Skip to Main content Skip to Navigation
Conference papers

Nilpotency and Limit Sets of Cellular Automata

Abstract : A one-dimensional cellular automaton is a dynamical system which consisting in a juxtaposition of cells whose state changes over discrete time according to that of their neighbors. One of its simplest behaviors is nilpotency: all con gurations of cells are mapped after a nite time into a given \null" con guration. Our main result is that nilpotency is equivalent to the condition that all con gurations converge towards the null con guration for the Cantor topology, or, equivalently, that all cells of all con gurations asymptotically reach a given state.
Document type :
Conference papers
Complete list of metadata

Cited literature [6 references]  Display  Hide  Download
Contributor : Pierre Guillon Connect in order to contact the contributor
Submitted on : Monday, October 3, 2011 - 1:49:17 PM
Last modification on : Saturday, January 15, 2022 - 3:56:37 AM
Long-term archiving on: : Tuesday, November 13, 2012 - 3:00:34 PM


Files produced by the author(s)


  • HAL Id : hal-00620283, version 1


Pierre Guillon, Gaétan Richard. Nilpotency and Limit Sets of Cellular Automata. 33rd International Symposium on Mathematical Foundations of Computer Science (MFCS'08), Aug 2008, Toruń, Poland, Poland. pp.375-386. ⟨hal-00620283⟩



Record views


Files downloads