On tree-restricted regular-controlled context-free grammars

摘要

This paper gives simple tree-based conditions under which regular-controlled context-free grammars generate context-free languages of finite index, so they cannot even generate all context-free languages. It defines the notion of path-changing derivation step which corresponds to performing two consecutive rewritings of nonterminal symbols present in the different branches of the derivation tree. It proves that if there exists a certain constant that limits the number of path-changing derivation steps, then, the regular-controlled grammar generates a context-free language of finite index. At the end, we generalize achieved result and provide some open problems for future study.