Myhill-nerode theorem, Theory of Computation

The Myhill-Nerode Theorem provided us with an algorithm for minimizing DFAs. Moreover, the DFA the algorithm produces is unique up to isomorphism: every minimal DFA that recognizes the same language will have the same number of states and the same edges, differing in no more than the particular names it gives the states. If we apply this to A and L(A) is empty then we will obtain a DFA that is isomorphic to any minimal DFA that recognizes ∅. In particular it will contain just a single state and that state will not be an accepting state. (Being a DFA, that state will have a self-edge for every symbol in the alphabet.) It's pretty easy to check if this is the case for the minimized version of A. We return "True" iff it is.

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