@InProceedings{ KariKS12, author = "Lila Kari and Steffen Kopecki and Shinnosuke Seki", title = "Iterated Hairpin Completions of Non-crossing Words", booktitle = "38th Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM), 2011", editor = "M{\'a}ria Bielikov{\'a} and Gerhard Friedrich and Georg Gottlob and Stefan Katzenbeisser and Gy{\"o}rgy Tur{\'a}n", publisher = "Springer", series = "Lecture Notes in Computer Science", volume = "7147", year = "2012", pages = "337--348", crossref = "DBLP:conf/sofsem/2012", bibsource = "DBLP, http://dblp.uni-trier.de", abstract = "Iterated hairpin completion is an operation on formal languages that is inspired by the hairpin formation in DNA biochemistry. Iterated hairpin completion of a word (or more precisely a singleton language) is always a context-sensitive language and for some words it is known to be non-context-free. However, it is unknown whether regularity of iterated hairpin completion of a given word is decidable. Also the question whether iterated hairpin completion of a word can be context-free but not regular was asked in literature. In this paper we investigate iterated hairpin completions of non-crossing words and, within this setting, we are able to answer both questions. For non-crossing words we prove that the regularity of iterated hairpin completions is decidable and that if iterated hairpin completion of a non-crossing word is not regular, then it is not context-free either.", doi = "10.1007/978-3-642-27660-6_28" }