Define a two-dimensional Turing machine to be a TM where each of its tapes is an infinite grid (and the machine can move not only Left and Right but also Up and Down). Show that for every (time-constructible) T : N → N and every Boolean function f, if f can be computed in time T(n) using a two-dimensional TM then f ∈ DTIME(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. solution