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(n 2) time and space. Furthermore, the new algorithm can also be used to minimize any DFCA, where the best previous method [1] takes O(n 4) time and space.
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References
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Körner, H. (2003). On Minimizing Cover Automata for Finite Languages in O(n log n) Time. In: Champarnaud, JM., Maurel, D. (eds) Implementation and Application of Automata. CIAA 2002. Lecture Notes in Computer Science, vol 2608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44977-9_11
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DOI: https://doi.org/10.1007/3-540-44977-9_11
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