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 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

Fingerprint

Algebraic Structure
Closed
Subset
Class
Language
Family
Hierarchy

Keywords

  • 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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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: $K_{m,n}\subset K_{m,n+1}$.",
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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

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 proceedingChapterAcademic

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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: $K_{m,n}\subset K_{m,n+1}$.

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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