Give pushdown automata that accept the following languages. Draw a state transition diagram and give an explanation of how each PDA works.

(a) {aⁿ b²ⁿ | n 0}.

(b) {w {0, 1}* | #₁(w) = #₀(w)}.

(c) {w {0, 1}* | |w| is even and the middle two bits of w are 11}.

(d) {0ⁿ 1^m | n < m}.

(e) {aⁱ b^j c^k d^l | i = k or j = l}.