Directional Resolution: The Davis-Putnam Procedure, Revisited

The paper presents algorithm directional resolution, a variation on the original DavisPutnam algorithm, and analyzes its worstcase behavior as a function of the topological structure of the theories. The notions of induced width and diversity are shown to play a key role in bounding the complexity of the procedure. The importance of our analysis lies in highlighting structure-based tractable classes of satis ability and in providing theoretical guarantees on the time and space complexity of the algorithm. Contrary to previous assessments, we show that for many theories directional resolution could be an e ective procedure. Our empirical tests con rm theoretical prediction, showing that on problems with special structures, like chains, directional resolution greatly outperforms one of the most e ective satis ability algorithm known to date, namely the popular DavisPutnam procedure.