Resolution trees with lemmas: Resolution refinements that characterize DLL algorithms with clause learning

Logical Methods in Computer Science

Volumn 4, Issue 4, 2008, Pages

  Buss, Samuel R ^a   Hoffmann, Jan ^b   Johannsen, Jan ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

Clause learning; DLL algoritm; Propositional proof complexity; Resolution; SAT solving

Indexed keywords

CLAUSE LEARNING; DLL ALGORITM; EXTENSION METHODS; PROOF TRACES; PROPOSITIONAL PROOF COMPLEXITY; REGULARITY CONDITION; SAT-SOLVING; UNIT PROPAGATION; PROOF SEARCH;

FORESTRY; OPTICAL RESOLVING POWER; DELAY LOCK LOOPS;

LEARNING ALGORITHMS;

EID: 64449089060     PISSN: None     EISSN: 18605974     Source Type: Journal    
DOI: 10.2168/LMCS-4(4:13)2008     Document Type: Article

References (26)

1. Michael Alekhnovich, Jan Johannsen, Toniann Pitassi, and Alasdair Urquhart. An exponential separation between regular and general resolution. Theory of Computing, 3: 81-102, 2007.
2. Paul Beame, Henry A. Kautz, and Ashish Sabharwal. Towards understanding and harnessing the potential of clause learning. J. Artif. Intell. Res. (JAIR), 22: 319-351, 2004.
3. Daniel Le Berre and Laurent Simon. The essentials of the SAT 2003 competition. In Proc. 6th Interna-tional Conference on Theory and Applications of Satisfiability (SAT 2003), LNCS 2919, pages 452-467. Springer, 2003.
4. Daniel Le Berre and Laurent Simon. Fifty-five solvers in Vancouver: The SAT 2004 competition. In Theory and Applications of Satisfiability Testing: 7th International Conference, SAT 2004, LNCS 3542, pages 321-344. Springer, 2004.
5. Daniel Le Berre and Laurent Simon. Preface to the special volume on the SAT 2005 competitions and evaluations. Journal on Satisfiability, Boolean Modeling and Computation, 2: i-xiv, 2005.
6. Maria Luisa Bonet, Juan Luis Esteban, Nicola Galesi, and Jan Johannsen. On the relative complexity of resolution restrictions and cutting planes proof systems. SIAM Journal on Computing, 30: 1462-1484, 2000.
7. Samuel R. Buss and Toniann Pitassi. Resolution and the weak pigeonhole principle. In Mogens Nielsen and Wolfgang Thomas, editors, Computer Science Logic, 11th International Workshop CSL '97, pages 149-156. Springer LNCS 1414, 1998.
8. C. L. Chang. The unit proof and the input proof in theorem proving. J. ACM, 17(4): 698-707, 1970.
9. Martin Davis, George Logemann, and Donald W. Loveland. A machine program for theorem-proving. Commun. ACM, 5(7): 394-397, 1962.
10. Martin Davis and Hilary Putnam. A computing procedure for quantification theory. J. ACM, 7(3): 201-215, 1960.
11. Niklas Eén and Armin Biere. Effective preprocessing in SAT through variable and clause elimination. In Proc. 8th International Conference on Theory and Applications of Satisfiability Testing (SAT'05), LNCS 3569, pages 61-75. Springer, 2005.
12. JonW. Freeman. Improvements to Propositional Satisfiability Search Algorithms. PhD thesis, University of Pennsylvania, Philadelphia, PA, USA, 1995.
13. Zhaohui Fu, Yogesh Mahajan, and Sharad Malik. New features of the SAT'04 version of zChaff. SAT Competition 2004-Solver Description, http://www. princeton. edu/chaff/zchaff/sat04. pdf, 2004.
14. Andreas Goerdt. Regular resolution versus unrestricted resolution. SIAM J. Comput., 22(4): 661-683, 1993.
15. Armin Haken. The intractability of resolution. Theor. Comput. Sci., 39: 297-308, 1985.
16. Philipp Hertel, Fahiem Bacchus, Toniann Pitassi, and Allen Van Gelder. Clause learning can effectively p-simulate general propositional resolution. In Dieter Fox and Carla P. Gomes, editors, Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, pages 283-290. AAAI Press, 2008.
17. Jan Hoffmann. Resolution proofs and DLL-algorithms with clause learning. Diploma Thesis, LMU München, 2007. http://www. tcs. ifi. lmu. de/~hoffmann.
18. Kazuo Iwama and Shuichi Miyazaki. Tree-like resolution is superpolynomially slower than dag-like resolution for the pigeonhole principle. In Proceedings of the 10th International Symposium on Algorithms and Computation (ISAAC), pages 133-142, 1999.
19. Roberto J. Bayardo Jr. and Robert C. Schrag. Using CSP look-back techniques to solver real-world SAT instances. In Proc. 14th Natl. Conference on Artificial Intelligence, pages 203-208, 1997.
20. Yogesh S. Mahajan, Zhaohui Fu, and Sharad Malik. Zchaff2004: An efficient SAT solver. In Theory and Applications of Satisfiability Testing: 7th International Conference, SAT 2004, LNCS 3542, pages 360-375. Springer, 2004.
21. Matthew W. Moskewicz, Conor F. Madigan, Ying Zhao, Lintao Zhang, and Sharad Malik. Chaff: Engineering an efficient SAT solver. In Proc. 38th Design Automation Conference (DAC'01), pages 530-535, 2001.
22. Alexander Nadel. Backtrack search algorithms for propositional logic satisfiability: Review and innovations. Master's thesis, Hebrew University of Jerusalem, Israel, 2002.
23. João P. Marques Silva and Karem A. Sakallah. GRASP-a new search algorithm for satisfiability. In Proc. IEEE/ACM International Conference on Computer Aided Design (ICCAD), pages 220-227, 1996.
24. G. S. Tseitin. On the complexity of derivation in propositional calculus. Studies in Constructive Math-ematics and Mathematical Logic, Part 2, pages 115-125, 1968.
25. Allen Van Gelder. Pool resolution and its relation to regular resolution and DPLL with clause learning. In Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), LNAI 3835, pages 580-594, Montego Bay, Jamaica, 2005. Springer-Verlag.
26. Lintao Zhang, Conor F. Madigan, Matthew W. Moskewicz, and Sharad Malik. Efficient conflict driven learning in a Boolean satisfiability solver. In Proc. IEEE/ACM International Conference on Computer Aided Design (ICCAD), pages 279-285, 2001.