2. In the postfix (or reverse Polish) notation of expressions, the operator always tollows its arguments, so "aaa" is represented as "a a a" and "(a + a) a" as a a a *" (the postfix notation does not use parentheses at all) Find a pushdown automaton which accepts correct epressions in the postfix notation. Hint: In correct postfix epxressions, each (binary) operator must follow its two arguments. The pushdown automaton can push all arguments (represented by "a") on the stack and for each (binary) operator check if the two arguments are on the stack, replacing them by the result of the operation (i.e., a single "a"). After such checking, what remains on the stack is a single element which represents the result of the expression. 3. Consider a context-free grammar 9 generating language L and a set D of leftmost derivations of strings a from L. Observe that a grammar 9' generating the set D can be derived from G by modifying the righthand sides of productions; more specifically, by removing all termi- nal symbols from the righthand sides and inserting new terminal symbols (the production numbers) in front of the remaining nonterminals. (a) Find a context-free grammar G for which the grammar G' is regular. (b) Find a context-free grammar g for which the grammar g' is also context-free. (c) Find two dfferent context-free grammars gi and 92 such that their sets of leftmost derivations are the same. (d) Is g' ambiguous if g is ambiguous? Explain why and provide an example illustrating vour