i. If A is a push down automata accepts L by final state, we can find a pda B accepting L by empty store. Construct B form A where A is as follows. A = ({40, 91. 9), fa, b, c), fa, b. Z}. 8. 9o. Z {9}) is a pda, where 8 is defined as 8(90. a. Z) = {(90, az)), 8(90, b. Z) = {lgo. bz)} 8(90. a. a) = {(go, aa)), digo, b, a) = {(4o.ba)) 8(9o. a. b) = {(9o. ab)}, 8(90. b, b) = {(go, bb)} 8(90. c. a) = {(9. a)}, 8(90. c. b) = {(91. b)}, 8(90, c, Z) = {(g. 20)} 819. a, a) = o(as. b. b) = f(qA)} 819. A. Z) = {(4x Z)}