The domino problem is undecidable on surface groups

Nathalie Aubrun (1) , Sebastián Barbieri (2) , Etienne Moutot (3, 2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 MC2 - Modèles de calcul, Complexité, Combinatoire
3 Department of Mathematics and Statistics, University of Turku

We show that the domino problem is undecidable on orbit graphs of non-deterministic substitutions which satisfy a technical property. As an application, we prove that the domino problem is undecidable for the fundamental group of any closed orientable surface of genus at least 2.

Domaines: Mathématique discrète [cs.DM]

Nathalie Aubrun, Sebastián Barbieri, Etienne Moutot. The domino problem is undecidable on surface groups. MFCS2019 44th International Symposium on Mathematical Foundations of Computer Science, Aug 2019, Aachen, Germany. ⟨hal-02157971⟩