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See Ullman's book [1] for more details on formal proofs.

Basically you can emulate the Turing machine's tape on the left side of the head with one stack and on the right side with the second stack.

An important question to now ask would be what happens if the tape in the machine has more than two directions; say for example it has a two-dimensional tape. The head may move left, right, but also up and down. It can be proven that such a machine would not be any more capable than the Turing machine with a 1D tape. Again see Ullman's book for details.

[1] http://www.amazon.com/Introduction-Automata-Theory-Languages...




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