Hyper-Minimization in O(n2)

Two formal languages are f-equivalentif their symmetric difference L 1 i¾? L 2 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 Di¾? such that L(D) and L(Di¾?) are f-equivalent. Finally, we present a technique that combines this hyper-minimizationwith 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.