I am supposed to write a two-tape Turing machine (low level, all states, complete 7-tuple) to decide the following language: L = {w : w has exactly i a’s, exactly j b’s, and exactly k c’s, and k > i + j}, Σ = {a, b, c}. I then have to define a transition function δ appropriately for the machine and represent it as a table.
I was told the solution to this problem was uses exactly four states, two of which are the halting states qaccept and qreject. How would I go about doing this in only four states? I am confused on how to keep track of the i's, j's and k's with the second tape. I know that I would use the second tape to do this somehow.
Also, what would the alphabet for the second tape be? I know or the first, it would most probably be a,b,c and blank.
