Problem 1 Given a Turing machine M, describe how to convert it into a Turing machine M' so that L(M) = L(M'), but M' only halts with an empty tape. In other words, M' makes its tape entirely blank before halting. Beware that the given M might write blanks in the middle of its tape. It might also do daft things, like trying to step left off the left end of its tape. (Note: both M and M' should be "Sipser-style" Turing machines, they expect to see their input on a one-way-infinite tape). Problem 1 Given a Turing machine M, describe how to convert it into a Turing machine M' so that L(M) = L(M'), but M' only halts with an empty tape. In other words, M' makes its tape entirely blank before halting. Beware that the given M might write blanks in the middle of its tape. It might also do daft things, like trying to step left off the left end of its tape. (Note: both M and M' should be "Sipser-style" Turing machines, they expect to see their input on a one-way-infinite tape)