TY - JOUR

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

AU - Koshiba, Takeshi

PY - 1997/7

Y1 - 1997/7

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

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U2 - 10.3233/fi-1997-3114

DO - 10.3233/fi-1997-3114

M3 - Article

AN - SCOPUS:0031189427

VL - 31

SP - 41

EP - 47

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

IS - 1

ER -