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

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

2008-06-10

arxiv.org/abs/0806.1602v2

The Injectivity of the Global Function of a Cellular Automaton in the Hyperbolic Plane is Undecidable, Fundamenta Informaticae

Computer Science

Computational Geometry

9 figures this paper completely solves the problem tackled in arXiv:0712.2577v2. This version is simply an improvement of the

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 show that the answer is also positive for the hyperbolic plane: the problem is undecidable.

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