On a special class of primitive words

When representing DNA molecules as words, it is necessary to take into account the fact that a word u encodes basically the same information as its Watson-Crick complement θ(u), where θ denotes the Watson-Crick complementarity function. Thus, an expression which involves only a word u and its complement can be still considered as a repeating sequence. In this context, we define and investigate the properties of a special class of primitive words, called θ-primitive, which cannot be expressed as such repeating sequences. For instance, we prove the existence of a unique θ-primitive root of a given word, and we give some constraints forcing two distinct words to share their θ-primitive root. Also, we present an extension of the well-known Fine and Wilf Theorem, for which we give an optimal bound.

• Type: Journal
• Year: 2010
• Where: TCS
• Authors: Elena Czeizler, Lila Kari, Shinnosuke Seki
• Keywords: TCS 2010, Theoretical Computer Science, Unique θ-primitive Root, Watson-Crick Complementarity Function, θ-primitive Root