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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

  1. Aaronson, S.: Shtetl-Optimized - the blog of Scott Aaronson. http://www.scottaaronson.com/blog/?p=1896. Accessed 17 Sept 2014

  2. Cook, M.: Universality in elementary cellular automata. Complex Syst. 15(1), 1–40 (2004)

    MathSciNet  MATH  Google Scholar 

  3. Delvenne, J.-C., Kurka, P., Blondel, V.D.: Decidability and universality in symbolic dynamical systems. Fundam. Inform. 74(4), 463–490 (2006)

    MathSciNet  MATH  Google Scholar 

  4. Janzing, D.: Is there a physically universal cellular automaton or Hamiltonian? ArXiv e-prints, September 2010

    Google Scholar 

  5. Kari, J.: Universal pattern generation by cellular automata. Theor. Comput. Sci. 429, 180–184 (2012). Magic in Science

    Article  MathSciNet  MATH  Google Scholar 

  6. Neary, T., Woods, D.: P-completeness of cellular automaton Rule 110. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 132–143. Springer, Heidelberg (2006). doi:10.1007/11786986_13

    Chapter  Google Scholar 

  7. Ollinger, N.: The intrinsic universality problem of one-dimensional cellular automata. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 632–641. Springer, Heidelberg (2003). doi:10.1007/3-540-36494-3_55

    Chapter  Google Scholar 

  8. Schaeffer, L.: A physically universal cellular automaton. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 21, p. 84 (2014)

    Google Scholar 

  9. Schaeffer, L.: A physically universal cellular automaton. In: ITCS 2015–Proceedings of the 6th Innovations in Theoretical Computer Science, pp. 237–246 (2015)

    Google Scholar 

  10. Schaeffer, L.: A physically universal quantum cellular automaton. In: Kari, J. (ed.) AUTOMATA 2015. LNCS, vol. 9099, pp. 46–58. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47221-7_4

    Chapter  Google Scholar 

  11. Toffoli, T.: Reversible computing. In: de Bakker, J., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 632–644. Springer, Heidelberg (1980). doi:10.1007/3-540-10003-2_104

    Chapter  Google Scholar 

  12. von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Champaign (1966)

    Google Scholar 

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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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Corresponding author

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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