Checking NFA equivalence with bisimulations up to congruence
Résumé
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.
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