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The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable

Authors
  • Maurice, Margenstern
Type
Published Article
Publication Date
Jun 16, 2008
Submission Date
Jun 10, 2008
Source
arXiv
License
Yellow
External links

Abstract

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane 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. In the present paper, we show that the answer is also positive for the hyperbolic plane: the problem is undecidable.

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