Bounded hairpin completion

  • Authors:
  • Masami Ito;Peter Leupold;Florin Manea;Victor Mitrana

  • Affiliations:
  • Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Department of Mathematics, Kyoto 603-8555, Japan;Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Department of Mathematics, Kyoto 603-8555, Japan;Otto-von-Guericke-University Magdeburg, Faculty of Computer Science, PSF 4120, D-39016 Magdeburg, Germany and University of Bucharest, Faculty of Mathematics and Computer Science, Str. Academiei 1 ...;University of Bucharest, Faculty of Mathematics and Computer Science, Str. Academiei 14, 010014, Bucharest, Romania and Dept. Organización y Estructura de la Información Universidad Poli ...

  • Venue:
  • Information and Computation
  • Year:
  • 2011

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Abstract

Hairpin completion is a formal operation inspired from biochemistry. Here we consider a restricted variant of hairpin completion called bounded hairpin completion. Applied to a word encoding a single stranded molecule x such that either a suffix or a prefix of x is complementary to a subword of x, hairpin completion produces a new word z, which is a prolongation of x to the right or to the left by annealing. Although this operation is a purely mathematical one and the biological reality is just a source of inspiration, it seems rather unrealistic to impose no restriction on the length of the prefix or suffix added by the hairpin completion. The restriction considered here concerns the length of all prefixes and suffixes that are added to the current word by hairpin completion. They cannot be longer than a given constant. Closure properties of some classes of formal languages under the non-iterated and iterated bounded hairpin completion are investigated. We consider the bounded hairpin completion distance between two words and generalize this distance to languages and discuss algorithms for computing them. Finally also the inverse operation, namely bounded hairpin reduction, as well as the set of all primitive bounded hairpin roots of a regular language are considered.