The linear landscape of external contextual languages

Abstract.

The class of external contextual languages is strictly included in the class of linear languages. A reason for the strict inclusion in linear languages is that external contextual grammars generate languages in the exhaustive way: each sentential form belongs to the language of a grammar. In this paper we study the effect of adding various squeezing mechanisms to the basic classes of exhaustive contextual grammars. We obtain in this way a characterization of linear languages and a whole landscape of sublinear families. By restricting the contexts to be one-sided (only left-sided or only right-sided) we obtain a characterization of regular languages – here the subregular landscape reduces to two families.