About the domino problem in the hyperbolic plane from an algorithmic point of view
نویسنده
چکیده
In this paper, we prove that the general problem of tiling the hyperbolic plane with à la Wang tiles is undecidable.
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In this paper, we improve the approach of the previous paper about the domino problem in the hyperbolic plane[8, 9]. This time, we prove that the general problem of tiling the hyperbolic plane withà la Wang tiles is undecidable.
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In this paper, we complete the construction of paper [9, 11]. Together with the proof contained in [9, 11], this paper definitely proves that the general problem of tiling the hyperbolic plane withà la Wang tiles is undecidable.
متن کاملAbout the domino problem in the hyperbolic plane, a new solution: complement
In this paper, we complete the construction of paper [9, 11]. Together with the proof contained in [9, 11], this paper definitely proves that the general problem of tiling the hyperbolic plane with à la Wang tiles is undecidable.
متن کاملA hierarchical strongly aperiodic set of tiles in the hyperbolic plane
We give a new construction of strongly aperiodic set of tiles in H, exhibiting a kind of hierarchical structure, simplifying the central framework of Margenstern’s proof that the Domino problem is undecidable in the hyperbolic plane [13]. Ludwig Danzer once asked whether, in the hyperbolic plane, where there are no similarities, there could be any notion of hierarchical tiling—an idea which pla...
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عنوان ژورنال:
- ITA
دوره 42 شماره
صفحات -
تاریخ انتشار 2008