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Universality of Turing Tumble of Finite Size

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Machines, Computations, and Universality (MCU 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15270))

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Abstract

The Turing Tumble is a mechanical puzzle game that simulates the operations of a computer processor using marbles and various mechanical components. The game allows for a visual representation of the computation and is widely used in the educational context. It was shown to be Turing-complete providing that an appropriate infinite configuration of the board, an infinite marble supply and the possibility to construct arbitrarily long frictionless gear chains are available. In this paper we show the computational universality of the game for a finite configuration and no unbounded gear chains. The only source of infinity is the supply of marbles and the unbounded drop capacity. We also provide a thoughtful analysis of the computation representation in Turing Tumble and discuss the possible input and output types.

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Author information

Authors and Affiliations

  1. Vladimir Andrunachievici Institute of Mathematics and Computer Science, Academiei 5, Chişinău, 2028, Moldova

    Artiom Alhazov

  2. Faculty of Informatics, TU Wien, Favoritenstraße 9–11, 1040, Wien, Austria

    Rudolf Freund

  3. Université Paris-Saclay, Université Évry, IBISC, 91020, Évry-Courcouronnes, France

    Sergiu Ivanov

  4. Univ. Paris Est Creteil, LACL, 94010, Creteil, France

    Sergey Verlan

Authors
  1. Artiom Alhazov
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  2. Rudolf Freund
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  3. Sergiu Ivanov
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  4. Sergey Verlan
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Corresponding author

Correspondence to Sergey Verlan .

Editor information

Editors and Affiliations

  1. Université Côte d'Azur, Sophia Antipolis, France

    Enrico Formenti

  2. University of Orléans, Orléans, France

    Jérôme Durand-Lose

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Alhazov, A., Freund, R., Ivanov, S., Verlan, S. (2025). Universality of Turing Tumble of Finite Size. In: Formenti, E., Durand-Lose, J. (eds) Machines, Computations, and Universality. MCU 2024. Lecture Notes in Computer Science, vol 15270. Springer, Cham. https://doi.org/10.1007/978-3-031-81202-6_5

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  • DOI: https://doi.org/10.1007/978-3-031-81202-6_5

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  • Online ISBN: 978-3-031-81202-6

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