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About the domino problem in the hyperbolic plane from an algorithmicpoint of view

Published online by Cambridge University Press:  18 January 2008

Maurice Margenstern
Maurice Margenstern*
Affiliation:
Université Paul Verlaine - Metz, IUT de Metz; margens@univ-metz.fr
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Abstract

This paper is a contribution to the general tiling problem for the hyperbolic plane. It is an intermediary result between the result obtained by R. Robinson [Invent. Math.44 (1978) 259–264] and the conjecture that the problem is undecidable.

Keywords

Tilingstiling problemhyperbolic planeorigin-constrained problem
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 1: A nonstandard spirit among computer scientists:a tribute to Serge Grigorieff at the occasion of his 60th birthday , January 2008 , pp. 21 - 36
Copyright
© EDP Sciences, 2007

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References

Berger, R., The undecidability of the domino problem. Mem. Amer. Math. Soc. 66 (1966) 1–72.
Ch. Goodman-Strauss, A strongly aperiodic set of tiles in the hyperbolic plane. Invent. Math. 159 (2005) 119–132. CrossRef
Margenstern, M., New tools for cellular automata of the hyperbolic plane. J. Univ. Comput. Sci. 6 (2000) 1226–1252.
M. Margenstern, About the domino problem in the hyperbolic plane from an algorithmic point of view, Technical report, 2006–101, LITA, Université Paul Verlaine - Metz (2006), available at: http://www.lita.sciences.univ-metz.fr/ ~margens/hyp_dominoes.ps.gzip
Margenstern, M., Fibonacci numbers and words in tilings of the hyperbolic plane. TUCS Gen. Publ. 43 (2007) 36–41.
M. Margenstern, About the domino problem in the hyperbolic plane, a new solution, arXiv:cs.CG/0701096 (2007).
M. Margenstern, The domino problem of the hyperbolic plane is undecidable, arXiv:0706.4161 (2007).
M. Margenstern, Cellular Automata in Hyperbolic Spaces, Volume 1, Theory. OCP, Philadelphia (2007).
Robinson, R.M., Undecidability and nonperiodicity for tilings of the plane. Invent. Math. 12 (1971) 177–209. CrossRef
Robinson, R.M., Undecidable tiling problems in the hyperbolic plane. Invent. Math. 44 (1978) 259–264. CrossRef
Wang, H., Proving theorems by pattern recognition. Bell System Tech. J. 40 (1961) 1–41. CrossRef