On a hierarchy of slender languages based on control sets

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
Pages (from-to)41-47
Number of pages7
JournalFundamenta Informaticae
Volume31
Issue number1
Publication statusPublished - 1997
Externally publishedYes

Fingerprint

Context sensitive languages
Control Sets
Context free languages
Formal languages
Context-free Languages
Union
Regular Languages
Term
Hierarchy
Language
Context
Form

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

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

In: Fundamenta Informaticae, Vol. 31, No. 1, 1997, p. 41-47.

Research output: Contribution to journalArticle

@article{b0b8f6da2fe544138712508e66b182e3,
title = "On a hierarchy of slender languages based on control sets",
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 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.",
keywords = "Control sets, Cryptosystems, Slender languages",
author = "Takeshi Koshiba",
year = "1997",
language = "English",
volume = "31",
pages = "41--47",
journal = "Fundamenta Informaticae",
issn = "0169-2968",
publisher = "IOS Press",
number = "1",

}

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 -