Exponential lower bounds for the running time of DPLL algorithms on satisfiable formulas

Journal of Automated Reasoning

Volumn 35, Issue 1-3, 2005, Pages 51-72

  Alekhnovich, Michael ^a   Hirsch, Edward A ^b   Itsykson, Dmitry ^c  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^c ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

DPLL algorithms; Satisfiability

Indexed keywords

HEURISTIC METHODS; PROBLEM SOLVING; RANDOM PROCESSES; TREES (MATHEMATICS);

DPLL ALGORITHMS; EXPONENTIAL LOWER BOUNDS; RUNNING TIME; SATISFIABILITY;

ALGORITHMS;

EID: 33750301291     PISSN: 01687433     EISSN: 15730670     Source Type: Journal    
DOI: 10.1007/s10817-005-9006-x     Document Type: Article

References (19)

1. Achlioptas, D., Beame, P. and Molloy, M.: A sharp threshold in proof complexity, J. Comput. Syst. Sci. (2003).
2. Achlioptas, D., Beame, P. and Molloy, M.: Exponential bounds for DPLL below the satisfiability threshold, in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'04, 2004, pp. 139-140.
3. Achlioptas, D. and Sorkin, G. B.: Optimal myopic algorithms for random 3-SAT, in Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, FOCS'00, 2000.
4. Alekhnovich, M. and Ben-Sasson, E.: Analysis of the random walk algorithm on random 3-CNFs, Manuscript, 2002.
5. Alekhnovich, M., Ben-Sasson, E., Razborov, A. and Wigderson, A.: Pseudorandom generators in propositional complexity, in Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, FOCS'00,
6. Journal version is to appear in SIAM Journal on Computing, 2000.
7. Alekhnovich, M., Borodin, A., Buresh-Oppenheim, J., Impagliazzo, R., Magen, A. and Pitassi, T.: Toward a model for backtracking and dynamic programming, in Proceedings of the 20th Annual Conference on Computational Complexity, 2005, pp. 308-322.
8. Alekhnovich, M. and Razborov, A.: Lower bounds for the polynomial calculus: Non-binomial case, in Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, 2001.
9. Ben-Sasson, E. and Wigderson, A.: Short proofs are narrow - resolution made simple, J. ACM 48(2) (2001), 149-169.
10. Davis, M., Logemann, G. and Loveland, D.: A machine program for theorem-proving, Commun. ACM 5 (1962), 394-397.
11. Davis, M. and Putnam, H.: A computing procedure for quantification theory, J. ACM 7 (1960), 201-215.
12. Hirsch, E. A.: SAT local search algorithms: Worst-case study, J. Autom. Reason. 24(1/2) (2000), 127-143.
13. Also reprinted in "Highlights of Satisfiability Research in the Year 2000", Volume 63 in Frontiers in Artificial Intelligence and Applications, IOS.
14. Iwama, K. and Tamaki, S.: Improved upper bounds for 3-SAT, in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'04, 2004, pp. 328-328.
15. Nikolenko, S. I.: Hard satisfiable formulas for DPLL-type algorithms, Zap. Nauc. Semin. POMI 293 (2002), 139-148.
16. English translation is to appear in Journal of Mathematical Sciences: Consultants Bureau, N.Y., March 2005, Vol. 126, No. 3, pp. 1205-1209.
17. Pudlák, P. and Impagliazzo, R.: A lower bound for DLL algorithms for k-SAT, in Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'00, 2000.
18. Simon, L., Le Berre, D. and Hirsch, E. A.: The SAT 2002 Competition, Ann. Math. Artif. Intell. 43 (2005), 307-342.
19. Tseitin, G. S.: On the complexity of derivation in the prepositional calculus, Zap. Nauc. Semin. LOMI 8 (1968), 234-259. English translation of this volume; Consultants Bureau, N.Y., 1970, pp. 115-125.