On aperiodic sets of Wang tiles

  • Karel Culik
  • Jarkko Kari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1337)


Finite Automaton Sequential Machine Balance Representation Deterministic Finite Automaton Output Alphabet 
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  1. 1.
    S. Beatty, Problem 3173, Am. Math. Monthly 33 (1926) 159; solutions in 34, 159 (1927).CrossRefMathSciNetGoogle Scholar
  2. 2.
    R. Berger, The Undecidability of the Domino Problem, Mem. Amer. Math. Soc. 66 (1966).Google Scholar
  3. 3.
    K. Culik II, An aperiodic set of 13 Wang tiles, Discrete Mathematics, to appear.Google Scholar
  4. 4.
    K. Culik II, L. P. Hurd and S. Yu, computation theoretic aspects of cellular automata, Physica D 45, 357–378 (1990).CrossRefMathSciNetGoogle Scholar
  5. 5.
    K. Culik II and S. Yu, Cellular automata, ww-regular sets, and Sofic Systems, Discrete Applied Mathematics 32, 85–102 (1991).CrossRefMathSciNetGoogle Scholar
  6. 6.
    J. E. Hopcroft and J. D. Ullman, Introduction to automata theory, languages and computation, Addison-Wesley (1979).Google Scholar
  7. 7.
    K. Culik II and J. Kari, An aperiodic set of Wang cubes, Journal of Universal Computer Science 1, 675–686 (1995).MathSciNetGoogle Scholar
  8. 8.
    B. Grünbaum and G.C. Shephard, Tilings and Patterns, W.H.Freeman and Company, New York (1987).Google Scholar
  9. 9.
    M.V. Jaric, Introduction to the Mathematics of Quasicrystals, Academic Press, Inc., San Diego (1989).Google Scholar
  10. 10.
    J. Kari, A small aperiodic set of Wang tiles, Discrete Mathematics, to appear.Google Scholar
  11. 11.
    D. E. Knuth, The Art of Computer Programming, Vol.1, p.384, Addison-Wesley, Reading, MA (1968).Google Scholar
  12. 12.
    R. M. Robinson, Undecidability and Nonperiodicity for Tilings of the Plane. Inventiones Mathematicae 12, 177–209 (1971).zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    R. M. Robinson, Undecidable tiling problems in the hyperbolic plane, Inventiones Mathematicae 44, 259–264 (1978).zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Karel Culik
    • 1
  • Jarkko Kari
    • 2
  1. 1.Depart. of Comp. ScienceUniversity of South CarolinaColumbia
  2. 2.Depart. of Comp. ScienceUniversity of IowaIowa City

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