On the hairpin incompletion

Fumiya Okubo, Takashi Yokomori

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)255-269
    Number of pages15
    JournalFundamenta Informaticae
    Volume110
    Issue number1-4
    DOIs
    Publication statusPublished - 2011

    Fingerprint

    Formal languages
    Molecular biology
    Completion
    Closed
    Regular Sets
    Closure Properties
    Formal Languages
    Substitution reactions
    Derivatives
    Concatenation
    Molecular Biology
    Substitution
    Permutation
    Union
    Intersection
    Language
    Derivative
    Family

    ASJC Scopus subject areas

    • Information Systems
    • Computational Theory and Mathematics
    • Theoretical Computer Science
    • Algebra and Number Theory

    Cite this

    On the hairpin incompletion. / Okubo, Fumiya; Yokomori, Takashi.

    In: Fundamenta Informaticae, Vol. 110, No. 1-4, 2011, p. 255-269.

    Research output: Contribution to journalArticle

    Okubo, Fumiya ; Yokomori, Takashi. / On the hairpin incompletion. In: Fundamenta Informaticae. 2011 ; Vol. 110, No. 1-4. pp. 255-269.
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