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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Please refer to the source code of CaDiCaL provided at http://fmv.jku.at/chrono.
References
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
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
Biere, A.: CaDiCaL at the SAT Race 2019. In: Proceedings of SAT Race (2019, Submitted)
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)
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
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
Marić, F., Janičić, P.: Formalization of abstract state transition systems for SAT. Logical Methods Comput. Sci. 7(3), 1–37 (2011)
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)
Marques-Silva, J.P., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: Proceedings of ICCAD 1996, pp. 220–227 (1996)
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
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)
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)
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)
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
Oh, C.: Improving SAT solvers by exploiting empirical characteristics of CDCL. Ph.D. Thesis, New York University, Department of Computer Science (2016)
van der Tak, P., Ramos, A., Heule, M.: Reusing the assignment trail in CDCL solvers. JSAT 7(4), 133–138 (2011)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
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)