On external contextual grammars with subregular selection languages

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 Fn 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 Fn. 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.