Some Undecidable Dynamical Properties for One-Dimensional Reversible Cellular Automata

  • Jarkko KariEmail author
  • Ville Lukkarila
Part of the Natural Computing Series book series (NCS)


Using the fact that the tiling problem of Wang tiles is undecidable even if the given tile set is deterministic by two opposite corners, it is shown that the question whether there exists a trajectory which belongs to the given open and closed set is undecidable for one-dimensional reversible cellular automata. This result holds even if the cellular automaton is mixing. Furthermore, it is shown that left expansivity of a reversible cellular automaton is an undecidable property. Also, the tile set construction gives yet another proof for the universality of one-dimensional reversible cellular automata.


Cellular Automaton Turing Machine Color Pair Tiling Problem Global Rule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland
  2. 2.Turku Centre for Computer ScienceTurkuFinland

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