The domino problem of the hyperbolic plane is undecidable
نویسنده
چکیده
In this paper, we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is undecidable for the Euclidean plane, initially proved by Robert Berger in 1966.
منابع مشابه
About the domino problem in the hyperbolic plane, a new solution
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.
متن کاملThe Periodic Domino Problem Is Undecidable in the Hyperbolic Plane
In this paper, we consider the periodic tiling problem which was proved undecidable in the Euclidean plane by Yu. Gurevich and I. Koriakov, see [3]. Here, we prove that the same problem for the hyperbolic plane is also undecidable.
متن کاملAbout the domino problem in the hyperbolic plane from an algorithmic point of view
In this paper, we prove 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...
متن کامل1 M ay 2 00 7 About 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 withà la Wang tiles is undecidable.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Bulletin of the EATCS
دوره 93 شماره
صفحات -
تاریخ انتشار 2007