Checking NFA equivalence with bisimulations up to congruence

Filippo Bonchi (1) , Damien Pous (2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages

We introduce \emph{bisimulation up to congruence} as a technique for proving language equivalence of non-deterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp~\cite{HopcroftKarp} that, instead of computing the whole determinised automata, explores only a small portion of it. Although the optimised algorithm remains exponential in worst case (the problem is PSPACE-complete), experimental results show improvements of several orders of magnitude over the standard algorithm.

Mots clés: Language Equivalence; Non-deterministic Finite Automata; Bisimulation; Coinduction; Up-to techniques; Congruence

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

Filippo Bonchi, Damien Pous. Checking NFA equivalence with bisimulations up to congruence. 2012. ⟨hal-00639716v4⟩