Morphic characterizations of language families based on local and star languages

Fumiya Okubo, Takashi Yokomori

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    New morphic characterizations in the form of a noted Chomsky-Schützenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(Tk ∩ FR) for some 2-star language FR, an extended 2-star language Tk and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(Dn ∩ FL) for some 2-local language FL and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language FL and a weak coding h such that L = h(Bn ∩ FL), where Dn and Bn are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.

    Original languageEnglish
    Pages (from-to)323-341
    Number of pages19
    JournalFundamenta Informaticae
    Volume154
    Issue number1-4
    DOIs
    Publication statusPublished - 2017

    Fingerprint

    Context free languages
    Formal languages
    Stars
    Chemical reactions
    Star
    Context-free Languages
    Regular Languages
    Chemical Reaction
    Automata
    Coding
    Language
    Family
    Projection
    Theorem

    Keywords

    • Chemical reaction automata
    • Context-free languages
    • Local languages
    • Morphic characterizations
    • Regular languages
    • Star languages

    ASJC Scopus subject areas

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

    Cite this

    Morphic characterizations of language families based on local and star languages. / Okubo, Fumiya; Yokomori, Takashi.

    In: Fundamenta Informaticae, Vol. 154, No. 1-4, 2017, p. 323-341.

    Research output: Contribution to journalArticle

    @article{50166a73d1544400afb738f9411f0ee3,
    title = "Morphic characterizations of language families based on local and star languages",
    abstract = "New morphic characterizations in the form of a noted Chomsky-Sch{\"u}tzenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(Tk ∩ FR) for some 2-star language FR, an extended 2-star language Tk and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(Dn ∩ FL) for some 2-local language FL and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language FL and a weak coding h such that L = h(Bn ∩ FL), where Dn and Bn are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.",
    keywords = "Chemical reaction automata, Context-free languages, Local languages, Morphic characterizations, Regular languages, Star languages",
    author = "Fumiya Okubo and Takashi Yokomori",
    year = "2017",
    doi = "10.3233/FI-2017-1569",
    language = "English",
    volume = "154",
    pages = "323--341",
    journal = "Fundamenta Informaticae",
    issn = "0169-2968",
    publisher = "IOS Press",
    number = "1-4",

    }

    TY - JOUR

    T1 - Morphic characterizations of language families based on local and star languages

    AU - Okubo, Fumiya

    AU - Yokomori, Takashi

    PY - 2017

    Y1 - 2017

    N2 - New morphic characterizations in the form of a noted Chomsky-Schützenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(Tk ∩ FR) for some 2-star language FR, an extended 2-star language Tk and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(Dn ∩ FL) for some 2-local language FL and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language FL and a weak coding h such that L = h(Bn ∩ FL), where Dn and Bn are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.

    AB - New morphic characterizations in the form of a noted Chomsky-Schützenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(Tk ∩ FR) for some 2-star language FR, an extended 2-star language Tk and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(Dn ∩ FL) for some 2-local language FL and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language FL and a weak coding h such that L = h(Bn ∩ FL), where Dn and Bn are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.

    KW - Chemical reaction automata

    KW - Context-free languages

    KW - Local languages

    KW - Morphic characterizations

    KW - Regular languages

    KW - Star languages

    UR - http://www.scopus.com/inward/record.url?scp=85027304818&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85027304818&partnerID=8YFLogxK

    U2 - 10.3233/FI-2017-1569

    DO - 10.3233/FI-2017-1569

    M3 - Article

    AN - SCOPUS:85027304818

    VL - 154

    SP - 323

    EP - 341

    JO - Fundamenta Informaticae

    JF - Fundamenta Informaticae

    SN - 0169-2968

    IS - 1-4

    ER -