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Universal logic elements constructed on the Turing Tumble

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Abstract

This paper presents a mathematical model for a mechanical computer called the Turing Tumble. We show that our model called Turing Tumble Model (TTM) is computationally universal under the assumptions that a configuration of TTM is sufficiently large and that local interactions between elements can be transferred without limitations. The Turing Tumble has a strict constraint, based on gravity, since signals can only move from top to bottom. We introduce a uniform scheme that takes into account this restriction in directionality to construct universal machines in the TTM based on directed acyclic graphs. This model may be useful for implementing computers that exploit mechanical interactions in nature, especially those on micrometer-scales.

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Acknowledgements

We would like to thank the anonymous reviewers for their useful comments. This work was partially supported by the National Key R&D Program of China 2018YFD1100300.

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Authors and Affiliations

  1. Graduate School of Engineering, University of Hyogo, Himeji, Hyogo, Japan

    Takahiro Tomita, Teijiro Isokawa, Takayuki Yumoto & Naotake Kamiura

  2. College of Computer Science, Chongqing University, Chongqing, China

    Jia Lee

  3. Center for Information and Neural Networks, National Institute of Information and Communications Technology, and Osaka University, Osaka, Japan

    Ferdinand Peper

Authors
  1. Takahiro Tomita
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  2. Jia Lee
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  3. Teijiro Isokawa
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  4. Ferdinand Peper
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  5. Takayuki Yumoto
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  6. Naotake Kamiura
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Correspondence to Takahiro Tomita.

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Tomita, T., Lee, J., Isokawa, T. et al. Universal logic elements constructed on the Turing Tumble. Nat Comput 19, 787–795 (2020). https://doi.org/10.1007/s11047-019-09760-8

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  • DOI: https://doi.org/10.1007/s11047-019-09760-8

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