Fixed Parameter Undecidability for Wang Tilesets

Emmanuel Jeandel
(LIRMM, France)
Nicolas Rolin
(LIP6 - ENS Cachan, France)

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.

In Enrico Formenti: Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires (AUTOMATA&JAC 2012), La Marana, Corsica, September 19-21, 2012, Electronic Proceedings in Theoretical Computer Science 90, pp. 69–85.
Published: 13th August 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.90.6 bibtex PDF
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