An Improved Upper Bound for SAT

We give a randomized algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. Its running time is at most 2n(1−1/α) up to a polynomial factor, where α = ln (m/n) + O(ln ln m) and n, m are respectively the number of variables and the number of clauses in the input formula. This bound is asymptotically better than the previously best known 2n(1−1/log(2m)) bound for SAT.

[1]  Evgeny Dantsin,et al.  Algorithms for SAT Based on Search in Hamming Balls , 2004, STACS.

[2]  U. Schöning.  A probabilistic algorithm for k-SAT and constraint satisfaction problems , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[3]  Walter Kern,et al.  An improved deterministic local search algorithm for 3-SAT , 2004, Theor. Comput. Sci..

[4]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[5]  Michael E. Saks,et al.  An improved exponential-time algorithm for k-SAT , 2005, JACM.

[6]  Uwe Schöning,et al.  A Probabilistic Algorithm for k -SAT Based on Limited Local Search and Restart , 2002, Algorithmica.

[7]  J. H. Lint.  Concrete mathematics : a foundation for computer science / R.L. Graham, D.E. Knuth, O. Patashnik , 1990 .

[8]  Jon M. Kleinberg,et al.  A deterministic (2-2/(k+1))n algorithm for k-SAT based on local search , 2002, Theor. Comput. Sci..

[9]  Rainer Schuler,et al.  An algorithm for the satisfiability problem of formulas in conjunctive normal form , 2005, J. Algorithms.

[10]  Pavel Pudlák,et al.  Satisfiability Coding Lemma , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[11]  Walter Kern,et al.  An improved local search algorithm for 3-SAT , 2004, Electron. Notes Discret. Math..

[12]  Pavel Pudlák,et al.  Satisfiability - Algorithms and Logic , 1998, MFCS.

[13]  Kazuo Iwama,et al.  Improved upper bounds for 3-SAT , 2004, SODA '04.

[14]  Evgeny Dantsin,et al.  Derandomization of Schuler's Algorithm for SAT , 2004, SAT.