Let L = {w {0, 1}*| w has even parity}. And let f: {0, 1}* {0, 1}* be the function computed by a deterministic finite state transducer that does the following: for the first bit the DFT writes it out as is. Then for any bit it writets a 0 if it is different than the previous bit and outputs a 1 if it is the same as the previous one. Produce DFA that accepts f(L).