Wang tiles are unit size squares with colored edges. To know if a given finite set of Wang tiles can tile the plane while respecting colors on edges is undecidable. Berger's proof of this result shows the equivalence between tilings and Turing machines and thus tilings can be seen as a computing model. We thus have tilings that are Turing-universal, but there lacks a proper notion of universality for tilings. In this paper, we introduce natural notions of universality and completeness for tilings. We construct some universal tilings and try to make a first hierarchy of tile sets with a universality criteria. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Lafitte, G., & Weiss, M. (2007). Universal tilings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4393 LNCS, pp. 367–380). Springer Verlag. https://doi.org/10.1007/978-3-540-70918-3_32
Mendeley helps you to discover research relevant for your work.