1. (25 points) Define a two-dimensional Turing machine to be a TM where each of its tapes is an infinite grid (and the read/write head can move not only Left and Right but also Up and Down). Show that for every T : N → N, any two-dimensional TM that runs in time T(n) can be simulated by a standard (one-dimensional) TM in time O(T(n) 2 ). Note: You may assume that the tapes of the two-dimensional TM start at (0, 0) and can only access points with non-negative integer coordinates. The function T(n) is not known in advance.

answer

it would be true.

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