Optimizing Clause Resolution: Beyond Uni cation Factoring

While clause resolution is central to logic programming, practical eeorts to optimize resolution have largely concerned eecient clause indexing. One recent exception is Uniication Factoring 5], which optimizes backtracking through clause heads. Here we consider the problem of optimizing clause resolution in a more general setting than Uniication Factoring. One fundamental change is to use mode informationto distinguish between elementary matching and uniication operations that arise in unifying a term. In addition, we expand the traditional notion of clause resolution to allow for tabled predicates. The result is that our optimization technique becomes relevant for both top-down and bottom-up evaluations. In this expanded setting, we introduce Clause Resolution Automata (CRA), to model clause resolution and to capture its cost. Furthermore, CRAs can be readily implemented as a source transformation. We consider the problem of constructing optimal CRAs. We show that the complexity of construction depends on a variety of conditions: on whether a predicate is tabled, on whether clause order is to be preserved, and on whether information is known about modes. For classes of programs where optimal CRAs can be constructed in polynomial time, dynamic programming algorithms are speciied for their construction. For programs in which optimal CRA construction is NP-complete or NP-hard, we develop heuristics for construction of CRAs. Finally, we present experimental results that show the impact of our approach on performance and space usage of a set of representative programs.