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1) Consider the language L = L1 ∩ L2, where L1 = {ww^R : w ∈ {a, b}* and L2 = {a^n b*a^n: 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.
d) Prove that L is not regular.
We showed to prove that if L can be identified by DFA then the language left half(L) = {x ∈ ∑*|∃y xy ∈ L and |x| = |y|} is also regular; here |x| means length of x.
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