Is the injectivity of the global function of a cellular automaton in the hyperbolic plane undecidable?

Details Is the injectivity of the global function of a cellular automaton in the hyperbolic plane undecidable? Is the injectivity of the global function of a cellular automaton in the hyperbolic plane undecidable?

2007-12-16

arxiv.org/abs/0712.2577v2

Computer Science

Discrete Mathematics

16 pages, 8 figures. A few words were missing in the initial version

Scientific paper

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 give a partial answer: when the configurations are restricted to a certain condition, the problem is undecidable.

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