On the regularity of iterated hairpin completion of a single word

Hairpin completion is an abstract operation modeling a DNA biooperation which receives as input a DNA strand w = xαyα, and outputs w = xαy¯αx, where x denotes the Watson-Crick complement of x. In this paper, we focus on the problem of finding conditions under which the iterated hairpin completion of a given word is regular. According to the numbers of words α and α that initiate hairpin completion and how they are scattered, we classify the set of all words w. For some basic classes of words w containing small numbers of occurrences of α and α, we prove that the iterated hairpin completion of w is regular. For other classes with higher numbers of occurrences of α and α, we prove a necessary and sufficient condition for the iterated hairpin completion of a word in these classes to be regular.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Lila Kari, Steffen Kopecki, Shinnosuke Seki
• Keywords: CORR 2011, Education, Hairpin Completion, Iterated Hairpin Completion, Regular