Complexity Issues in the Davis and Putnam Scheme
The Davis and Putnam (D&P) scheme has been intensively studied during this last decade. Nowadays, its good empirical perfor- mances are well-known. Here, we deal with its theoretical side which has been relatively less studied until now. Thus, we propose a strictely lin- ear D&P algorithm for the most well known tractable classes: Horn-SAT and 2-SAT. Specifically, the strictely linearity of our proposed D&P algo- rithm improves significantly the previous existing complexities that were quadratic for Horn-SAT and even exponential for 2-SAT. As a conse- quence, the D&P algorithm designed to deal with the general SAT problem runs as fast (in terms of complexity) as the specialised algorithms designed to work exclusively with a specific tractable SAT subclass.
KeywordsAutomated Reasoning Computational Complexity Search Theorem Proving
Unable to display preview. Download preview PDF.
- 1.G. Ausiello and G. F. Italiano. Online algorithms for poly normally solvable satisfiability problems. Journal of Logic Programming, 10(1), 1991.Google Scholar
- 2.C.M. Li and Anbulagan. Heuristics based on unit propagation for satisfiability problems. In Proceedings of the 15th IJCAI, pages 366–371, 1997.Google Scholar
- 3.J.M. Crawford and L. D. Auton. Experimental results on the crossover point in satisfiability problems. In Proc. of the Eleventh National Conference on Artificial Intelligence, AAAI-93, pages 21–27, 1993.Google Scholar
- 7.R. Dechter and I. Rish. Rirectional resolution: the davis and putnam procedure revisited. In Proceedings of Knowledge Representattion International Conference, KR-94, pages 134–145, 1994.Google Scholar
- 9.D. Dubois, P. Andre, Y. Boufkhad, and J. Carlier. Sat versus unsat. In Proceedings of the Second DIM ACS Challenge, 1993.Google Scholar
- 14.H. Kautz and B. Selman. Planing as satisfiability. In Proceeding of the 10th EC AI, pages 359–363. European Conference on Artificial Intelligence, 1992.Google Scholar
- 15.A. Rauzy. Polynomial restrictions of sat: What ca be done with an efficient implementation of the davis and putnam’s procedure. In U. Mntanari and F. Rossi, editors, Principles and Practice of Constraint Programming, CP’95, volume 976 of Lecture Notes in Computer Science, pages 515–532. Fisrt International Conference on Principles and Practice of Constraint Programming, Cassis, France, Springer-verlag, 1995.Google Scholar
- 17.H. Zhang. Sato: An efficient prepositional prover. In proceedings of the 13th Conference on Automated Deduction, pages 272–275, 1997.Google Scholar
- 18.H. Zhang and M. E. Stickel. An efficient algorithm for unit propagation. In International Symposium on Artificial Intelligence and Mathematics, 1996.Google Scholar
- 19.H Zhang and M. E. Stickel. Implementing the davis-putnam algorithm by tries. Technical report, The University of Iowa, 1994.Google Scholar