Theoretical Computer Science
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Theoretical Computer Science
On Aperiodic Sets of Wang Tiles
Foundations of Computer Science: Potential - Theory - Cognition, to Wilfried Brauer on the occasion of his sixtieth birthday
Tilings: recursivity and regularity
Theoretical Computer Science
An Almost Totally Universal Tile Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Constructing New Aperiodic Self-simulating Tile Sets
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
A topological study of tilings
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Tilings: Simulation and universality
Mathematical Structures in Computer Science
Subshifts as models for MSO logic
Information and Computation
The two-handed tile assembly model is not intrinsically universal
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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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.