Completion for Multiple Path Orderings Based on Precedence and Binary Decision Diagrams

Abstract

In this paper, we propose a completion procedure (called MKB_po) for term rewriting systems. Based on the existing procedure MKB which works with multiple reduction orderings and the ATMS nodes, the MKB_po improves its performance by restricting the class of reduction orderings to precedence-based path orderings, representing them by logical functions in which a logical variable x_fg represents the precedence f > g. By using BDD (binary decision diagrams) as a representation of logical functions, the procedure can be implemented efficiently. This makes it possible to save the number of quasi-parallel processes effectively and suppress the rapid increase in the amount of computation time asymptotically.