An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Tilings: recursivity and regularity
Theoretical Computer Science
Two-by-Two Substitution Systems and the Undecidability of the Domino Problem
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Fixed Point and Aperiodic Tilings
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
High Complexity Tilings with Sparse Errors
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Compact error-resilient computational DNA tiling assemblies
DNA'04 Proceedings of the 10th international conference on DNA computing
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We study the error robustness of tilings of the plane. The fundamental question is the following: given a tileset, what happens if we allow a small probability of errors? Are the objects we obtain close to an error-free tiling of the plane? We prove that tilesets that produce only periodic tilings are robust to errors. For this proof, we use a hierarchical construction of islands of errors (see [6,7]). We also show that another class of tilesets, those that admit countably many tilings is not robust and that there is no computable way to distinguish between these two classes.