An O(n2) Algorithm for Constructing Minimal Cover Automata for Finite Languages

Abstract Cover automata were introduced in [1] as an efficient representation of finite languages. In [1], an algorithm was given to transform a DFA that accepts a finite language to a minimal deterministic finite cover automaton (DFCA) with the time complexity O(n4), where n is the number of states of the given DFA. In this paper, we introduce a new efficient transformation algorithm with the time complexity O(n2), which is a significant improvement from the previous algorithm. 1 Introduction Finite languages have many practical applications [6, 2]. However, the finite languages used in applications are generally very large, which need thousands or even millions of states if represented by deterministic finite automata (DFA) or similar structures. In [1], deterministic finite cover automata (DFCA) were introduced as an alternative representation of finite languages. Experiments have shown that, in many cases, DFCA are much smaller in size than their corresponding minimal DFA [5]