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Article type: Research Article
Authors: Margenstern, Maurice
Affiliations: Laboratoire d'Informatique Théorique et Appliquée, EA 3097, Université de Metz, I.U.T. de Metz, Département d'Informatique Île du Saulcy, 57045 Metz Cedex, France. margens@univ-metz.fr
Note: [] Address for correspondence: Laboratoire d'Informatique Théorique et Appliquée, EA 3097, Université de Metz, I.U.T. de Metz, Département d'Informatique, ÎIle du Saulcy, 57045 Metz Cedex, France
Abstract: In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [6, 22, 9, 12] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994, see [4]. In the present paper, we show that the answer is also positive for the hyperbolic plane: the problem is undecidable.
Keywords: cellular automata, hyperbolic plane, tessellations
DOI: 10.3233/FI-2009-118
Journal: Fundamenta Informaticae, vol. 94, no. 1, pp. 63-99, 2009
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