Testing the Equivalence of Regular Languages

TL;DR

This paper improves algorithms for testing the equivalence of regular languages, extending to non-deterministic automata, and relates these methods to coalgebraic approaches, with experimental comparisons.

Contribution

It introduces an improved algorithm for automata equivalence testing, extends it to non-deterministic automata, and explores connections with coalgebraic methods.

Findings

Enhanced best-case running time for automata equivalence testing

Extended algorithm applicability to non-deterministic automata

Provided experimental comparative results

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 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.