Optimal Time Bounds for Parallel Term Matching

Term Matching is a fundamental operation in term rewriting, functional programming and logic programming. Parallel algorithms for this operation have attracted much attention recently. However nontrivial lower bounds for term matching are as yet unknown. In this paper, we obtain lower bounds on parallel time for this problem. We also establish the tightness of our lower bounds for some representations and several models, by giving matching upper bounds with as few processors as possible.