Abstract
Recently Schuler [17] presented a randomized algorithm that solves SAT in expected time at most \(2^{n(1-1/{\rm log}_{2}(2m))}\) up to a polynomial factor, where n and m are, respectively, the number of variables and the number of clauses in the input formula. This bound is the best known upper bound for testing satisfiability of formulas in CNF with no restriction on clause length (for the case when m is not too large comparing to n). We derandomize this algorithm using deterministic k-SAT algorithms based on search in Hamming balls, and we prove that our deterministic algorithm has the same upper bound on the running time as Schuler’s randomized algorithm.
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
Baumer, S., Schuler, R.: Improving a probabilistic 3-SAT algorithm by dynamic search and independent clause pairs. Electronic Colloquium on Computational Complexity, Report No. 10 (February 2003)
Dantsin, E., Goerdt, A., Hirsch, E.A., Kannan, R., Kleinberg, J., Papadimitriou, C., Raghavan, P., Schöning, U.: A deterministic (2 − 2/(k + 1))n algorithm for k-SAT based on local search. Theoretical Computer Science 289(1), 69–83 (2002)
Dantsin, E., Goerdt, A., Hirsch, E.A., Schöning, U.: Deterministic algorithms for k-SAT based on covering codes and local search. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 236–247. Springer, Heidelberg (2000)
Dantsin, E., Hirsch, E.A., Wolpert, A.: Algorithms for SAT based on search in Hamming balls. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 141–151. Springer, Heidelberg (2004)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of the ACM 5, 394–397 (1962)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)
Hirsch, E.A.: New worst-case upper bounds for SAT. Journal of Automated Reasoning 24(4), 397–420 (2000)
Hofmeister, T., Schöning, U., Schuler, R., Watanabe, O.: A probabilistic 3-SAT algorithm further improved. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 192–202. Springer, Heidelberg (2002)
Iwama, K., Tamaki, S.: Improved upper bounds for 3-SAT. Electronic Colloquium on Computational Complexity, Report No. 53 (July 2003)
Kullmann, O.: New methods for 3-SAT decision and worst-case analysis. Theoretical Computer Science 223(1-2), 1–72 (1999)
Paturi, R., Pudlák, P., Saks, M.E., Zane, F.: An improved exponential-time algorithm for k-SAT. In: Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, FOCS 1998, pp. 628–637 (1998)
Paturi, R., Pudlák, P., Zane, F.: Satisfiability coding lemma. In: Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, FOCS 1997, pp. 566–574 (1997)
Pudlák, P.: Satisfiability — algorithms and logic. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 129–141. Springer, Heidelberg (1998)
Rolf, D.: 3-SAT in RTIME(O(1.32793n)) — improving randomized local search by initializing strings of 3-clauses. Electronic Colloquium on Computational Complexity, Report No. 54 (July 2003)
Schöning, U.: A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, FOCS 1999, pp. 410–414 (1999)
Schöning, U.: A probabilistic algorithm for k-SAT based on limited local search and restart. Algorithmica 32(4), 615–623 (2002)
Schuler, R.: An algorithm for the satisfiability problem of formulas in conjunctive normal form. To appear in Journal of Algorithms (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dantsin, E., Wolpert, A. (2005). Derandomization of Schuler’s Algorithm for SAT. In: Hoos, H.H., Mitchell, D.G. (eds) Theory and Applications of Satisfiability Testing. SAT 2004. Lecture Notes in Computer Science, vol 3542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527695_7
Download citation
DOI: https://doi.org/10.1007/11527695_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27829-0
Online ISBN: 978-3-540-31580-3
eBook Packages: Computer ScienceComputer Science (R0)