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.

• Type: Conference
• Year: 2005
• Where: SAT
• Authors: Evgeny Dantsin, Alexander Wolpert
• Keywords: Boolean Formulas, Conjunctive Normal Form, Randomized Algorithm, SAT 2005