Complexity Results and the Growths of Hairpin Completions of Regular Languages (Extended 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 in [6] 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(n(8)), this improves [6], which provided O(n(20)). 3.) For the one-sided case (which is closer to DNA computing) the time is O(n(2)), only. 4.) The hairpin completion 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.