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New real-time simulations of multihead tape units

Just as the Church-Turing thesis has simplified proofs of computability [8], efficient simulations of one computer model by another have simplified proofs of complexity upper bounds. A good example of this is Fischer, Meyer, and Rosenberg's real-time simulation of multihead Turing machines by multitape Turing machines [5]. Without this result, for example, even Slisenko [11] may have found it hopeless to show that a multitape Turing machine can recognize palindromes in real time. In this paper we give a comparatively simple proof of the Fischer-Meyer-Rosenberg result, dramatically reduce the number of single-head tapes required for the simulation, and generalize the result to multidimensional tapes. In the case of Slisenko's palindrome-recognizer, for example, our best simulation brings the number of tapes for a multitape Turing machine implementation down from 41 to 20.