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Undecidability of the Surjectivity of the Subshift Associated to a Turing Machine

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Reversible Computation (RC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7581))

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Abstract

We consider Turing machines (TM) from a dynamical system point of view, and in this context, we associate a subshift by taking the sequence of symbols and states that the head has at each instant. Taking a subshift that select only a part of the state of a system is a classical technic in dynamical systems that plays a central role in their analysis. Surjectivity of Turing machines is equivalent to their reversibility and it can be simply identified from the machine rule. Nevertheless, the associated subshift can be surjective even if the machine is not, and the property results to be undecidable in the symbolic system.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática, Centro de Investigación en Ingeniería Matemática, Centro de Modelamiento Matemático, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Rodrigo Torres & Anahí Gajardo

  2. LIFO, Université d’Orléans, BP 6759, F-45067, Orléans Cedex 2, France

    Nicolas Ollinger

Authors
  1. Rodrigo Torres
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  2. Nicolas Ollinger
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  3. Anahí Gajardo
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Editors and Affiliations

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

    Robert Glück

  2. Department of Software Engineering, Nanzan University, 489-0863, Seto, Japan

    Tetsuo Yokoyama

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Torres, R., Ollinger, N., Gajardo, A. (2013). Undecidability of the Surjectivity of the Subshift Associated to a Turing Machine. In: Glück, R., Yokoyama, T. (eds) Reversible Computation. RC 2012. Lecture Notes in Computer Science, vol 7581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36315-3_4

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  • DOI: https://doi.org/10.1007/978-3-642-36315-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36314-6

  • Online ISBN: 978-3-642-36315-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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