Two-by-two Substitution Systems and the Undecidability of the Domino Problem

Nicolas Ollinger (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

Thanks to a careful study of elementary properties of two-by-two substitution systems, we give a complete self-contained elementary construction of an aperiodic tile set and sketch how to use this tile set to elementary prove the undecidability of the classical Domino Problem.

Mots clés: aperiodic tile sets; formal languages; tilings; undecidability

Domaines: Mathématique discrète [cs.DM]

Nicolas Ollinger. Two-by-two Substitution Systems and the Undecidability of the Domino Problem. 2008. ⟨hal-00204625v2⟩