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 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 x₁yⁱ ₁x₂yⁱ ₂ ··· x_nyⁱ _nx_n+1.