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

Authors:
Nicolas Ollinger
Affiliations:
Laboratoire d'informatique fondamentale de Marseille (LIF), Aix-Marseille Université, CNRS, Marseille, France 13013
Venue:
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Year:
2008

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Abstract

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.