# 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 results 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 ${\cal C}_m$ ($m\geq1$) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (${\cal C}_m\supset{\cal C}_{m+1}$). In turn each class ${\cal C}_m$ contains a countably infinite hierarchy, i.e., a countably infinite chain of language families $K_{m,n}$ ($n\geq1$) such that (i) each $K_{m,n}$ is closed under the operations that determine ${\cal C}_m$, and (ii) each $K_{m,n}$ is properly included in the next one: $K_{m,n}\subset K_{m,n+1}$.
Original language English Where Mathematics, Computer Science, Liguistics and Biology Meet Essays in honour of Gheorghe Păun Carlos Martin-Vide, Victor Mitrana Dordrecht, The Netherlands Kluwer 175-186 12 978-94-015-9634-3 978-90-481-5607-8 https://doi.org/10.1007/978-94-015-9634-3_15 Published - 2001

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Algebraic Structure
Closed
Subset
Class
Language
Family
Hierarchy

• EWI-6644
• IR-63355
• METIS-202102

### Cite this

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
Asveld, Peter R.J. / An Infinite Sequence of Full AFL-structures, Each of Which Possesses an Infinite Hierarchy. Where Mathematics, Computer Science, Liguistics and Biology Meet: Essays in honour of Gheorghe Păun. editor / Carlos Martin-Vide ; Victor Mitrana. Dordrecht, The Netherlands : Kluwer, 2001. pp. 175-186
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title = "An Infinite Sequence of Full AFL-structures, Each of Which Possesses an Infinite Hierarchy",
abstract = "We investigate different sets of operations on languages which results 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 ${\cal C}_m$ ($m\geq1$) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (${\cal C}_m\supset{\cal C}_{m+1}$). In turn each class ${\cal C}_m$ contains a countably infinite hierarchy, i.e., a countably infinite chain of language families $K_{m,n}$ ($n\geq1$) such that (i) each $K_{m,n}$ is closed under the operations that determine ${\cal C}_m$, and (ii) each $K_{m,n}$ is properly included in the next one: $K_{m,n}\subset K_{m,n+1}$.",
keywords = "EWI-6644, IR-63355, METIS-202102",
author = "Asveld, {Peter R.J.}",
note = "Imported from HMI",
year = "2001",
doi = "10.1007/978-94-015-9634-3_15",
language = "English",
isbn = "978-90-481-5607-8",
pages = "175--186",
editor = "Carlos Martin-Vide and Victor Mitrana",
booktitle = "Where Mathematics, Computer Science, Liguistics and Biology Meet",
publisher = "Kluwer",

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Asveld, PRJ 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. Kluwer, Dordrecht, The Netherlands, pp. 175-186. https://doi.org/10.1007/978-94-015-9634-3_15
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 proceedingChapterAcademic

TY - CHAP

T1 - An Infinite Sequence of Full AFL-structures, Each of Which Possesses an Infinite Hierarchy

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N2 - We investigate different sets of operations on languages which results 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 ${\cal C}_m$ ($m\geq1$) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (${\cal C}_m\supset{\cal C}_{m+1}$). In turn each class ${\cal C}_m$ contains a countably infinite hierarchy, i.e., a countably infinite chain of language families $K_{m,n}$ ($n\geq1$) such that (i) each $K_{m,n}$ is closed under the operations that determine ${\cal C}_m$, and (ii) each $K_{m,n}$ is properly included in the next one: $K_{m,n}\subset K_{m,n+1}$.

AB - We investigate different sets of operations on languages which results 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 ${\cal C}_m$ ($m\geq1$) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (${\cal C}_m\supset{\cal C}_{m+1}$). In turn each class ${\cal C}_m$ contains a countably infinite hierarchy, i.e., a countably infinite chain of language families $K_{m,n}$ ($n\geq1$) such that (i) each $K_{m,n}$ is closed under the operations that determine ${\cal C}_m$, and (ii) each $K_{m,n}$ is properly included in the next one: $K_{m,n}\subset K_{m,n+1}$.

KW - EWI-6644

KW - IR-63355

KW - METIS-202102

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DO - 10.1007/978-94-015-9634-3_15

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BT - Where Mathematics, Computer Science, Liguistics and Biology Meet

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