Controlled Pure Grammar Systems

formal languages, pure grammar systems, controlled derivations

This paper discusses grammar systems that have only terminals, work in the leftmost way, and generate their languages under the regulation by control languages over rule labels. It establishes three results concerning their generative power. First, without any control languages, these systems are not even able to generate all context-free languages. Second, with regular control languages, these systems, having no more than two components, characterize the family of recursively enumerable languages. Finally, with control languages that are themselves generated by regular-controlled context-free grammars, these systems over unary alphabets generate nothing but regular languages. In its introductory section, the paper gives a motivation for introducing these systems, and in the concluding section, it formulates several open problems.