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Definition of CFGs

A grammar G = (V, T, S, P) is a context free grammar (cfg) if all productions in P have the form
A

x where

A V, and
x (V T)*.

Recall that the general form of a production is
A

B where

A (V T), and
x (V T)*.

Since V

, the productions for a context-free grammar are a restricted form of the productions allowed for a general grammar. Thus, a context-free grammar is a grammar.