Technical Report: DCC-2009-01

Testing the Equivalence of Regular Languages

Marco Almeida and Nelma Moreira and Rogério Reis

DCC-FC&LIACC, Universidade do Porto
R. do Campo Alegre 1021/1055 , 4169-007 Porto, Portugal
Phone: +351 220402919 , Fax: 351 22 402 950
E-mail: {mfa,nam,rvr}

June 2009


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 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 automaton, and establish a relationship between this algorithm and the one proposed in Almeida {\em 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.