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Fixed Parameter Undecidability for Wang Tilesets

Emmanuel Jeandel 1 Nicolas Rolin
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the tiling problem remains undecidable if the difference between the number of tiles and the number of colors is bounded by 43. One of the main new tool is the concept of Wang bars, which are equivalently inflated Wang tiles or thin polyominoes.
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https://hal.inria.fr/hal-00739038
Contributor : Emmanuel Jeandel <>
Submitted on : Friday, October 5, 2012 - 3:36:48 PM
Last modification on : Thursday, May 24, 2018 - 3:59:23 PM

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Emmanuel Jeandel, Nicolas Rolin. Fixed Parameter Undecidability for Wang Tilesets. JAC - 3rd International Symposium Journées Automates Cellulaires - 2012, Enrico Formenti, Sep 2012, Bastia, France. pp.69-85, ⟨10.4204/EPTCS.90.6⟩. ⟨hal-00739038⟩

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