2022
DOI: 10.48550/arxiv.2202.07377
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The aperiodic Domino problem in higher dimension

Antonin Callard,
Benjamin Hellouin de Menibus

Abstract: The classical Domino problem asks whether there exists a tiling in which none of the forbidden patterns given as input appear. In this paper, we consider the aperiodic version of the Domino problem: given as input a family of forbidden patterns, does it allow an aperiodic tiling? The input may correspond to a subshift of finite type, a sofic subshift or an effective subshift.[8] proved that this problem is co-recursively enumerable (Π 1 0 -complete) in dimension 2 for geometrical reasons. We show that it is mu… Show more

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