Two formal languages are f-equivalent if their symmetric difference L1 △ L2 is a finite set -that is, if they differ on only finitely many words. The study of f-equivalent languages, and particularly the DFAs that accept them, was recently introduced [1]. First, we restate the fundamental results in this new area of research. Second, our main result is a faster algorithm for the natural minimization problem: given a starting DFA D, find the smallest (by number of states) DFA D ′ such that L(D)

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... nd L(D ′ ) are f-equivalent. Finally, we present a technique that combines this hyperminimization with the well-studied notion of a deterministic finite cover automaton [2-4], or DFCA, thereby extending the application of DFCAs from finite to infinite regular languages.