Abstract
The hairpin completion is a natural operation on formal languages which has been inspired by biochemistry and DNA-computing. In this paper we solve two problems which were posed first in 2008 and 2009, respectively, and still left open:
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It is known that the iterated hairpin completion of a regular language is not context-free in general, but it was open whether the iterated hairpin completion of a singleton or finite language is regular or at least context-free. We will show that it can be non-context-free.
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A restricted but also very natural variant of the hairpin completion is the bounded hairpin completion. It was unknown whether the iterated bounded hairpin completion of a regular language remains regular. We prove that this is indeed the case.
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References
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Kopecki, S. (2010). On the Iterated Hairpin Completion. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_42
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DOI: https://doi.org/10.1007/978-3-642-14455-4_42
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