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

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... 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.