1. Design a Turing machine which recognizes the language consisting of all strings of Os whose length is a power of 2. i.e., it decides the language L = {0~ |n203. 2. Design a Turing machine which recognizes the language L = {w# ww{0,1}}. 3. Design a Turing machine which recognizes the language L = {a'biclix j = k and i, j, k 2 1}. 4. Design a deterministic Turing machine (DTM) to accept the language L = {a'b'c' i 20). 5. Define a DTMs to accept the following languages. Specify the 5-tuple in each. (Use multi-tape machine if necessary). (a) {xx|x E{0,1}} (b) {x|x (0,1}* and x = x"} 6. Design DTMs to compute the following functions. (Input number can be in unary, i.e., n is encoded as 1"). (a) Successor function: f:N N where f(n) = n + 1