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### Paper:

TR05-030 | 12th February 2005 00:00

#### An Improved Upper Bound for SAT

TR05-030
Authors: Evgeny Dantsin, Alexander Wolpert
Publication: 7th March 2005 16:56
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 $2^{n(1-1/\alpha)}$ up to a polynomial factor, where $\alpha = \ln(m/n) + O(\ln \ln m)$ 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 $2^{n(1-1/\log(2m))}$ bound for SAT.