On minimizing cover automata for finite languages in O(n log n) time

Authors:
Heiko Körner
Affiliations:
Venue:
CIAA'02 Proceedings of the 7th international conference on Implementation and application of automata
Year:
2002

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Abstract

A deterministic finite automaton (DFA) A is called a cover automaton (DFCA) for a finite language L over some alphabet Σ if L = L(A) ∩ Σ≤l, with l being the length of some longest word in L. Thus a word w ∈ Σ* is in L if and only if |w| ≤ l and w ∈ L(A). The DFCA A is minimal if no DFCA for L has fewer states. In this paper, we present an algorithm which converts an n-state DFA for some finite language L into a corresponding minimal DFCA, using only O(n log n) time and O(n) space. The best previously known algorithm [2] requires O(n2) time and space. Furthermore, the new algorithm can also be used to minimize any DFCA, where the best previous method [1] takes O(n4) time and space.