Hyper-Minimization in O(n 2)

Abstract

Two formal languages are f-equivalent if their symmetric difference L 1 ∆ 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 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.KeywordsRegular LanguageMinimization AlgorithmClassical MinimizationEquivalence PartitionUnreachable StateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.