### Abstract

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 | |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- EWI-6644
- IR-63355
- METIS-202102

### Cite this

*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

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*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.

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

TY - CHAP

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

AU - Asveld, Peter R.J.

N1 - Imported from HMI

PY - 2001

Y1 - 2001

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

U2 - 10.1007/978-94-015-9634-3_15

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

M3 - Chapter

SN - 978-90-481-5607-8

SP - 175

EP - 186

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

A2 - Martin-Vide, Carlos

A2 - Mitrana, Victor

PB - Kluwer

CY - Dordrecht, The Netherlands

ER -