Combining Preorder and Postorder Resolution in a Satisfiability Solver

Recently, the classical backtracking-search satis ability algorithm of Davis, Putnam, Loveland and Logemann (DPLL) has been enhanced in two distinct directions: with more advanced reasoning methods, or with con ict-directed back-jumping (CBJ). Previous methods used one idea or the other, but not both (except that CBJ has been combined with the unit-clause rule). The diÆculty is that more advanced reasoning derives new clauses, but does not identify which backtrackable assumptions were relevant for the derivation. However CBJ needs this information. The linear-time decision procedure for binary-clause formulas is a good example of this phenomenon. This paper describes an eÆcient method to integrate several popular reasoning methods with CBJ. It includes binary-clause reasoning, equivalent-literal identi cation, variable-elimination resolution, and others. The main idea is to exploit the fact that DPLL can be viewed as an algorithm to construct a resolution refutation, rather than as backtracking-search for a model. Con ict sets in CBJ correspond to clauses in the resolution refutation. Incorporating advanced reasoning into this dual view of DPLL shows the way to combine it soundly with CBJ. Experiments show that the search space is reduced, but that memory has to be managed extremely carefully.