Question: 1. Find a Turing machine that changes a unary string to a string of the same length with alternating 1s and 0s.
2. Find a nonhalting Turing machine that begins with a single 1 on its tape and successively generates strings of the form 0n 10n , n ≥ 1, that is, such strings appear every so often on the tape.
3. Find a Turing machine that, given an initial tape containing a (possibly empty) string of 1s, adds a single 0 to the left end of the string if the number of 1s is even and adds two 0s to the left end of the string if the number of 1s is odd.