Undecidability and nonperiodicity for tilings of the plane - Inventiones mathematicae

1. Berger, R.: The undecidability of the domino problem. Mem. Amer. Math. Soc. no.66, (1966).

2. Büchi, J. R.: Turing-machines and the Entscheidungsproblem. Math. Ann.148, 201–213 (1962).

   Google Scholar 

3. Cocke, J., Minsky, M.: Universality of tag systems withP=2. J. Assoc. Comput. Mach.11, 15–20 (1964).

   Google Scholar 

4. Kahr, A. S., Moore, E. F., Wang, H.: Entscheidungsproblem reduced to the AEA case. Proc. Nat. Acad. Sci. U.S.A.48, 365–377 (1962).

   Google Scholar 

5. König, D.: Über eine Schlußweise aus dem Endlichen ins Unendliche. Acta Litt. Sci. Szeged3, 121–130 (1927).

   Google Scholar 

6. Minsky, M. L.: Computation: Finite and infinite machines. Englewood Cliffs, N.J.: Prentice-Hall 1967.

   Google Scholar 

7. Robinson, R. M.: Seven polygons which permit only nonperiodic tilings of the plane (abstract). Notices Amer. Math. Soc.14, 835 (1967).

   Google Scholar 

8. Wang, H.: Proving theorems by pattern recognition — II. Bell System Tech. J.40, 1–41 (1961).

   Google Scholar 

9. —: Dominoes and the AEA case of the decision problem, Mathematical theory of automata, p. 23–55. Brooklyn, N. Y.: Polytechnic Press 1963.

   Google Scholar 

Download references

Authors and Affiliations

1. Department of Mathematics, University of California, 94720, Berkeley, Calif., USA

   Raphael M. Robinson

Cite this article

Robinson, R.M. Undecidability and nonperiodicity for tilings of the plane. Invent Math 12, 177–209 (1971). https://doi.org/10.1007/BF01418780

Download citation

• Received: 14 September 1970

• Issue Date: September 1971

• DOI: https://doi.org/10.1007/BF01418780