Exercise 23.14

An augmented context-free grammar can represent languages that a regular context-free grammar cannot. Show an augmented context-free grammar for the language $a^nb^nc^n$. The allowable values for augmentation variables are 1 and $SUCCESSOR(n)$, where $n$ is a value. The rule for a sentence in this language is $S(n) \rightarrow}}A(n) B(n) C(n) \ .$ Show the rule(s) for each of ${\it A}$, ${\it B}$, and ${\it C}$.