The Periodic Domino Problem Is Undecidable in the Hyperbolic Plane

Margenstern, Maurice

doi:10.1007/978-3-642-04420-5_15

Cited by 7 publications

(3 citation statements)

References 11 publications

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“…Combined with the construction proving theorem 3 and a result of [20], the construction of the present paper allows us to establish the following result, see [17].…”

Section: Theoremmentioning

confidence: 80%

The domino problem of the hyperbolic plane is undecidable

Margenstern

2008

Theoretical Computer Science

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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.

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“…Combined with the construction proving theorem 3 and a result of [20], the construction of the present paper allows us to establish the following result, see [17].…”

Section: Theoremmentioning

confidence: 80%

The domino problem of the hyperbolic plane is undecidable

Margenstern

2008

Theoretical Computer Science

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“…Combining the construction proving Theorem 3 and the partition theorem which is proved in [16], chapter 4, section 4.5.2 about the splitting of Fibonacci patchworks, also see [11], the construction of this paper allows us to establish the following result, see [14].…”

Section: Theoremmentioning

confidence: 90%

The domino problem of the hyperbolic plane is undecidable, new proof

Margenstern¹

2022

Preprint

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The present paper is a new visit to the proof given in a previous paper of the author proving 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. The present construction strongly reduces the number of prototiles.

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“…A bit later, two other problems about tiling, also connected to this one were proved undecidable by the author: the finite tiling problem, see [18], and the periodic tiling problem, see [19].…”

Section: The Tiling Problemmentioning

confidence: 99%