Problem $4.[15$ points$]$ A palindrome is a string that reads the same backward as it does forward. For example, abaaaba is a palindrome. Suppose that we need to define a language that generates palindromes. $($a$)$ Define a phase structure grammar that generates the set of all palindromes over the alphabet $\{$a$,$b$\}$ clearly describing the recursive rules that generates palindromes. Use the notation Symbol $$ rule. The empty set is denoted by $.$ Clearly identify the terminal and non$-$terminal symbols in your grammar. $($b$)$ Show that the palindrome abaaaba can be recognized by your grammar. To show this, show all steps of parsing the expression abaaaba using the rules you defined above.