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.
|Title of host publication||Where Mathematics, Computer Science, Liguistics and Biology Meet|
|Subtitle of host publication||Essays in honour of Gheorghe Păun|
|Editors||Carlos Martin-Vide, Victor Mitrana|
|Place of Publication||Dordrecht, The Netherlands|
|Number of pages||12|
|Publication status||Published - 2001|
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