The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable
Computational Geometry
2009-07-07 v2 Logic in Computer Science
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.
Keywords
Cite
@article{arxiv.0806.1602,
title = {The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable},
author = {Margenstern Maurice},
journal= {arXiv preprint arXiv:0806.1602},
year = {2009}
}
Comments
9 figures this paper completely solves the problem tackled in arXiv:0712.2577v2. This version is simply an improvement of the proof of the result deposited in 0806.1602