We introduce bisimulation up to congruence as a technique for proving language equivalence of nondeterministic finite automata. Exploiting this technique, we devise an optimization of the classic algorithm by Hopcroft and Karp.13 We compare our approach to the recently introduced antichain algorithms and we give concrete examples where we exponentially improve over antichains. Experimental results show significant improvements.
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Checking language equivalence of finite automata is a classic problem in computer science, with many applications in areas ranging from compilers to model checking.
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