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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
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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).
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Robinson, R.M., Undecidable tiling problems in the hyperbolic plane. Invent. Math. 44 (1978) 259–264. CrossRef
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