### Abstract

We study slender context-sensitive languages, i.e., those containing at most a constant number of words of each length. Recently, it was proved that every slender regular language can be described by a finite union of terms of the form uv^{i}w [9] and every slender context-free language can be described by a finite union of terms of the form uv^{i}wx^{i} y [4, 10]. We show a hierarchy of slender languages which is properly contained in the family of context-sensitive languages and which starts with the family of slender context-free languages, or slender regular languages. Each slender context-sensitive language in the hierarchy can be described by a finite union of terms of the form x_{1}y_{1}^{i}x_{2}y_{2} ^{i}⋯x_{n}y_{n}^{i}x_{n+1}.

Original language | English |
---|---|

Pages (from-to) | 41-47 |

Number of pages | 7 |

Journal | Fundamenta Informaticae |

Volume | 31 |

Issue number | 1 |

Publication status | Published - 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Control sets
- Cryptosystems
- Slender languages

### ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

### Cite this

*Fundamenta Informaticae*,

*31*(1), 41-47.

**On a hierarchy of slender languages based on control sets.** / Koshiba, Takeshi.

Research output: Contribution to journal › Article

*Fundamenta Informaticae*, vol. 31, no. 1, pp. 41-47.

}

TY - JOUR

T1 - On a hierarchy of slender languages based on control sets

AU - Koshiba, Takeshi

PY - 1997

Y1 - 1997

N2 - We study slender context-sensitive languages, i.e., those containing at most a constant number of words of each length. Recently, it was proved that every slender regular language can be described by a finite union of terms of the form uviw [9] and every slender context-free language can be described by a finite union of terms of the form uviwxi y [4, 10]. We show a hierarchy of slender languages which is properly contained in the family of context-sensitive languages and which starts with the family of slender context-free languages, or slender regular languages. Each slender context-sensitive language in the hierarchy can be described by a finite union of terms of the form x1y1ix2y2 i⋯xnynixn+1.

AB - We study slender context-sensitive languages, i.e., those containing at most a constant number of words of each length. Recently, it was proved that every slender regular language can be described by a finite union of terms of the form uviw [9] and every slender context-free language can be described by a finite union of terms of the form uviwxi y [4, 10]. We show a hierarchy of slender languages which is properly contained in the family of context-sensitive languages and which starts with the family of slender context-free languages, or slender regular languages. Each slender context-sensitive language in the hierarchy can be described by a finite union of terms of the form x1y1ix2y2 i⋯xnynixn+1.

KW - Control sets

KW - Cryptosystems

KW - Slender languages

UR - http://www.scopus.com/inward/record.url?scp=0031189427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031189427&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031189427

VL - 31

SP - 41

EP - 47

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

IS - 1

ER -