Antimirov and Mosses's Rewrite System Revisited

Antimirov and Mosses proposed a rewrite system for deciding the equivalence of two (extended) regular expressions. They argued that this method could lead to a better average-case algorithm than those based on the comparison of the equivalent minimal deterministic finite automata. In this paper we present a functional approach to that method, prove its correctness, and give some experimental comparative results. Besides an improved functional version of Antimirov and Mosses’s algorithm, we present an alternative one using partial derivatives. Our preliminary results lead to the conclusion that, indeed, these methods are feasible and, most of the time, faster than the classical methods.