The 4-way deterministic Periodic Domino Problem is undecidable - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2014

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.

Domains

Other [cs.OH]
Fichier principal
Vignette du fichier
per4way.pdf (464.39 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00985482 , version 1 (29-04-2014)

Identifiers

  • HAL Id : hal-00985482 , version 1

Cite

Bastien Le Gloannec. The 4-way deterministic Periodic Domino Problem is undecidable. 2014. ⟨hal-00985482⟩
203 View
262 Download

Share

Gmail Facebook X LinkedIn More