On Nilpotency and Asymptotic Nilpotency of Cellular Automata

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object , Other literature type 13 Aug 2012Embargo end date: 01 May 2012 English Publisher:Open Publishing AssociationJournal:Electronic Proceedings in Theoretical Computer Science, volume 90, pages 86-96 (eissn: 2075-2180,

Copyright policy )Funded by:AKA | Cellular automata and dis...

Authors: Ville Salo;

doi: 10.4204/eptcs.90.7 , 10.48550/arxiv.1205.6714

arXiv: 1205.6714

On Nilpotency and Asymptotic Nilpotency of Cellular Automata

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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.

In Proceedings AUTOMATA&JAC 2012, arXiv:1208.2498

Related Organizations

University of Turku
Finland
TURUN YLIOPISTO
Finland
Turku Centre for Computer Science
Finland

Keywords

ta113, FOS: Computer and information sciences, Formal Languages and Automata Theory (cs.FL), Cellular Automata and Lattice Gases (nlin.CG), ta111, FOS: Physical sciences, Computer Science - Formal Languages and Automata Theory, QA75.5-76.95, Dynamical Systems (math.DS), Electronic computers. Computer science, QA1-939, FOS: Mathematics, F.1.2, Mathematics - Dynamical Systems, F.1.3, F.1.1; F.1.2; F.1.3, Nonlinear Sciences - Cellular Automata and Lattice Gases, F.1.1, Mathematics

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