Ullman (Compiler Design) Edition 2 Exercise 2.2 Question 1 (Page No. 51)

Question

Consider the context-free grammar

$S\rightarrow SS+\mid SS^{\ast}\mid a$

1. Show how the string $aa+a^{\ast}$ can be generated by this grammar.
2. Construct a parse tree for this string.
3. What language does this grammar generate? Justify your answer.