First, this paper discusses tree-controlled grammars with root-to-leaf derivation-tree paths restricted by control languages. It demonstrates that if the control languages are regular, these grammars generate the family of context-free languages. Then, in a similar way, the paper introduces tree-controlled grammars with derivation-tree cuts restricted by control languages. It proves that if the cuts are restricted by regular languages, these grammars generate the family of recursively enumerable languages. In addition, it places a binary-relation-based restriction upon these grammars and demonstrate that this additional restriction does not affect the generative power of these grammars.
cuts, context-free grammars, tree-controlled grammars, restricted derivation trees, paths, language families