Watson---Crick palindromes in DNA computing

  • Authors:

  • Lila Kari;Kalpana Mahalingam

  • Affiliations:

  • Department of Computer Science, University of Western Ontario, London, Canada N6A 5B7;Department of Computer Science, University of Western Ontario, London, Canada N6A 5B7 and Department of Mathematics, Indian Institute of Technology, Chennai, India 600035

  • Venue:
  • Natural Computing: an international journal
  • Year:
  • 2010

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Abstract

This paper provides an overview of existing approaches to encoding information on DNA strands for biocomputing, with a focus on the notion of Watson---Crick (WK) palindromes. We obtain a closed form for, as well as several properties of WK palindromes: The set of WK-palindromes is dense, context-free, but not regular, and is in general not closed under catenation and insertion. We obtain some properties that link the WK palindromes to classical notions such as that of primitive words. For example we show that the set of WK-palindromic words that cannot be written as the product of two nonempty WK-palindromes equals the set of primitive WK-palindromes. We also investigate various simultaneous Watson---Crick conjugate equations of words and show that the equations have, in most cases, only Watson---Crick palindromic solutions. Our results hold for more general functions, such as arbitrary morphic and antimorphic involutions.