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

Peter R.J. Asveld

doi:10.1007/978-94-015-9634-3_15

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 proceeding › Chapter › Academic

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 C_m(m⩾1) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (C_m ⊃ C_{m +1}). In turn each class C_m contains a countably infinite hierarchy, i.e. a countably infinite chain of language families K_m,n (n⩾1) such that (i) each K_m,n is closed under the operations that determine C m and (ii) each K m,n is properly included in the next one: K_m,n ⊂ K_m,n+1.

Original language	English
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
Publisher	Kluwer
Pages	175-186
Number of pages	12
ISBN (Electronic)	978-94-015-9634-3
ISBN (Print)	978-90-481-5607-8
DOIs	https://doi.org/10.1007/978-94-015-9634-3_15
Publication status	Published - 2001

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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{\textquoteright}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.",

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An Infinite Sequence of Full AFL-structures, Each of Which Possesses an Infinite Hierarchy. / Asveld, Peter R.J.

Where Mathematics, Computer Science, Liguistics and Biology Meet: Essays in honour of Gheorghe Păun. ed. / Carlos Martin-Vide; Victor Mitrana. Dordrecht, The Netherlands : Kluwer, 2001. p. 175-186.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

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