About the domino problem in the hyperbolic plane from an algorithmic point of view
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 1, pp. 21-36.

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.

DOI : 10.1051/ita:2007045
Classification : 52C20, 05B45
Mots-clés : tilings, tiling problem, hyperbolic plane, origin-constrained problem 
@article{ITA_2008__42_1_21_0,
     author = {Margenstern, Maurice},
     title = {About the domino problem in the hyperbolic plane from an algorithmic point of view},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {21--36},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {1},
     year = {2008},
     doi = {10.1051/ita:2007045},
     mrnumber = {2382542},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita:2007045/}
}
TY  - JOUR
AU  - Margenstern, Maurice
TI  - About the domino problem in the hyperbolic plane from an algorithmic point of view
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2008
SP  - 21
EP  - 36
VL  - 42
IS  - 1
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ita:2007045/
DO  - 10.1051/ita:2007045
LA  - en
ID  - ITA_2008__42_1_21_0
ER  - 
%0 Journal Article
%A Margenstern, Maurice
%T About the domino problem in the hyperbolic plane from an algorithmic point of view
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2008
%P 21-36
%V 42
%N 1
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ita:2007045/
%R 10.1051/ita:2007045
%G en
%F ITA_2008__42_1_21_0
Margenstern, Maurice. About the domino problem in the hyperbolic plane from an algorithmic point of view. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 1, pp. 21-36. doi : 10.1051/ita:2007045. http://archive.numdam.org/articles/10.1051/ita:2007045/

[1] R. Berger, The undecidability of the domino problem. Mem. Amer. Math. Soc. 66 (1966) 1-72. | MR | Zbl

[2] Ch. Goodman-Strauss, A strongly aperiodic set of tiles in the hyperbolic plane. Invent. Math. 159 (2005) 119-132. | MR | Zbl

[3] M. Margenstern, New tools for cellular automata of the hyperbolic plane. J. Univ. Comput. Sci. 6 (2000) 1226-1252. | MR | Zbl

[4] M. Margenstern, About the domino problem in the hyperbolic plane from an algorithmic point of view2006), available at: http://www.lita.sciences.univ-metz.fr/~margens/hyp_dominoes.ps.gzip

[5] M. Margenstern, Fibonacci numbers and words in tilings of the hyperbolic plane. TUCS Gen. Publ. 43 (2007) 36-41.

[6] M. Margenstern, About the domino problem in the hyperbolic plane, a new solution, arXiv:cs.CG/0701096 (2007). | MR

[7] M. Margenstern, The domino problem of the hyperbolic plane is undecidable, arXiv:0706.4161 (2007). | MR | Zbl

[8] M. Margenstern, Cellular Automata in Hyperbolic Spaces, Volume 1, Theory. OCP, Philadelphia (2007). | Zbl

[9] R.M. Robinson, Undecidability and nonperiodicity for tilings of the plane. Invent. Math. 12 (1971) 177-209. | MR | Zbl

[10] R.M. Robinson, Undecidable tiling problems in the hyperbolic plane. Invent. Math. 44 (1978) 259-264. | MR | Zbl

[11] H. Wang, Proving theorems by pattern recognition. Bell System Tech. J. 40 (1961) 1-41.

Cité par Sources :