Representations and characterizations of languages in Chomsky hierarchy by means of insertion-deletion systems

Gheorghe Pǎun, Mario J. Pérez-Jiménez, Takashi Yokomori

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability and characterizations or representations of languages in Chomsky hierarchy were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schützenberger representation of context-free languages, i.e., in the form L h(L(γ) ∩ D), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages this time using insertion systems of weight (3, 0) and star languages.

    Original languageEnglish
    Pages (from-to)859-871
    Number of pages13
    JournalInternational Journal of Foundations of Computer Science
    Volume19
    Issue number4
    DOIs
    Publication statusPublished - 2008 Aug

    Fingerprint

    Context free languages
    Stars
    Formal languages
    Linguistics
    DNA

    Keywords

    • Context-free languages
    • Insertion-deletion systems
    • Recursively enumerable languages
    • Regular languages

    ASJC Scopus subject areas

    • Computer Science (miscellaneous)

    Cite this

    Representations and characterizations of languages in Chomsky hierarchy by means of insertion-deletion systems. / Pǎun, Gheorghe; Pérez-Jiménez, Mario J.; Yokomori, Takashi.

    In: International Journal of Foundations of Computer Science, Vol. 19, No. 4, 08.2008, p. 859-871.

    Research output: Contribution to journalArticle

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