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

@inproceedings{Margenstern2008OnTI, title={On the injectivity of the global function of a cellular automaton in the hyperbolic plane (extended abstract)}, author={Maurice Margenstern}, booktitle={CSP}, year={2008} }

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…

## One Citation

### Research Notices: The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable

- MathematicsSIGA
- 2008

This paper considers cellular automata in the hyperbolic plane and considers the global function defined on all possible configurations and gives a partial answer: when the configurations are restricted to a certain condition, the problem is undecidable.

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This paper considers cellular automata in the hyperbolic plane and considers the global function defined on all possible configurations and gives a partial answer: when the configurations are restricted to a certain condition, the problem is undecidable.

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