On dynamical complexity of surjective ultimately right-expansive cellular automata
Joonatan Jalonen; Jarkko Kari
https://urn.fi/URN:NBN:fi-fe2021042719682
Tiivistelmä
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.
Kokoelmat
- Rinnakkaistallenteet [19207]