Average time complexity of the SAT 1.2 algorithm

Abstract

In this paper, we give an efficient algorithm, the SAT1.2 algorithm, for the SAT problem. For randomly generated formulas with n clauses, m variables, and l literals per clause, the average run time of the SAT1.2 algorithm is O(m ^o(1) n ²) for l≥3 and n/m≤α2^l/l, where α<l is a constant. Real algorithm executions indicate that the SAT1.2 algorithm is much more efficient than the well known Davis-Putnam algorithm for certain classes of CNF formulas with small l. This is important in practice, since for large l, most vectors in {0, 1}^m are the solutions of the problem. Thus, a random exhaustive search can efficiently solve the problem. The SAT1.2 algorithm can find a solution for a satisfiable CNF formula efficiently but gives an answer in O(m ^o(1)2^m) time to an unsatisfiable CNF formula. 3

This research was supported in part by NSERC Strategic Grant MEF0045793 and is presently supported in part by NSERC Research Grant OGP0046423.