On dynamical complexity of surjective ultimately right-expansive cellular automata - Joonatan Jalonen; Jarkko Kari (Switzerland, 2022)
We prove that surjective ultimately right-expansive cellular automata over full shifts are chain-transitive. This immediately implies Boyle’s result that expansive cellular automata are chain-transitive. This means that the chain-recurrence assumption can be dropped from Nasu’s result that surjective ultimately right-expansive cellular automata with right-sided neighborhoods have the pseudo-orbit tracing property, which also implies that the (canonical) trace subshift is sofic. We also provide a theorem with a simple proof that comprises many known results including aforementioned result by Nasu. Lastly we show that there exists a right-expansive reversible cellular automaton that has a non-sofic trace and thus does not have the pseudo-orbit tracing property. In this paper we only consider cellular automata over full shifts, while both Nasu and Boyle obtain their results over more general shift spaces.
Cellular Automata and Discrete Complex Systems