Abstract
Many real world problems are solved with satisfiability testing (SAT). However, SAT solvers have documented bugs and therefore the answer that a formula is unsatisfiable can be incorrect. Certifying algorithms are an attractive approach to increase the reliability of SAT solvers. For unsatisfiable formulas an unsatisfiability proof has to be created. This paper presents certificate constructions for various formula simplification techniques, which are crucial to the success of modern SAT solvers.
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References
Arnold, H.: A linearized DPLL calculus with clause learning. Tech. rep., Universität Potsdam. Institut für Informatik (2009)
Audemard, G., Lagniez, J.-M., Mazure, B., Saïs, L.: On freezing and reactivating learnt clauses. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 188–200. Springer, Heidelberg (2011)
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)
Bacchus, F., Winter, J.: Effective preprocessing with hyper-resolution and equality reduction. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 341–355. Springer, Heidelberg (2004)
Beame, P., Kautz, H., Sabharwal, A.: Towards understanding and harnessing the potential of clause learning. Journal of Artificial Intelligene Research 22(1), 319–351 (2004)
Biere, A., Cimatti, A., Clarke, E.M., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: DAC 1999, pp. 317–320 (1999)
Blum, M., Kannan, S.: Designing programs that check their work. In: Johnson, D.S. (ed.) STOC 1989, pp. 86–97. ACM (1989)
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)
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)
Gelder, A.V.: Extracting (easily) checkable proofs from a satisfiability solver that employs both preorder and postorder resolution. In: ISAIM 2002 (2002)
Goldberg, E., Novikov, Y.: Verification of proofs of unsatisfiability for CNF formulas. In: DATE 2003, pp. 10886–10891. IEEE Computer Society, Washington, DC (2003)
Großmann, P., Hölldobler, S., Manthey, N., Nachtigall, K., Opitz, J., Steinke, P.: Solving periodic event scheduling problems with SAT. In: Jiang, H., Ding, W., Ali, M., Wu, X. (eds.) IEA/AIE 2012. LNCS, vol. 7345, pp. 166–175. Springer, Heidelberg (2012)
Hamadi, Y., Jabbour, S., Sais, L.: Control-based clause sharing in parallel SAT solving. In: Boutilier, C. (ed.) IJCAI 2009, pp. 499–504. Morgan Kaufmann Publishers Inc., Pasadena (2009)
Han, H., Somenzi, F.: On-the-fly clause improvement. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 209–222. Springer, Heidelberg (2009)
Heule, M., Hunt Jr., W.A., Wetzler, N.: Trimming while checking clausal proofs. In: Jobstman, B., Ray, S. (eds.) FMCAD 2013, pp. 181–188. IEEE (2013)
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)
Heule, M., Järvisalo, M., Biere, A.: Clause elimination procedures for CNF formulas. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 357–371. Springer, Heidelberg (2010)
Heule, M., Järvisalo, M., Biere, A.: Covered clause elimination. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR 2010. LNCS, vol. 6397, pp. 41–46. Springer, Heidelberg (2010)
Heule, M.J.H., Järvisalo, M., Biere, A.: Efficient CNF simplification based on binary implication graphs. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 201–215. Springer, Heidelberg (2011)
Hölldobler, S., Manthey, N., Philipp, T., Steinke, P.: Generic CDCL – A formalization of modern propositional satisfiability solvers. In: POS 2014 (accepted, 2014)
Järvisalo, M., Biere, A., Heule, M.: Blocked clause elimination. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 129–144. Springer, Heidelberg (2010)
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)
Kaufmann, M., Kottler, S.: Beyond unit propagation in SAT solving. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 267–279. Springer, Heidelberg (2011)
Kautz, H., Selman, B.: Planning as satisfiability. In: Neumann, B. (ed.) ECAI 1992, pp. 359–363. John Wiley & Sons, Inc., New York (1992)
Kullmann, O.: On a generalization of extended resolution. Discrete Applied Mathematics 96-97, 149–176 (1999)
Li, C.M.: Integrating equivalency reasoning into davis-putnam procedure. In: Kautz, H.A., Porter, B.W. (eds.) IAAI 2000, pp. 291–296. AAAI Press, Menlo Park (2000)
Lynce, I., Marques-Silva, J.: Efficient haplotype inference with Boolean satisfiability. In: AAAI 2006, pp. 104–109. AAAI Press, Menlo Park (2006)
Lynce, I., Marques-Silva, J.P.: Probing-based preprocessing techniques for propositional satisfiability. In: ICTAI 2003, pp. 105–110. IEEE Computer Society, Sacramento (2003)
Manthey, N., Heule, M.J.H., Biere, A.: Automated reencoding of Boolean formulas. In: Biere, A., Nahir, A., Vos, T. (eds.) HVC. LNCS, vol. 7857, pp. 102–117. Springer, Heidelberg (2013)
Manthey, N., Philipp, T., Wernhard, C.: Soundness of inprocessing in clause sharing SAT solvers. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 22–39. Springer, Heidelberg (2013)
Marić, F.: Formalization and implementation of modern SAT solvers. Journal of Automated Reasoning 43(1), 81–119 (2009)
McConnell, R.M., Mehlhorn, K., Näher, S., Schweitzer, P.: Certifying algorithms. Computer Science Review 5(2), 119–161 (2011)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Abstract DPLL and abstract DPLL modulo theories. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 36–50. Springer, Heidelberg (2005)
Piette, C., Hamadi, Y., Sais, L.: Vivifying propositional clausal formulae. In: Ghallab, M., Spyropoulos, C.D., Fakotakis, N., Avouris, N.M. (eds.) ECAI 2008, pp. 525–529. IOS Press (2008)
Rintanen, J.: Engineering efficient planners with SAT. In: Raedt, L.D., Bessière, C., Dubois, D., Doherty, P., Frasconi, P., Heintz, F., Lucas, P.J.F. (eds.) ECAI 2012. Frontiers in Artificial Intelligence and Applications, vol. 242, pp. 684–689. IOS Press (2012)
Subbarayan, S., Pradhan, D.K.: NiVER: Non-increasing variable elimination resolution for preprocessing SAT instances. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 276–291. Springer, Heidelberg (2005)
Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Siekmann, J.H., Wrightson, G. (eds.) Automation of Reasoning. Symbolic Computation, pp. 466–483. Springer, Heidelberg (1983)
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)
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Manthey, N., Philipp, T. (2014). Formula Simplifications as DRAT Derivations. In: Lutz, C., Thielscher, M. (eds) KI 2014: Advances in Artificial Intelligence. KI 2014. Lecture Notes in Computer Science(), vol 8736. Springer, Cham. https://doi.org/10.1007/978-3-319-11206-0_12
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DOI: https://doi.org/10.1007/978-3-319-11206-0_12
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