On hairpin-free words and languages

  • Authors:

  • Lila Kari;Stavros Konstantinidis;Petr Sosík;Gabriel Thierrin

  • Affiliations:

  • Department of Computer Science, The University of Western Ontario, London, ON, Canada;Dept. of Mathematics and Computing Science, Saint Mary's University, Halifax, Nova Scotia, Canada;Institute of Computer Science, Silesian University, Opava, Czech Republic;Department of Mathematics, The University of Western Ontario, London, ON, Canada

  • Venue:
  • DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
  • Year:
  • 2005

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Abstract

The paper examines the concept of hairpin-free words motivated from the biocomputing and bioinformatics fields. Hairpin (-free) DNA structures have numerous applications to DNA computing and molecular genetics in general. A word is called hairpin-free if it cannot be written in the form xvyθ (v)z, with certain additional conditions, for an involution θ (a function θ with the property that θ2 equals the identity function). We consider three involutions relevant to DNA computing: a) the mirror image function, b) the DNA complementarity function over the DNA alphabet {A,C,G,T} which associates A with T and C with G, and c) the Watson-Crick involution which is the composition of the previous two. We study elementary properties and finiteness of hairpin (-free) languages w.r.t. the involutions a) and c). Maximal length of hairpin-free words is also examined. Finally, descriptional complexity of maximal hairpin-free languages is determined.