On Contextual Grammars with Subregular Selection Languages

Abstract

In this paper, we study the power of external contextual grammars with selection languages from subfamilies of the family of regular languages. If we consider families $\mathcal F_n$ which are obtained by restriction to n states or nonterminals or productions or symbols to accept or to generate regular languages, we obtain four infinite hierarchies of the corresponding families of languages generated by external contextual grammars with selection languages in $\mathcal F_n$. Moreover, we give some results on the power of external contextual grammars with regular commutative, regular circular, definite, suffix-free, ordered, combinational, nilpotent, and union-free selection languages.