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Two Small Universal Reversible Turing Machines

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Advances in Unconventional Computing

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 22))

Abstract

We study the problem of constructing small universal Turing machines (UTMs) under the constraint of reversibility, which is a property closely related to physical reversibility. Let URTM(m,n) denote an m-state n-symbol universal reversible Turing machine (URTM). Then, the problem is to find URTM(m,n) with small m and n. So far, several kinds of small URTMs have been given. Here, we newly construct two small URTMs. They are URTM(13,7) and URTM(10,8) that can simulate cyclic tag systems, a kind of universal string rewriting systems proposed by Cook. We show how these URTMs can be designed, and compare them with other existing URTMs.

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 15K00019.

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Authors and Affiliations

  1. Hiroshima University, Higashi-hiroshima, 739-8527, Japan

    Kenichi Morita

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  1. Kenichi Morita
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Correspondence to Kenichi Morita .

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Editors and Affiliations

  1. Unconventional Computing Centre, University of the West of England Unconventional Computing Centre, Bristol, United Kingdom

    Andrew Adamatzky

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Morita, K. (2017). Two Small Universal Reversible Turing Machines. In: Adamatzky, A. (eds) Advances in Unconventional Computing. Emergence, Complexity and Computation, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-33924-5_10

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  • DOI: https://doi.org/10.1007/978-3-319-33924-5_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33923-8

  • Online ISBN: 978-3-319-33924-5

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