Describe a one-tape, deterministic Turing machine that recognizes the language L= {w w is a binary string that contains (exactly) twice as many 0's as I's }. Provide enough details in clear, precise English that describe the operation of the Turing machine: how it moves its head, changes state, writes data on the tape etc. You do not have to give a formal definition (although you may do so if you wish). 2. [7 points] Suppose now that you can use any (constant) number of tapes. Describe informally a multitape (deterministic) Turing machine that recognizes the same language, such that the number of steps executed before it halts for any input of length n is O(n log n) (i.e. at most c n log n for some constant c). (Hint: The machine of problem 4 may be useful here.)