Document Open Access Logo

On Local Symmetries and Universality in Cellular Automata

Authors Laurent Boyer, Guillaume Theyssier



PDF
Thumbnail PDF

File

LIPIcs.STACS.2009.1836.pdf
  • Filesize: 189 kB
  • 12 pages

Document Identifiers

Author Details

Laurent Boyer
Guillaume Theyssier

Cite AsGet BibTex

Laurent Boyer and Guillaume Theyssier. On Local Symmetries and Universality in Cellular Automata. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 195-206, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.STACS.2009.1836

Abstract

Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically) universal CA, that is CA able to fully simulate any other CA. In this paper, we show that the asymptotic density of universal cellular automata is 1 in several families of CA defined by local symmetries. We extend results reviously established for captive cellular automata in two significant ways. First, our results apply to well-known families of CA (e.g. the family of outer-totalistic CA containing the Game of Life) and, second, we obtain such density results with both increasing number of states and increasing neighbourhood. Moreover, thanks to universality-preserving encodings, we show that the universality problem remains undecidable in some of those families.
Keywords
  • Cellular automata
  • Universality
  • Asymptotic density

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail