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A One-Dimensional Physically Universal Cellular Automaton

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Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

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Abstract

Physical universality of a cellular automaton was defined by Janzing in 2010 as the ability to implement an arbitrary transformation of spatial patterns. In 2014, Schaeffer gave a construction of a two-dimensional physically universal cellular automaton. We construct a one-dimensional version of the automaton and a reversibly universal automaton.

Research supported by the Academy of Finland Grant 131558.

V. Salo was partially supported by CONICYT Proyecto Anillo ACT 1103.

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References

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Acknowledgments

We are thankful to Charalampos Zinoviadis for introducing this problem to us, and for many fruitful discussions on the proof, and Luke Schaeffer for his Golly implementation of our physically universal CA. We would also like to thank Scott Aaronson for popularizing the concept in his blog [1].

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Authors and Affiliations

  1. Department of Matematics and Statistics, University of Turku, Turku, Finland

    Ville Salo & Ilkka Törmä

Authors
  1. Ville Salo
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  2. Ilkka Törmä
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Correspondence to Ilkka Törmä .

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Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. Christian-Albrechts-University of Kiel, Kiel, Germany

    Florin Manea

  3. Åbo Akademi University, Turku, Finland

    Ion Petre

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Salo, V., Törmä, I. (2017). A One-Dimensional Physically Universal Cellular Automaton. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_35

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  • DOI: https://doi.org/10.1007/978-3-319-58741-7_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

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