Abstract
The aim of this invited talk is to discuss strengths, limitations and challenges around one of the simplest yet most powerful practical automated deduction formalisms, namely propositional SAT and its extensions. We will see some of the reasons why CDCL SAT solvers are so effective for finding solutions to so diverse real-world problems, using a single fully automatic push-button strategy, and, by extending them to SAT Modulo Theories (SMT), also to optimization problems and problems with complex (e.g., arithmetic) constraints for which a full encoding into SAT would be too large and/or inefficient. We will give some examples of trade-offs regarding full SAT encodings vs SMT theory solvers, and discuss why SAT and even SMT are just binary resolution strategies, the consequences of this fact, and possible ways to overcome it. Many aspects of the discussion carry over to first-order logic and beyond.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Audemard, G., Katsirelos, G., Simon, L.: A restriction of extended resolution for clause learning sat solvers. In: Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence. AAAI (2010)
AsÃn, R., Nieuwenhuis, R., Oliveras, A., RodrÃguez-Carbonell, E.: Cardinality networks: a theoretical and empirical study. Constraints 16(2), 195–221 (2011)
AbÃo, I., Stuckey, P.J.: Conflict-directed lazy decomposition (submitted, 2012)
Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press (February 2009)
Barrett, C., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability Modulo Theories. In: Biere, et al. (eds.) [BHvMW09], vol. 185, ch. 26, pp. 825–885 (February 2009)
Huang, J.: Extended clause learning. Artif. Intell. 174(15), 1277–1284 (2010)
Larrosa, J., Nieuwenhuis, R., Oliveras, A., RodrÃguez-Carbonell, E.: A framework for certified boolean branch-and-bound optimization. J. Autom. Reasoning 46(1), 81–102 (2011)
Nieuwenhuis, R., Oliveras, A.: On SAT Modulo Theories and Optimization Problems. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 156–169. Springer, Heidelberg (2006)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT Modulo Theories: from an Abstract Davis-Putnam-Logemann-Loveland Procedure to DPLL(T). Journal of the ACM 53(6), 937–977 (2006)
Ohrimenko, O., Stuckey, P.J., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009)
Zhang, L., Malik, S.: Validating SAT Solvers Using an Independent Resolution-Based Checker: Practical Implementations and Other Applications. In: 2003 Conference on Design, Automation and Test in Europe Conference, DATE 2003, pp. 10880–10885. IEEE Computer Society (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nieuwenhuis, R. (2012). SAT and SMT Are Still Resolution: Questions and Challenges. In: Gramlich, B., Miller, D., Sattler, U. (eds) Automated Reasoning. IJCAR 2012. Lecture Notes in Computer Science(), vol 7364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31365-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-31365-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31364-6
Online ISBN: 978-3-642-31365-3
eBook Packages: Computer ScienceComputer Science (R0)