Formal languages
Handbook of Formal Languages
Hairpin Completion Versus Hairpin Reduction
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Two complementary operations inspired by the DNA hairpin formation: Completion and reduction
Theoretical Computer Science
On some algorithmic problems regarding the hairpin completion
Discrete Applied Mathematics
On the iterated hairpin completion
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Information and Computation
On hairpin-free words and languages
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Language theoretical properties of hairpin formations
Theoretical Computer Science
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Hairpin completion and its variant called bounded hairpin completion are operations on formal languages, inspired by a hairpin formation in molecular biology. Another variant called hairpin lengthening has been recently introduced, and the related closure properties and algorithmic problems concerning several families of languages have been studied. In this paper, we introduce a new operation of this kind, called hairpin incompletion which is not only an extension of bounded hairpin completion, but also a restricted (bounded) variant of hairpin lengthening. Further, the hairpin incompletion operation provides a formal language theoretic framework that models a bio-molecular technique nowadays known as Whiplash PCR. We study the closure properties of language families under both the operation and its iterated version. We show that a family of languages closed under intersection with regular sets, concatenation with regular sets, and finite union is closed under one-sided iterated hairpin incompletion, and that a family of languages containing all linear languages and closed under circular permutation, left derivative and substitution is also closed under iterated hairpin incompletion.