An Infinite Sequence of Full AFL-Structures, Each of Which Possesses an Infinite Hierarchy

Peter R.J. Asveld

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    Abstract

    We investigate different sets of operations on languages which result in corresponding algebraic structures, viz. in different types of full AFL’s (full Abstract Family of Languages). By iterating control on ETOL-systems we show that there exists an infinite sequence Cm(m⩾1) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (Cm ⊃ Cm +1). In turn each class Cm contains a countably infinite hierarchy, i.e. a countably infinite chain of language families Km,n (n⩾1) such that (i) each Km,n is closed under the operations that determine C m and (ii) each K m,n is properly included in the next one: Km,n ⊂ Km,n+1.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherCentre for Telematics and Information Technology (CTIT)
    Number of pages11
    Publication statusPublished - 1999

    Publication series

    NameCTIT Technical Report Series
    PublisherUniversity of Twente, CTIT
    No.99-06
    ISSN (Print)1381-3625

    Keywords

    • HMI-SLT: Speech and Language Technology

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      • An Infinite Sequence of Full AFL-structures, Each of Which Possesses an Infinite Hierarchy

        Asveld, P. R. J., 2001, Where Mathematics, Computer Science, Liguistics and Biology Meet: Essays in honour of Gheorghe Păun. Martin-Vide, C. & Mitrana, V. (eds.). Dordrecht, The Netherlands: Kluwer, p. 175-186 12 p.

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