An improved proof for a theorem of N. Chomsky

Masako Takahashi
1969 Proceedings of the Japan Academy  
A context-free grammar is said to be self-embedding if and only if it is reduced and contains a derivation of the form uv, where $ is a variable and u, v are some non-e words. It is known that Theorem. A language L is regular if and only if there is a nonself-embedding grammar generating L. This theorem was first presented in Chomsky [1] with a lengthy proof. Later a simplified proof was given in Chomsky [2]. In this note, the proof is improved by introducing some equivalence classes of the
more » ... ables. Our notations generally follow Ginsburg [3] with the additional convention that the variables are denoted by Greek small letters and words by Latin small letters.
doi:10.3792/pja/1195520719 fatcat:a5vf4ssapvgbpktr4ckablmxyi