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Time Complexity of Tape Reduction for Reversible Turing Machines

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Reversible Computation (RC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7165))

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Abstract

Studies of reversible Turing machines (RTMs) often differ in their use of static resources such as the number of tapes, symbols and internal states. However, the interplay between such resources and computational complexity is not well-established for RTMs. In particular, many foundational results in reversible computing theory are about multitape machines with two or more tapes, but it is non-obvious what these results imply for reversible complexity theory.

Here, we study how the time complexity of multitape RTMs behaves under reductions to one and two tapes. For deterministic Turing machines, it is known that the reduction from k tapes to 1 tape in general leads to a quadratic increase in time. For k to 2 tapes, a celebrated result shows that the time overhead can be reduced to a logarithmic factor. We show that identical results hold for multitape RTMs.

This establishes that the structure of reversible time complexity classes mirrors that of irreversible complexity theory, with a similar hierarchy.

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Author information

Authors and Affiliations

  1. DIKU, Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100, Copenhagen, Denmark

    Holger Bock Axelsen

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  1. Holger Bock Axelsen
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Editors and Affiliations

  1. University of Gent, Sint Pietersnieuwstraat 41, 9000, Gent, Belgium

    Alexis De Vos

  2. University of Bremen, Bibliothekstr. 1, 28215, Bremen, Germany

    Robert Wille

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Axelsen, H.B. (2012). Time Complexity of Tape Reduction for Reversible Turing Machines. In: De Vos, A., Wille, R. (eds) Reversible Computation. RC 2011. Lecture Notes in Computer Science, vol 7165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29517-1_1

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  • DOI: https://doi.org/10.1007/978-3-642-29517-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29516-4

  • Online ISBN: 978-3-642-29517-1

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