Hairpin Completion Versus Hairpin Reduction

  • Authors:
  • Florin Manea;Victor Mitrana

  • Affiliations:
  • Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 70109, Bucharest, Romania;Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 70109, Bucharest, Romania and Research Group in Mathematical Linguistics, Rovira i Virgili University, Pl. ...

  • Venue:
  • CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
  • Year:
  • 2007

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Abstract

We define the hairpin reduction as the inverse operation of a formal operation on words and languages suggested by DNA biochemistry, namely the hairpin completion, introduced in [3]. We settle the closure properties of some classes in the Chomsky hierarchy as well as some complexity classes under the non-iterated version of the hairpin reduction, in comparison with the hairpin completion. Then an algorithm that decides whether or not a regular language coincides with its primitive hairpin root is presented. Finally, we discuss a cubic time algorithm for computing the common ancestors of two given words. This algorithm may be used also for computing the closest or farthest primitive hairpin root of a given word.