The 4-way deterministic Periodic Domino Problem is undecidable

Abstract : The most fundamental undecidable question on tilings is the Domino Problem that asks whether a Wang tileset tiles the discrete plane. Lukkarila proved in 2009 that it remains undecidable when restricting the input to the class of 4-way deterministic tilesets. Due to the existence of aperiodic tilesets, the most natural distinct variant of this problem is the Periodic Domino Problem which asks whether a Wang tileset admits a periodic tiling of the plane. This problem is also undecidable. Jeandel recently discovered a new and elegant proof for this result. Inspired by this new proof technique and some ingredients from Lukkarila's construction, we prove that it remains undecidable when restricted to 4-way deterministic tilesets.
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Pré-publication, Document de travail
2014
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https://hal.archives-ouvertes.fr/hal-00985482
Contributeur : Bastien Le Gloannec <>
Soumis le : mardi 29 avril 2014 - 18:31:14
Dernière modification le : jeudi 17 janvier 2019 - 15:06:06
Document(s) archivé(s) le : mardi 29 juillet 2014 - 13:50:59

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  • HAL Id : hal-00985482, version 1

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Bastien Le Gloannec. The 4-way deterministic Periodic Domino Problem is undecidable. 2014. 〈hal-00985482〉

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