Show that a 2-push-down automaton (which is a push-down automaton with 2 stacks) can simulate a Turing machine (the basic model, with 1 tape). In your solution you must include:

(a) A description of how the 2-PDA stores the tape of the TM. Take as an example a TM M in the configuration aaq1abbbb. Make a diagram that represents the content of the 2 stacks of the 2-PDA simulating M.

(b) A precise explanation on how the 2-PDA simulates a move of the TM of the form ?(q1, a) = (r, b, L), containing the sequence of push and pop operations for the 2 stacks. Use the example from (a), and show the contents of the 2 stacks of the 2-PDA after simulating this move.

(c) A precise explanation on how the 2-PDA simulates a move of the TM of the form ?(q1, a) = (r, b, R), containing the sequence of push and pop operations for the 2 stacks. Use the example from (a), and show the contents of the 2 stacks of the 2-PDA after simulating this move. Describe your solution in a clear and concise way, in plain English.