Question

Implement a Turing machine that subtracts two from the input string corresponding a ternary number. More specifically, suppose w = a_n−1a_n−2 . . . a₁a₀ is the input string with a_i ∈ {0, 1, 2}. Your Turing machine should subtract two from w “in-place”, i.e., at the end of the computation the tape should contain the result, w − 2 and the tape head should be at the start of that string. Upon a successful operation, halt on accept. Otherwise, i.e., when the input is empty or the number is too small, halt on reject. Test your machine with w₀ = 01, w₁ = 1000 and w₂ = 2011.