Complexity Results and the Growths of Hairpin Completions of Regular Languages (Extended Abstract)

  • Volker Diekert
  • Steffen Kopecki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6482)

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 \(\mathcal{O}(n^{8})\), this improves [6], which provided \(\mathcal{O}(n^{20})\). 3.) For the one-sided case (which is closer to DNA computing) the time is \(\mathcal{O}(n^{2})\), 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.

Keywords

Polynomial Time Formal Language Decision Algorithm Complexity Result Regular Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Volker Diekert
    • 1
  • Steffen Kopecki
    • 1
  1. 1.FMIUniversität StuttgartStuttgartGermany

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