. IEEE/ACM International Conference on Computer Aided Design (ICCAD), pp. 220–227 (1996)

    Google Scholar 

  23. Stålmarck, G.: Short resolution proofs for a sequence of tricky formulas. Acta Informatica 33, 277–280 (1996)

    Article  MathSciNet  Google Scholar 

  24. Tseitin, G.: On the complexity of derivation in propositional calculus. Studies in Constructive Mathematics and Mathematical Logic, Part 2, pp. 115–125 (1968)

    Google Scholar 

  25. Zhang, L., Madigan, C.F., Moskewicz, M.W., Malik, S.: Efficient conflict driven learning in a Boolean satisfiability solver. In: Proc. IEEE/ACM International Conference on Computer Aided Design (ICCAD), pp. 279–285 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, Technion – Israel Institute of Technology, Haifa, Israel

    Eli Ben-Sasson

  2. Institut für Informatik, LMU München, Munich, Germany

    Jan Johannsen

Authors
  1. Eli Ben-Sasson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Johannsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technion, Technion City, 32000, Haifa, Israel

    Ofer Strichman

  2. Vienna University of Technology, Favoritenstr. 9-11, 1040, Vienna, Austria

    Stefan Szeider

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ben-Sasson, E., Johannsen, J. (2010). Lower Bounds for Width-Restricted Clause Learning on Small Width Formulas. In: Strichman, O., Szeider, S. (eds) Theory and Applications of Satisfiability Testing – SAT 2010. SAT 2010. Lecture Notes in Computer Science, vol 6175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14186-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14186-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14185-0

  • Online ISBN: 978-3-642-14186-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation