Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

DRAT Proofs for XOR Reasoning

  • Conference paper
  • First Online:
Logics in Artificial Intelligence (JELIA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10021))

Included in the following conference series:

Abstract

Unsatisfiability proofs in the DRAT format became the de facto standard to increase the reliability of contemporary SAT solvers. We consider the problem of generating proofs for the XOR reasoning component in SAT solvers and propose two methods: direct translation transforms every XOR constraint addition inference into a DRAT proof, whereas T-translation avoids the exponential blow-up in direct translations by using fresh variables. T-translation produces DRAT proofs from Gaussian elimination records that are polynomial in the size of the input CNF formula. Experiments show that a combination of both approaches with a simple prediction method outperforms the BDD-based method.

A. Rebola-Pardo—Supported by the LogiCS doctoral program W1255-N23 of the Austrian Science Fund (FWF), and by the Vienna Science and Technology Fund (WWTF) through grant VRG11-005.

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
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

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    https://github.com/zhihan/bdd-scala.

References

  1. Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult SAT instances in the presence of symmetry. In: DAC 2002, pp. 731–736. ACM (2002)

    Google Scholar 

  2. Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Boutilier, C. (ed.) IJCAI 2009, pp. 399–404. Morgan Kaufmann Publishers Inc., Pasadena (2009)

    Google Scholar 

  3. Beame, P., Kautz, H., Sabharwal, A.: Towards understanding and harnessing the potential of clause learning. J. Artif. Intell. Res. 22(1), 319–351 (2004)

    MathSciNet  MATH  Google Scholar 

  4. Belov, A., Diepold, D., Heule, M.J., Järvisalo, M. (eds.): Proceedings of SAT Competition 2014, Department of Computer Science Series of Publications B, vol. B-2014-2. University of Helsinki, Helsinki (2014)

    Google Scholar 

  5. Biere, A.: Yet another local search solver and lingeling and friends entering the SAT competition 2014. In: Belov et al. [4], pp. 39–40

    Google Scholar 

  6. Brace, K.S., Rudell, R.L., Bryant, R.E.: Efficient implementation of a BDD package. In: DAC, pp. 40–45 (1990)

    Google Scholar 

  7. Brummayer, R., Biere, A.: Fuzzing and delta-debugging SMT solvers. In: Workshop SMT 2010, pp. 1–5. ACM (2009)

    Google Scholar 

  8. Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)

    Article  MATH  Google Scholar 

  9. Courtois, N.T., Bard, G.V.: Algebraic cryptanalysis of the data encryption standard. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 152–169. Springer, Heidelberg (2007). doi:10.1007/978-3-540-77272-9_10

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005). doi:10.1007/11499107_5

    Chapter  Google Scholar 

  12. 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). doi:10.1007/978-3-540-24605-3_37

    Chapter  Google Scholar 

  13. Eén, N., Sörensson, N.: Translating pseudo-Boolean constraints into SAT. J. Satisf. Boolean Model. Comput. 2, 1–26 (2006)

    MATH  Google Scholar 

  14. Gwynne, M., Kullmann, O.: On SAT representations of XOR constraints. In: Dediu, A.-H., Martín-Vide, C., Sierra-Rodríguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 409–420. Springer, Heidelberg (2014). doi:10.1007/978-3-319-04921-2_33

    Chapter  Google Scholar 

  15. Heule, M.J.H., Hunt, W.A., Wetzler, N.: Expressing symmetry breaking in DRAT proofs. In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS (LNAI), vol. 9195, pp. 591–606. Springer, Heidelberg (2015). doi:10.1007/978-3-319-21401-6_40

    Chapter  Google Scholar 

  16. Heule, M.J.H., Biere, A.: Proofs for satisfiability problems. In: All About Proofs, Proofs for All (2015)

    Google Scholar 

  17. Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the Boolean Pythagorean Triples problem via cube-and-conquer. CoRR abs/1605.00723 (2016)

    Google Scholar 

  18. Heule, M.: March. Towards a lookahead SAT solver for general purposes. Master’s thesis (2004)

    Google Scholar 

  19. Järvisalo, M., Heule, M.J.H., Biere, A.: Inprocessing rules. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 355–370. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31365-3_28

    Chapter  Google Scholar 

  20. Laitinen, T.: Extending SAT solver with parity reasoning. Ph.D. thesis (2014)

    Google Scholar 

  21. Laitinen, T., Junttila, T., Niemelä, I.: Classifying and propagating parity constraints. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 357–372. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33558-7_28

    Chapter  Google Scholar 

  22. Manthey, N.: Coprocessor 2.0 – a flexible CNF simplifier. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 436–441. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31612-8_34

    Chapter  Google Scholar 

  23. Manthey, N.: Riss 4.27. In: Belov et al. [4], pp. 65–67

    Google Scholar 

  24. Manthey, N., Lindauer, M.: SpyBug: automated bug detection in the configuration space of SAT solvers. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 554–561. Springer, Heidelberg (2016). doi:10.1007/978-3-319-40970-2_36

    Chapter  Google Scholar 

  25. Rebola-Pardo, A.: Unsatisfiability proofs in SAT solving with parity reasoning. Master thesis, Technische Universität Dresden, Informatik Fakultät (2015)

    Google Scholar 

  26. Roussel, O., Manquinho, V.M.: Pseudo-Boolean and cardinality constraints. In: Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 695–733. IOS Press (2009)

    Google Scholar 

  27. Silva, J.P.M., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: ICCAD 1996, pp. 220–227. IEEE Computer Society, Washington (1996)

    Google Scholar 

  28. Sinz, C., Biere, A.: Extended resolution proofs for conjoining BDDs. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 600–611. Springer, Heidelberg (2006). doi:10.1007/11753728_60

    Chapter  Google Scholar 

  29. Soos, M.: Enhanced Gaussian elimination in DPLL-based SAT solvers. In: POS 2010 (2010)

    Google Scholar 

  30. Soos, M.: Cryptominisat v4. In: Belov et al. [4], pp. 23–34

    Google Scholar 

  31. Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 244–257. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02777-2_24

    Chapter  Google Scholar 

  32. Wetzler, N., Heule, M.J.H., Hunt, 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). doi:10.1007/978-3-319-09284-3_31

    Google Scholar 

Download references

Acknowledgements

We would like to thank an anonymous reviewer who pointed out that the BDD-based approach could be used as a baseline.

Author information

Authors and Affiliations

  1. International Center for Computational Logic, Technische Universität Dresden, 01062, Dresden, Germany

    Tobias Philipp

  2. TU Wien, Wien, Austria

    Adrián Rebola-Pardo

Authors
  1. Tobias Philipp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adrián Rebola-Pardo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tobias Philipp .

Editor information

Editors and Affiliations

  1. Open University of Cyprus, Nicosia, Cyprus

    Loizos Michael

  2. University of Cyprus, Nicosia, Cyprus

    Antonis Kakas

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Philipp, T., Rebola-Pardo, A. (2016). DRAT Proofs for XOR Reasoning. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48758-8_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48757-1

  • Online ISBN: 978-3-319-48758-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation