An Extension of the Lyndon Schützenberger Result to Pseudoperiodic Words

  • Authors:

  • Elena Czeizler;Eugen Czeizler;Lila Kari;Shinnosuke Seki

  • 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;Department of Computer Science, University of Western Ontario, London, Canada N6A 5B7;Department of Computer Science, University of Western Ontario, London, Canada N6A 5B7

  • Venue:
  • DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
  • Year:
  • 2009

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Abstract

One of the particularities of information encoded as DNA strands is that a string u contains basically the same information as its Watson-Crick complement, denoted here as 驴(u). Thus, any expression consisting of repetitions of u and 驴(u) can be considered in some sense periodic. In this paper we give a generalization of Lyndon and Schützenberger's classical result about equations of the form u l = v n w m , to cases where both sides involve repetitions of words as well as their complements. Our main results show that, for such extended equations, if l 驴 5, n, m 驴 3, then all three words involved can be expressed in terms of a common word t and its complement 驴(t). Moreover, if l 驴 5, then n = m = 3 is an optimal bound. We also obtain a complete characterization of all possible overlaps between two expressions that involve only some word u and its complement 驴(u).