$4)$ Consider the language L $=$ L$1$ L$2,$ where L$1=\{$wwR : w $\{$a$,$ b$\}*$ and L$2=\{$anb$*$an: n $0\}.$

a$)$ List the first four strings in the lexicographic enumeration of L$?$

b$)$ Write a context$-$free grammar to generate L$.$

c$)$ Show a natural PDA for L$.($In other words, don$$t just build it from the grammar using one of the two$-$state

constructions presented in this chapter.$)$

d$)$ Prove that L is not regular.