Give a nondeterministic turing machine which recognizes the

Question

1. Give an offline TM which when started with x#y on its read only input tape outputs ?xy? on its output tape. Assume {0,1,#} is the input alphabet and numbers are in binary (lead zeros not allowed). On bad inputs your TM should halt, with # on the tape. If y is 0 output #. If x is 0 and y is a nonzero integer the output should be 0.
2. Given the offline TM above use the construction from class to give a diagram of a usual TM computing the same function.
3. Give the RAM that would result from applying the construction of class to the TM from Problem 2.
4. Give a nondeterministic Turing machine which recognizes the language of binary strings of integers nsuch that n is a product of integers x and y both of which are greater than 1. You can give a high level description of your NTM.