Abstract
Most state of the art SAT solvers for industrial problems are based on the Conflict Driven Clause Learning (CDCL) paradigm. Although this paradigm evolved from the systematic DPLL search algorithm, modern techniques of far backtracking and restarts make CDCL solvers non-systematic. CDCL solvers do not systematically examine all possible truth assignments as does DPLL.
Local search solvers are also non-systematic and in this paper we show that CDCL can be reformulated as a local search algorithm: a local search algorithm that through clause learning is able to prove UNSAT. We show that the standard formulation of CDCL as a backtracking search algorithm and our new formulation of CDCL as a local search algorithm are equivalent, up to tie breaking.
In the new formulation of CDCL as local search, the trail no longer plays a central role in the algorithm. Instead, the ordering of the literals on the trail is only a mechanism for efficiently controlling clause learning. This changes the paradigm and opens up avenues for further research and algorithm design. For example, in QBF the quantifier places restrictions on the ordering of variables on the trail. By making the trail less important, an extension of our local search algorithm to QBF may provide a way of reducing the impact of these variable ordering restrictions.
Supported by Natural Sciences and Engineering Research Council of Canada.
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References
Audemard, G., Lagniez, J.-M., Mazure, B., Sais, L.: Learning in local search. In: ICTAI, pp. 417–424 (2009)
Belov, A., Stachniak, Z.: Improved Local Search for Circuit Satisfiability. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 293–299. Springer, Heidelberg (2010)
Biere, A.: Adaptive Restart Strategies for Conflict Driven SAT Solvers. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 28–33. Springer, Heidelberg (2008)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5, 394–397 (1962)
Fang, H.: Complete local search for propositional satisfiability. In: Proceedings of AAAI, pp. 161–166 (2004)
Gableske, O., Heule, M.J.H.: EagleUP: Solving Random 3-SAT Using SLS with Unit Propagation. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 367–368. Springer, Heidelberg (2011)
Gomes, C.P., Selman, B., Crato, N.: Heavy-Tailed Distributions in Combinatorial Search. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 121–135. Springer, Heidelberg (1997)
Hirsch, E.A., Kojevnikov, A.: Unitwalk: A new sat solver that uses local search guided by unit clause elimination. Ann. Math. Artif. Intell. 43(1), 91–111 (2005)
Huang, J.: A Case for Simple SAT Solvers. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 839–846. Springer, Heidelberg (2007)
Katebi, H., Sakallah, K.A., Marques-Silva, J.P.: Empirical Study of the Anatomy of Modern Sat Solvers. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 343–356. Springer, Heidelberg (2011)
Lonsing, F., Biere, A.: Depqbf: A dependency-aware qbf solver. JSAT 7(2-3), 71–76 (2010)
Pipatsrisawat, K., Darwiche, A.: A lightweight component caching scheme for satisfiability solvers. In: 10th International Conference on Theory and Applications of Satisfiability Testing, pp. 294–299 (2007)
Pipatsrisawat, K., Darwiche, A.: On the Power of Clause-Learning SAT Solvers with Restarts. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 654–668. Springer, Heidelberg (2009)
Ramos, A., van der Tak, P., Heule, M.J.H.: Between Restarts and Backjumps. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 216–229. Springer, Heidelberg (2011)
Selman, B., Kautz, H., Cohen, B.: Local Search Strategies for Satisfiability Testing. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 521–532. Springer, Heidelberg (1995)
Tompkins, D.A.D., Balint, A., Hoos, H.H.: Captain Jack: New Variable Selection Heuristics in Local Search for SAT. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 302–316. Springer, Heidelberg (2011)
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Goultiaeva, A., Bacchus, F. (2012). Off the Trail: Re-examining the CDCL Algorithm. 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_4
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