Abstract
In 1985, Dymond and Tompa showed that every deterministic Turing machine with linear tapes and time complexity T can be simulated by an alternating Turing machine with linear tapes that runs in time O( T log T ) . We extend their result to multidimensional Turing machines. We show that every deterministic Turing machine with d-dimensional tapes and time complexity T can be simulated by an alternating Turing machine with linear tapes that runs in time O( T ( log T) 1 d )
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