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 θ 2 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.
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Kari, L., Konstantinidis, S., Sosík, P., Thierrin, G. (2005). On Hairpin-Free Words and Languages. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_26
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DOI: https://doi.org/10.1007/11505877_26
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