The domino problem of the hyperbolic plane is undecidable

Authors:
Maurice Margenstern
Affiliations:
Laboratoire dInformatique Théorique et Appliquée, EA 3097, Université de Metz, I.U.T. de Metz, Département dInformatique, Île du Saulcy, 57045 Metz Cedex, France
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

In this paper, we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is undecidable for the Euclidean plane, initially proved by Robert Berger in 1966.