Parallel Processing of Resolution

In this paper, PArallel Resolution Algorithm (PARA) is described to improve the execution efficiency in resolution process. PARA consists of two parts: parallel unification and generation of a resolvent. The first part is characteristic of PARA, which partitions whole set of expressions W into independent clusters as pre-processing and unifies each cluster in parallel. The efficient implementation for the processing peculiar to PARA is presented and checked by means of the experiment in comparison of execution efficiency of resolution. Experimental results show PARA is very effective in occurrence of many clusters. 1.INTRODUCTION Unification in first-order logic is to match corresponding arguments in two predicates. This processing is important in resolution [1] and the efficient implementation for it has been the subject, of much investigation [2]-[5l. But this research in unification was out of parallel-process ing. With regard to unification (resolution) parallelism, two representative ways, the post-processing way and the pre-processing way, would be considered. In case of the former, after unification, the consistency of substitution must be checked and each substitution component must be composed. This processing would be computed with unification and so the post-processing way is considered to cost much. On the contrary, in case of the latter, the pre-processing way to partition a set of expressions firstly could cost little, because this processing could be computed without unification. from this consideration, in this paper, PARA is presented as one of the pre-processing ways. The characteristic of PARA lies in partitioning whole set of expressions W (the pairs of corresponding arguments in resolved literals) into clusters (sets of pairs of arguments such that each set has no variables in common) as pre-processing and unifying each cluster independently in parallel. 2.PARALLEL RESOLUTION ALGORITHM Resolution consists of unification and generation of a resolvent. It costs more time to execute unification and so unification must be executed efficiently. The unification problem can be expressed as simultaneous equations [5] and the solution of them can be considered as most general unifier (mgu). The ordinary serial unification is process which solves simultaneous equations sequentially. They could, however, be divided Into subsets of equations which are parallel-processed independen tly. ParalleI resolution consists of two parts: parallel-processing of unification and generation of a resolvent. FIg.1 shows PARA. Firstly PARA partitions whole sets of expressions W into clusters of Wl-Wm which include no variables in common as pre-processing. Secondly, after this pre-processing, PARA tries to unify …