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Authors: Diekert, Volker
Kopecki, Steffen
Title: Complexity results and the growths of hairpin completions of regular languages
Issue Date: 2010 Arbeitspapier
Series/Report no.: Technischer Bericht / Universität Stuttgart, Fakultät Informatik, Elektrotechnik und Informationstechnik;2010,4
Abstract: The hairpin completion is a natural operation on formal languages which has been inspired by molecular phenomena in biology and by DNA-computing. In 2009 we presented a (polynomial time) decision algorithm to decide regularity of the hairpin completion. In this paper we provide four new results: 1.) We show that the decision problem is NL-complete. 2.) There is a polynomial time decision algorithm which runs in time O(n8), this improves our previous results, which provided O(n^{20}). 3.) For the one-sided case (which is closer to DNA computing) the time is O(n2), only. 4.) The hairpin completion of a regular language is unambiguous linear context-free. This result allows to compute the growth (generating function) of the hairpin completion and to compare it with the growth of the underlying regular language.
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