For each of the following languages L, state whether L is regular, context-free but not regular, or not contextfree and prove your answer.
a) {w : w =uu
^R or w = ua
^n : n = |u|, u ∈ {a, b}*}.
b) {a
^n b^2n c^m} ∩ {a
^n b^m c^2m}.
c) L*, where L = {0*1
^i 0*1^i 0* : i ≥ 0}.
d) ¬L0, where L0 = {ww : w ∈ {a, b}*}.
e) {x ∈ {a, b}* : |x| is even and the first half of x has one more a than does the second half}.