The Tiling Problem Revisited (Extended Abstract)

  • Jarkko Kari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4664)

Abstract

We give a new proof for the undecidability of the tiling problem. Then we show how the proof can be modified to demonstrate the undecidability of the tiling problem on the hyperbolic plane, thus answering an open problem posed by R.M.Robinson 1971 [6].

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References

  1. 1.
    Berger, R.: Undecidability of the Domino Problem. Memoirs of the American Mathematical Society 66, 72 (1966)MathSciNetGoogle Scholar
  2. 2.
    Goodman-Strauss, C.: A strongly aperiodic set of tiles in the hyperbolic plane. Inventiones Mathematicae 159, 119–132 (2005)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Hooper, P.K.: The undecidability of the Turing machine immortality problem. The Journal of Symbolic Logic 31, 219–234 (1966)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kari, J.: A small aperiodic set of Wang tiles. Discrete Mathematics 160, 259–264 (1996)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Margenstern, M.: About the domino problem in the hyperbolic plane, a new solution. Manuscript, pp. 109 (2007), available at: arXiv:cs/0701096, same title, p. 60 and also see http://www.lita.univ-metz.fr/~margens/
  6. 6.
    Robinson, R.M.: Undecidability and nonperiodicity for tilings of the plane. Inventiones Mathematicae 12, 177–209 (1971)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Robinson, R.M.: Undecidable tiling problems in the hyperbolic plane. Inventiones Mathematicae 44, 259–264 (1978)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jarkko Kari
    • 1
  1. 1.Department of Mathematics, FIN-20014 University of TurkuFinland

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