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arXiv · 2404.04504

Undecidability of tiling the plane with a fixed number of Wang bars

Chao Yang·Zhujun Zhang
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Abstract

To study the fixed parameter undecidability of tiling problem for a set of Wang tiles, Jeandel and Rolin show that the tiling problem for a set of 44 Wang bars is undecidable. In this paper, we improve their result by proving that whether a set of 29 Wang bars can tile the plane is undecidable. As a consequence, the tiling problem for a set of Wang tiles with color deficiency of 25 is also undecidable.

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Chao Yang, Zhujun Zhang. 2024-04-06. Undecidability of tiling the plane with a fixed number of Wang bars. https://doi.org/10.1007/s40305-025-00666-0

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