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Matching upper and lower bounds for simulations of several linear tapes on one multidimensional tape

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Abstract.

We prove an O(t(n)d (t(n)) ½ / log t(n)) time bound for the sim-ulation of t(n) steps of a Turing machine using several one-dimensional work tapes on a Turing machine using one d-dimensional work tape, \( d \ge 2 \). We prove a matching lower bound which holds for the problem of recognizing languages on machines with a separate one-way input tape.

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Authors and Affiliations

  1. Fachbereich Informatik, Lehrstuhl II, Universität Dortmund, D-44221 Dortmund, Germany, e-mail: Dietzfelbinger@informatik.uni-dortmund.de , , , , , , DE

    M. Dietzfelbinger

  2. Fachbereich Informatik, Lehrstuhl II, Universität Dortmund, D-44221 Dortmund, Germany, e-mail: Martin.Huehne@informatik.uni-dortmund.de , , , , , , DE

    M. Hühne

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  1. M. Dietzfelbinger
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  2. M. Hühne
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Received: March 1995.

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Dietzfelbinger, M., Hühne, M. Matching upper and lower bounds for simulations of several linear tapes on one multidimensional tape. Comput. complex. 8, 371–392 (1999). https://doi.org/10.1007/s000370050006

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  • DOI: https://doi.org/10.1007/s000370050006

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