Skip to main content
SpringerLink
Log in
Book cover

International Conference on Automated Deduction

CADE 2015: Automated Deduction - CADE-25 pp 591–606Cite as

Expressing Symmetry Breaking in DRAT Proofs

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

Abstract

An effective SAT preprocessing technique is the addition of symmetry-breaking predicates: auxiliary clauses that guide a SAT solver away from needless exploration of isomorphic sub-problems. Symmetry-breaking predicates have been in use for over a decade. However, it was not known how to express the addition of these predicates in proofs of unsatisfiability. Hence, results obtained by symmetry breaking cannot be validated by existing proof checkers. We present a method to express the addition of symmetry-breaking predicates in DRAT, a clausal proof format supported by top-tier solvers. We applied this method to generate SAT problems that have not been previously solved without symmetry-breaking predicates. We validated these proofs with an ACL2-based, mechanically-verified DRAT proof checker and the proof-checking tool of SAT Competition 2014.

The authors are supported by DARPA contract number N66001-10-2-4087.

This is a preview of subscription content, 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 EPUB and 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

Learn about institutional subscriptions

Notes

  1. 1.

    available at http://www.cs.utexas.edu/~marijn/drat-trim/.

  2. 2.

    available at http://www.cs.utexas.edu/~marijn/sbp/.

References

  1. Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry-breaking predicates for search problems. In: KR 1996, pp. 148–159. Morgan Kaufmann (1996)

    Google Scholar 

  2. Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult sat instances in the presence of symmetry. In: Proceedings of the 39th Design Automation Conference, pp. 731–736 (2002)

    Google Scholar 

  3. Gent, I.P., Smith, B.M.: Symmetry breaking in constraint programming. In: Horn, W. (ed.) ECAI 2000, pp. 599–603. IOS Press (2000)

    Google Scholar 

  4. Wetzler, N., Heule, M.J.H., Hunt Jr, W.A.: DRAT-trim: efficient checking and trimming using expressive clausal proofs. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 422–429. Springer, Heidelberg (2014)

    Google Scholar 

  5. Konev, B., Lisitsa, A.: A SAT attack on the Erdős discrepancy conjecture. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 219–226. Springer, Heidelberg (2014)

    Google Scholar 

  6. Kouril, M., Paul, J.L.: The van der Waerden number W(2, 6) is 1132. Exp. Math. 17(1), 53–61 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Codish, M., Cruz-Filipe, L., Frank, M., Schneider-Kamp, P.: Twenty-five comparators is optimal when sorting nine inputs (and twenty-nine for ten). In: ICTAI 2014, pp. 186–193. IEEE Computer Society (2014)

    Google Scholar 

  8. Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient symmetry breaking for boolean satisfiability. IEEE Trans. Comput. 55(5), 549–558 (2006)

    Article  MATH  Google Scholar 

  9. Schaafsma, B., Heule, M.J.H., van Maaren, H.: Dynamic symmetry breaking by simulating zykov contraction. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 223–236. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Radziszowski, S.P.: Small Ramsey numbers. Electron. J. Comb. #DS1 (2014)

    Google Scholar 

  11. Wetzler, N.D.: Efficient, mechanically-verified validation of satisfiability solvers. Ph.D. dissertation, The University of Texas at Austin, May 2015

    Google Scholar 

  12. Kullmann, O.: On a generalization of extended resolution. Discrete Appl. Math. 96–97, 149–176 (1999)

    Article  MathSciNet  Google Scholar 

  13. Zhang, L., Malik, S.: Validating sat solvers using an independent resolution-based checker: practical implementations and other applications. In: DATE, pp. 10880–10885 (2003)

    Google Scholar 

  14. Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  15. Biere, A.: Picosat essentials. JSAT 4(2–4), 75–97 (2008)

    MATH  Google Scholar 

  16. Van Gelder, A.: Verifying rup proofs of propositional unsatisfiability. In: ISAIM (2008)

    Google Scholar 

  17. Heule, M.J.H., Hunt Jr, W.A., Wetzler, N.: Verifying refutations with extended resolution. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 345–359. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  18. Heule, M.J.H., Hunt Jr., W.A., Wetzler, N.: Trimming while checking clausal proofs. In: Formal Methods in Computer-Aided Design, pp. 181–188. IEEE (2013)

    Google Scholar 

  19. Heule, M.J.H., Hunt Jr, W.A., Wetzler, N.: Bridging the gap between easy generation and efficient verification of unsatisfiability proofs. Softw. Test. Verif. Reliab. (STVR) 24(8), 593–607 (2014)

    Article  Google Scholar 

  20. Järvisalo, M., Heule, M.J.H., Biere, A.: Inprocessing rules. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 355–370. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  21. Järvisalo, M., Biere, A., Heule, M.J.H.: Blocked clause elimination. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 129–144. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  22. Parberry, I.: The pairwise sorting network. Parallel Process. Lett. 2, 205–211 (1992)

    Article  MathSciNet  Google Scholar 

  23. Batcher, K.E.: Sorting networks and their applications. In: Proceedings of Spring Joint Computer Conference, AFIPS 1968, pp. 307–314. ACM (1968)

    Google Scholar 

  24. Darga, P.T., Liffiton, M.H., Sakallah, K.A., Markov, I.L.: Exploiting structure in symmetry detection for cnf. In: DAC 2004, pp. 530–534. ACM (2004)

    Google Scholar 

  25. Wetzler, N., Heule, M.J.H., Hunt Jr, W.A.: Mechanical verification of SAT refutations with extended resolution. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 229–244. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  26. Brummayer, R., Lonsing, F., Biere, A.: Automated testing and debugging of SAT and QBF solvers. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 44–57. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Texas, Austin, USA

    Marijn J. H. Heule, Warren A. Hunt Jr. & Nathan Wetzler

Authors
  1. Marijn J. H. Heule
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Warren A. Hunt Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nathan Wetzler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marijn J. H. Heule .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Heule, M.J.H., Hunt, W.A., Wetzler, N. (2015). Expressing Symmetry Breaking in DRAT Proofs. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_40

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21401-6_40

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation