Skip to main content
SpringerLink
Log in

Backing Backtracking

  • Conference paper
  • First Online:
Theory and Applications of Satisfiability Testing – SAT 2019 (SAT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11628))

Abstract

Non-chronological backtracking was considered an important and necessary feature of conflict-driven clause learning (CDCL). However, a SAT solver combining CDCL with chronological backtracking succeeded in the main track of the SAT Competition 2018. In that solver, multiple invariants considered crucial for CDCL were violated. In particular, decision levels of literals on the trail were not necessarily increasing anymore. The corresponding paper presented at SAT 2018 described the algorithm and provided empirical evidence of its correctness, but a formalization and proofs were missing. Our contribution is to fill this gap. We further generalize the approach, discuss implementation details, and empirically confirm its effectiveness in an independent implementation.

Supported by Austrian Science Fund (FWF) grant S11408-N23 (RiSE) and by the LIT Secure and Correct Systems Lab funded by the State of Upper Austria.

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 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

Notes

  1. 1.

    Please refer to the source code of CaDiCaL provided at http://fmv.jku.at/chrono.

References

  1. Artho, C., Biere, A., Seidl, M.: Model-based testing for verification back-ends. In: Veanes, M., Viganò, L. (eds.) TAP 2013. LNCS, vol. 7942, pp. 39–55. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38916-0_3

    Chapter  Google Scholar 

  2. Audemard, G., Simon, L.: Refining restarts strategies for SAT and UNSAT. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 118–126. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33558-7_11

    Chapter  Google Scholar 

  3. Biere, A.: CaDiCaL at the SAT Race 2019. In: Proceedings of SAT Race (2019, Submitted)

    Google Scholar 

  4. Biere, A.: CaDiCaL, Lingeling, Plingeling, Treengeling and YalSAT entering the SAT competition 2018. In: Proceedings of the SAT Competition 2018 - Solver and Benchmark Descriptions. Department of Computer Science Series of Publications B, vol. B-2018-1, pp. 13–14. University of Helsinki (2018)

    Google Scholar 

  5. Blanchette, J.C., Fleury, M., Weidenbach, C.: A verified SAT solver framework with learn, forget, restart, and incrementality. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS (LNAI), vol. 9706, pp. 25–44. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40229-1_4

    Chapter  Google Scholar 

  6. Goultiaeva, A., Bacchus, F.: Off the trail: re-examining the CDCL algorithm. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 30–43. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31612-8_4

    Chapter  Google Scholar 

  7. Marić, F., Janičić, P.: Formalization of abstract state transition systems for SAT. Logical Methods Comput. Sci. 7(3), 1–37 (2011)

    Article  MathSciNet  Google Scholar 

  8. Marques-Silva, J.P., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 131–153. IOS Press (2009)

    Google Scholar 

  9. Marques-Silva, J.P., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: Proceedings of ICCAD 1996, pp. 220–227 (1996)

    Google Scholar 

  10. Nadel, A., Ryvchin, V.: Chronological backtracking. In: Beyersdorff, O., Wintersteiger, C.M. (eds.) SAT 2018. LNCS, vol. 10929, pp. 111–121. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94144-8_7

    Chapter  Google Scholar 

  11. Nadel, A., Ryvchin, V.: Maple LCM dist ChronoBT: featuring chronological backtracking. In: Proceedings of SAT Competition 2018 - Solver and Benchmark Descriptions. Department of Computer Science Series of Publications B, vol. B-2018-1, p. 29. University of Helsinki (2018)

    Google Scholar 

  12. Niemetz, A., Preiner, M., Biere, A.: Model-based API testing for SMT solvers. In: Proceedings of SMT 2017, Affiliated with CAV 2017, p. 10 (2017)

    Google Scholar 

  13. Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: from an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). J. ACM 53(6), 937–977 (2006)

    Article  MathSciNet  Google Scholar 

  14. Oh, C.: Between SAT and UNSAT: the fundamental difference in CDCL SAT. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 307–323. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24318-4_23

    Chapter  Google Scholar 

  15. Oh, C.: Improving SAT solvers by exploiting empirical characteristics of CDCL. Ph.D. Thesis, New York University, Department of Computer Science (2016)

    Google Scholar 

  16. van der Tak, P., Ramos, A., Heule, M.: Reusing the assignment trail in CDCL solvers. JSAT 7(4), 133–138 (2011)

    MathSciNet  MATH  Google Scholar 

  17. Xiao, F., Luo, M., Li, C.M., Manyà, F., Lü, Z.: MapleLRB\_LCM, Maple\_LCM, Maple\_LCM\_Dist, MapleLRB\_LCMoccRestart, and Glucose-3.0+width in SAT Competition 2017. In: Proceedings of SAT Competition 2017 - Solver and Benchmark Descriptions. Department of Computer Science Series of Publications B, vol. B-2017-1, pp. 22–23. University of Helsinki (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Johannes Kepler University Linz, Linz, Austria

    Sibylle Möhle & Armin Biere

Authors
  1. Sibylle Möhle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Armin Biere
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sibylle Möhle .

Editor information

Editors and Affiliations

  1. University of Lisbon, Lisbon, Portugal

    Mikoláš Janota

  2. University of Lisbon, Lisbon, Portugal

    Inês Lynce

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Möhle, S., Biere, A. (2019). Backing Backtracking. In: Janota, M., Lynce, I. (eds) Theory and Applications of Satisfiability Testing – SAT 2019. SAT 2019. Lecture Notes in Computer Science(), vol 11628. Springer, Cham. https://doi.org/10.1007/978-3-030-24258-9_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-24258-9_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24257-2

  • Online ISBN: 978-3-030-24258-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation