Give a PDA for each of the following languages. For each PDA, you must specify the 7 components of the PDA (Q, , , , q0, Z0, F). In addition to the formal definition of , describe in words what the transition does; e.g., (q1, a, A) = {(q1, AA),(q2, )} would be described as in state q1 if a is the input and A is top of stack, then either push an additional A onto the stack and stay in state q1, or go to state q2 and pop A from the stack

= (g) L7 {w {a,b}* | na(w) > 2nb(w), where na(w), n(w) > 0} Note: na(w) is number of as in the string w and n(w) is number of bs in w. (h) L8 {w {a,b}* | na(w) = 3nb(w), where na(w), n(w) > 0}. Note: na(w) is number of a's in the string w and no(w) is number of bs in w. (i) Lg = {abj ckd | i = k or j = 1, where i, j, k, l >0}