determine regular languages equality. Antimirov and Mosses proposed

a rewrite system for deciding regular expressions equivalence of

which Almeida et al. presented an improved variant. Hopcroft

and Karp proposed an almost linear algorithm for testing the

equivalence of two deterministic finite automata that avoids

minimisation.

In this paper we improve the best-case running time, present an

extension of this algorithm to non-deterministic finite automata,

and establish a relationship between this algorithm and the one

proposed in Almeida et al. We also present some experimental

comparative results. All these algorithms are closely related with

the recent coalgebraic approach to automata proposed by Rutten.