A Uniquely Ergodic Cellular Automaton
Dynamical Systems
2014-08-29 v2 Formal Languages and Automata Theory
Abstract
We construct a one-dimensional uniquely ergodic cellular automaton which is not nilpotent. This automaton can perform asymptotically infinitely sparse computation, which nevertheless never disappears completely. The construction builds on the self-simulating automaton of G\'acs. We also prove related results of dynamical and computational nature, including the undecidability of unique ergodicity, and the undecidability of nilpotency in uniquely ergodic cellular automata.
Cite
@article{arxiv.1310.0670,
title = {A Uniquely Ergodic Cellular Automaton},
author = {Ilkka Törmä},
journal= {arXiv preprint arXiv:1310.0670},
year = {2014}
}
Comments
47 pages, 8 figures. Submitted to Journal of Computer and System Sciences