Q6 Q8: If any proof is done using a Pumping Lemma (PL) for a non-regular language, prove it by the following steps.

Choose your w, s.t. |w| m > 0 Note: your w must be a string in terms of m, not a specific example of w.

Decide your substrings x, y, and z after the partition of w=xyz, satisfying their requirements in PL. Explain your rationale for choosing x, y, z.

Decide your number of pumping i.

Show that your w_i = xyⁱz is not in L.

Q6. [15] Prove that L is regular or not regular.

L = L(ab*a*) L(a*b*a).

Hint: If L is regular, prove it either by giving a regular grammar G s.t. L = L(G), by constructing a FA M s.t. L = L(M), or applying the closure properties of regular languages. Otherwise, prove it by Pumping Lemma.