Abstract
We establish a first step towards a “Rice theorem” for tilings: for non-trivial sets, it is undecidable to know whether two different tile sets produce the same tilings of the place. Then, we study quasiperiodicity functions associated with tilings. This function is a way to measure the regularity of tilings. We prove that, not only almost all recursive functions can be obtained as quasiperiodicity functions, but also, a function which overgrows any recursive function.
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Cervelle, J., Durand, B. (2000). Tilings: Recursivity and Regularity. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_41
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DOI: https://doi.org/10.1007/3-540-46541-3_41
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