These are short answer questions concerning the pumping lemma for regular sets. Assume that we are in the middle of a pumping lemma proof designed to show that a language is not regular, and that the value N and all other preliminaries have been determined. The questions below address specifically the w string, chosen in Step 2 of the proof, and the i value, chosen in Step 4 of the proof.

b) Let L = {0i 1 j 0 k | i,j,k >= 0 and j<=2i} i) let w = 0N 1 N 0 N (1) is this an acceptable w string in Step 2 of the proof? Why or why not? (2) will it work in Step 4? Why or why not? ii) what w string do you recommend for a pumping lemma proof for this language? (1) Choose an i value, and give an argument that your choices for w and i will work in a pumping lemma proof.