Testing the Equivalence of Regular Languages

Abstract

The minimal deterministic finite automaton is generally used to 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 pro- posed an almost linear algorithm for testing the equivalence of two de- terministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algo- rithm to non-deterministic finite automaton, 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 pro- posed by Rutten.