An Almost Totally Universal Tile Set

  • Grégory Lafitte
  • Michael Weiss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


Wang tiles are unit size squares with colored edges. In this paper, we approach one aspect of the study of tilings computability: the quest for a universal tile set. Using a complex construction, based on Robinson’s classical construction and its different modifications, we build a tile set μ (pronounced ayin) which almost always simulates any tile set. By way of Banach-Mazur games on tilings topological spaces, we prove that the set of μ-tilings which do not satisfy the universality condition is meager in the set of μ-tilings.


Topological Space Turing Machine West Side Winning Strategy Colored Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Grégory Lafitte
    • 1
  • Michael Weiss
    • 2
  1. 1.Laboratoire d’Informatique Fondamentale de Marseille (LIF)CNRS – Aix-Marseille UniversitéMarseille Cedex 13France
  2. 2.Bicocca Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di MilanoMilanoItaly

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