Remarks on context-free grammars with subregular control languages

A context-free grammar with control language is a pair (G,R) where G is a context-free grammar and R is a regular set over the set of productions of G. Its language consists of all terminal words where the sequence of applied productions belongs to R. We study context-free grammars with control languages belonging to subsets of the set of regular languages. We prove that we can obtain only context-free languages if we use regular commutative and strictly locally 1-testable languages. By strictly locally k-testable, k≥2, ordered, union-free, ordered, and regular circular control languages, we have no loss in the generative power, i.e., we generate the same family which is obtained by arbitrary regular control sets.