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Time complexity of multidimensional Turing machines

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Abstract

It is proved that the work of an indeterminate m-dimensional Turing machine with time complexity t can be simulated on an indeterminate k-dimensional (k≤m) Turing machine with time complexity t1−(1/m)+(1/k)+ɛ (for any ε>0). Moreover, the following generalization to the multidimensional case of the familiar theorem of Hopcroft, Paul, and Valiant is proved: the work of an m-dimensional Turing machine with time complexity t log1/mt [t(n)≥n] can be simulated on an address machine working with time complexity t.

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Authors
  1. D. Yu. Grigor'ev
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 47–55, 1979.

The author expresses thanks to A. O. Slisenko for interest in the work, S.V. Pakhamov for helpful discussions, and A. P. Bel'tyukov for valuable comments.

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Grigor'ev, D.Y. Time complexity of multidimensional Turing machines. J Math Sci 20, 2290–2295 (1982). https://doi.org/10.1007/BF01629436

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  • DOI: https://doi.org/10.1007/BF01629436

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