SOFSEM 2008: Theory and Practice of Computer Science

Volume 4910 of the series Lecture Notes in Computer Science pp 74-82

On the Undecidability of the Tiling Problem

  • Jarkko KariAffiliated withDepartment of Mathematics, University of Turku

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The tiling problem is the decision problem to determine if a given finite collection of Wang tiles admits a valid tiling of the plane. In this work we give a new proof of this fact based on tiling simulations of certain piecewise affine transformations. Similar proof is also shown to work in the hyperbolic plane, thus answering an open problem posed by R.M.Robinson 1971 [9].