×

zbMATH — the first resource for mathematics

Nilpotency and limit sets of cellular automata. (English) Zbl 1173.68572
Ochmański, Edward (ed.) et al., Mathematical foundations of computer science 2008. 33rd international symposium, MFCS 2008, Toruń Poland, August 25–29, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-85237-7/pbk). Lecture Notes in Computer Science 5162, 375-386 (2008).
Summary: 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 configurations of cells are mapped after a finite time into a given “null” configuration. Our main result is that nilpotency is equivalent to the condition that all configurations converge towards the null configuration for the Cantor topology, or, equivalently, that all cells of all configurations asymptotically reach a given state.
For the entire collection see [Zbl 1154.68021].

MSC:
68Q80 Cellular automata (computational aspects)
37B15 Dynamical aspects of cellular automata
PDF BibTeX XML Cite
Full Text: DOI