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                <title xml:lang="en">On Dynamical Complexity of Surjective Ultimately Right-Expansive Cellular Automata</title>
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                  <title>24th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA)</title>
                  <date type="start">2018-06-20</date>
                  <date type="end">2018-06-22</date>
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                <editor>Jan M. Baetens</editor>
                <editor>Martin Kutrib</editor>
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              <p>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.</p>
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