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

Peter R.J. Asveld

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

    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
    Title of host publicationWhere Mathematics, Computer Science, Liguistics and Biology Meet
    Subtitle of host publicationEssays in honour of Gheorghe Păun
    EditorsCarlos Martin-Vide, Victor Mitrana
    Place of PublicationDordrecht, The Netherlands
    PublisherKluwer
    Pages175-186
    Number of pages12
    ISBN (Electronic)978-94-015-9634-3
    ISBN (Print)978-90-481-5607-8
    DOIs
    Publication statusPublished - 2001

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    Asveld, P. R. J. (2001). An Infinite Sequence of Full AFL-structures, Each of Which Possesses an Infinite Hierarchy. In C. Martin-Vide, & V. Mitrana (Eds.), Where Mathematics, Computer Science, Liguistics and Biology Meet: Essays in honour of Gheorghe Păun (pp. 175-186). Dordrecht, The Netherlands: Kluwer. https://doi.org/10.1007/978-94-015-9634-3_15