2007/12/16 by Maurice Margenstern, Margenstern Maurice, Maurice, Margenstern · 1 citation
Computer Science · Mathematics · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Mathematical Dynamics and Fractals #cs.DM #cs.LO
paper · pdf · doi:10.48550/arxiv.0712.2577
16 pages, 8 figures. A few words were missing in the initial version
arxiv created 2007/12/20 · arxiv updated 2009/12/01
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.