Solving SAT by algorithm transform of Wu’s method

Abstract

Recently algorithms for solving propositional satisfiability problem, or SAT, have aroused great interest, and more attention has been paid to transformation problem solving. The commonly used transformation is representation transform, but since its intermediate computing procedure is a black box from the viewpoint of the original problem, this approach has many limitations. In this paper, a new approach called algorithm transform is proposed and applied to solving SAT by Wu’s method, a general algorithm for solving polynomial equations. By establishing the correspondence between the primitive operation in Wu’s method and clause resolution in SAT, it is shown that Wu’s method, when used for solving SAT, is primarily a restricted clause resolution procedure. While Wu’s method introduces entirely new concepts, e.g. characteristic set of clauses, to resolution procedure, the complexity result of resolution procedure suggests an exponential lower bound to Wu’s method for solving general polynomial equations. Moreover, this algorithm transform can help achieve a more efficient implementation of Wu’s method since it can avoid the complex manipulation of polynomials and can make the best use of domain specific knowledge.