On a Hierarchy of Slender Languages Based on Control Sets

Article type: Research Article

Authors: Koshiba, Takeshi

Affiliations: High Performance Computing Research Center, Fujitsu Laboratoires Ltd., 4-1-1 Kamikodanaka, Nakahara-ku, Kawasaki-shi, Kanagawa 211, Japan. e-mail: koshiba@flab.fujitsu.co.jp

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 uviwxiy [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 x1yi1x2yi2 ··· xnyinxn+1.

Keywords: slender languages, control sets, cryptosystems

DOI: 10.3233/FI-1997-3114

Journal: Fundamenta Informaticae, vol. 31, no. 1, pp. 41-47, 1997