On the injectivity of the global function of a cellular automaton in the hyperbolic plane (extended abstract)

Details On the injectivity of the global function of a cellular automaton in the hyperbolic plane (extended abstract) On the injectivity of the global function of a cellular automaton in the hyperbolic plane (extended abstract)

2009-06-17

arxiv.org/abs/0906.3197v1

EPTCS 1, 2009, pp. 153-163

Computer Science

Computational Complexity

Scientific paper

10.4204/EPTCS.1.15

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, (see Margenstern, 2000, 2007 and Margenstern, Morita, 2001) 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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