A4 Article in conference proceedings
On dynamical complexity of surjective ultimately right-expansive cellular automata




List of Authors: Joonatan Jalonen, Jarkko Kari
Publisher: Springer Verlag
Publication year: 2018
Journal: Lecture Notes in Computer Science
Book title *: Cellular Automata and Discrete Complex Systems
Journal name in source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume number: 10875
ISBN: 978-3-319-92674-2
eISBN: 978-3-319-92675-9
ISSN: 0302-9743

Abstract

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.


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Last updated on 2019-29-01 at 10:44