2. (15 points) Consider the PDA: Q = {q0,91,92,94,93} S = {0, 1} T = {$.0} 8(90,, E) = {(q1, $)} 8(q1,0, ) = {(q1,0)} 8(q1,1,0) = {(q4, )} 8(q2,0, 5) = {(q2, )} 8(q3, , $) = {(q2, )} 8(q3, 1,0) = {(94, e)} 8(94, 1, ) = {(q3, )} 8(r, a, b) = 0 9 = 90 F = {90,92} otherwise (a) Draw the state diagram for the PDA. (b) Describe the language recognized by this PDA using set builder notation. (c) Use pumping lemma to prove this language that you described is non-regular