Hyper-minimization in O(n 2)

Abstract

Two formal languages are f-equivalent if their symmetric difference L 1 Δ 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) and L(D') are f-equivalent. Finally, we present a technique that combines this hyper-minimization 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. © 2008 Springer-Verlag Berlin Heidelberg.