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Towards the Frontier between Decidability and Undecidability for Hyperbolic Cellular Automata

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Reachability Problems (RP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6227))

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Abstract

In this paper, we look at two ways to implement one dimensional cellular automata into hyperbolic cellular automata in three contexts: the pentagrid, the heptagrid and the dodecagrid, these tilings being classically denoted by {5,4}, {7,3} and {5,3,4} respectively. As an application, this may give a hint for the boundary between decidable and undecidable problems for hyperbolic cellular automata.

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References

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

    MATH  MathSciNet  Google Scholar 

  2. Lindgren, K., Nordahl, M.G.: Universal computation in simple one-dimensional cellular automata. Complex Systems 4, 299–318 (1990)

    MATH  MathSciNet  Google Scholar 

  3. Margenstern, M.: Cellular Automata in Hyperbolic Spaces Theory, vol. 1, p. 422, OCP, Philadelphia (2007)

    Google Scholar 

  4. Margenstern, M.: Cellular Automata in Hyperbolic Spaces Implementation and computations, vol. 2, p. 360, OCP, Philadelphia (2008)

    Google Scholar 

  5. Margenstern, M.: A new universal cellular automaton on the ternary heptagrid, 35p (2009) arXiv:0903.2108[cs.FL]

    Google Scholar 

  6. Margenstern, M.: Surprising Areas in the Quest for Small Universal Devices. Electronic Notes in Theoretical Computer Science 225, 201–220 (2009)

    Article  Google Scholar 

  7. Margenstern, M.: A weakly universal cellular automaton in the hyperbolic 3D space with three states, 54p. (2010) arXiv:1002.4290[cs.FL]

    Google Scholar 

  8. Margenstern, M.: About the embedding of one dimensional cellular automata into hyperbolic cellular automata, 19p (2010) arXiv:1004.1830[cs.FL]

    Google Scholar 

  9. Margenstern, M.: A universal cellular automaton on the heptagrid of the hyperbolic plane with four states. Theoretical Computer Science (2010) (accepted)

    Google Scholar 

  10. Margenstern, M.: A weakly universal cellular automaton in the hyperbolic 3D space with three states, Discrete Mathematics and Theoretical Computer Science (to appear)

    Google Scholar 

  11. Margenstern, M., Skordev, G.: Tools for devising cellular automata in the hyperbolic 3D space. Fundamenta Informaticae 58(2), 369–398 (2003)

    MATH  MathSciNet  Google Scholar 

  12. Margenstern, M., Song, Y.: A new universal cellular automaton on the pentagrid. Parallel Processing Letters 19(2), 227–246 (2009)

    Article  MathSciNet  Google Scholar 

  13. Wolfram, S.: A new kind of science. Wolfram Media, Inc. (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Université Paul Verlaine - Metz, IUT de Metz, LITA EA 3097, UFR MIM, Campus du Saulcy, 57045, METZ Cédex 1, France

    Maurice Margenstern

Authors
  1. Maurice Margenstern
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Editors and Affiliations

  1. Faculty of Informatics, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Antonín Kučera

  2. Department of Computer Science, University of Liverpool, Ashton Building, L69 3BX, Liverpool, England

    Igor Potapov

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Margenstern, M. (2010). Towards the Frontier between Decidability and Undecidability for Hyperbolic Cellular Automata. In: Kučera, A., Potapov, I. (eds) Reachability Problems. RP 2010. Lecture Notes in Computer Science, vol 6227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15349-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-15349-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15348-8

  • Online ISBN: 978-3-642-15349-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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