English

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