Skip to main content
Springer Nature Link
Log in

An Improved Separation of Regular Resolution from Pool Resolution and Clause Learning

  • Conference paper
Theory and Applications of Satisfiability Testing – SAT 2012 (SAT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7317))

Abstract

We prove that the graph tautology principles of Alekhnovich, Johannsen, Pitassi and Urquhart have polynomial size pool resolution refutations that use only input lemmas as learned clauses and without degenerate resolution inferences. These graph tautology principles can be refuted by polynomial size DPLL proofs with clause learning, even when restricted to greedy, unit-propagating DPLL search.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Alekhnovich, M., Johannsen, J., Pitassi, T., Urquhart, A.: An exponential separation between regular and general resolution. Theory of Computation 3(4), 81–102 (2007)

    Article  MathSciNet  Google Scholar 

  2. Atserias, A., Fichte, J.K., Thurley, M.: Clause-learning algorithms with many restarts and and bounded-width resolution. Journal of Artificial Intelligence Research 40, 353–373 (2011)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  4. Beckmann, A., Buss, S.R.: Separation results for the size of constant-depth propositional proofs. Annals of Pure and Applied Logic 136, 30–55 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bonet, M.L., Galesi, N.: A study of proof search algorithms for resolution and polynomial calculus. In: 40th Annual IEEE Symp. on Foundations of Computer Science, pp. 422–431. IEEE Computer Society (1999)

    Google Scholar 

  6. Buss, S.R.: Pool resolution is NP-hard to recognise. Archive for Mathematical Logic 48(8), 793–798 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Buss, S.R., Hoffmann, J., Johannsen, J.: Resolution trees with lemmas: Resolution refinements that characterize DLL-algorithms with clause learning. Logical Methods of Computer Science 4, 4:13(4:13), 1–18 (2008)

    MathSciNet  Google Scholar 

  8. Goerdt, A.: Regular resolution versus unrestricted resolution. SIAM Journal on Computing 22(4), 661–683 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hertel, P., Bacchus, F., Pitassi, T., Van Gelder, A.: Clause learning can effectively p-simulate general propositional resolution. In: Proc. 23rd AAAI Conf. on Artificial Intelligence (AAAI 2008), pp. 283–290. AAAI Press (2008)

    Google Scholar 

  10. Huang, W., Yu, X.: A DNF without regular shortest consensus path. SIAM Journal on Computing 16(5), 836–840 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  11. Krishnamurthy, B.: Short proofs for tricky formulas. Acta Informatica 22(3), 253–275 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pipatsrisawat, K., Darwiche, A.: On the power of clause-learning sat solvers as resolution engines. Artificial Intelligence 172(2), 512–525 (2011)

    Article  MathSciNet  Google Scholar 

  13. 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)

    Article  MathSciNet  MATH  Google Scholar 

  14. Stålmarck, G.: Short resolution proofs for a sequence of tricky formulas. Acta Informatica 33(3), 277–280 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  15. Urquhart, A.: A near-optimal separation of regular and general resolution. SIAM Journal on Computing 40(1), 107–121 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Van Gelder, A.: Pool Resolution and Its Relation to Regular Resolution and DPLL with Clause Learning. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 580–594. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. Van Gelder, A.: Preliminary Report on Input Cover Number as a Metric for Propositional Resolution Proofs. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 48–53. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lenguajes y Sistemas Informáticos, Universidad Politécnica de Cataluña, Barcelona, Spain

    Maria Luisa Bonet

  2. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093-0112, USA

    Sam Buss

Authors
  1. Maria Luisa Bonet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sam Buss
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Center for Information Technology, Fondazione Bruno Kessler, via Sommarive 18, Povo, 38123, Trento, Italy

    Alessandro Cimatti

  2. Department of Information Engineering and Computer Science, University of Trento, via Sommarive 14, Povo, 38123, Trento, Italy

    Roberto Sebastiani

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bonet, M.L., Buss, S. (2012). An Improved Separation of Regular Resolution from Pool Resolution and Clause Learning. In: Cimatti, A., Sebastiani, R. (eds) Theory and Applications of Satisfiability Testing – SAT 2012. SAT 2012. Lecture Notes in Computer Science, vol 7317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31612-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31612-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31611-1

  • Online ISBN: 978-3-642-31612-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation