Introduction to Computer Theory by Daniel Cohen $,$ Chapter $13$

Qno$\mathrm{.}6$:

$($i$)$ For each of the CFG$\text{'}$s in Problems $1$ through $5$ determine whether

there is a word in the language that can be generated in two

substantially different ways. By "substantially," we mean that if

two steps are interchangeable and it does not matter which comes

first, then the different derivations they give are considered "substantially the same" otherwise they are "substantially different."

$($ii$)$ For those CFG$\text{'}$s that do have two ways of generating the same word,

show how the productions can be changed so that the language generated stays the same but all words are now generated by substantially

only one possible derivation.