To Guess or to Think? Hybrid Algorithms for SAT (Extended Abstract)

Complete algorithms for solving propositional satis ability fall into two main classes: backtracking search (e.g., the Davis-Putnam Procedure [1]) and resolution (e.g., Directional Resolution [4]). Backtracking may be viewed as a systematic \guessing" of variable assignments, while resolution invokes making inferences, i.e. \thinking". Experimental results show that \pure guessing" or \pure thinking" might be ine cient. We propose an approach that combines both techniques and yields a family of hybrid algorithms, parameterized by a bound on the "e ective" amount of resolution allowed. The idea is to divide the set of propositional variables into two classes: conditioning variables, which are assigned truth values, and resolution variables, which are resolved upon. We report on preliminary experimental results demonstrating that on certain classes of problems hybrid algorithms are more e cient than either of their components in isolation.