Two complementary operations inspired by the DNA hairpin formation: Completion and reduction

Florin Manea, Victor Mitrana, Takashi Yokomori

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    25 Citations (Scopus)


    We consider two complementary operations: Hairpin completion introduced in [D. Cheptea, C. Martin-Vide, V. Mitrana, A new operation on words suggested by DNA biochemistry: Hairpin completion, in: Proc. Transgressive Computing, 2006, pp. 216-228] with motivations coming from DNA biochemistry and hairpin reduction as the inverse operation of the hairpin completion. Both operations are viewed here as formal operations on words and languages. We settle the closure properties of the classes of regular and linear context-free languages under hairpin completion in comparison with hairpin reduction. While the class of linear context-free languages is exactly the weak-code image of the class of the hairpin completion of regular languages, rather surprisingly, the weak-code image of the class of the hairpin completion of linear context-free languages is a class of mildly context-sensitive languages. The closure properties with respect to the hairpin reduction of some time and space complexity classes are also studied. We show that the factors found in the general cases are not necessary for regular and context-free languages. This part of the paper completes the results given in the earlier paper, where a similar investigation was made for hairpin completion. Finally, we briefly discuss the iterated variants of these operations.

    Original languageEnglish
    Pages (from-to)417-425
    Number of pages9
    JournalTheoretical Computer Science
    Issue number4-5
    Publication statusPublished - 2009 Feb 17



    • DNA computing
    • Hairpin completion
    • Hairpin reduction
    • Mildly context-sensitive languages

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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