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On Nilpotency and Asymptotic Nilpotency of Cellular Automata

Ville Salo, On Nilpotency and Asymptotic Nilpotency of Cellular Automata. In: Enrico Formenti (Ed.), Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires, 86–96, Open Publishing Association, 2012.

http://dx.doi.org/10.4204/EPTCS.90.7

Abstract:

We prove a conjecture of P. Guillon and G. Richard by showing that cellular automata that eventually fix all cells to a fixed symbol 0 are nilpotent on S^Z^d for all d. We also briefly discuss nilpotency on other subshifts, and show that weak nilpotency implies nilpotency in all subshifts and all dimensions, since we do not know a published reference for this.

BibTeX entry:

@INPROCEEDINGS{inpSalo_Ville12b,
  title = {On Nilpotency and Asymptotic Nilpotency of Cellular Automata},
  booktitle = {Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires},
  author = {Salo, Ville},
  editor = {Formenti, Enrico},
  publisher = {Open Publishing Association},
  pages = {86–96},
  year = {2012},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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