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Aug 14, 2023 at 16:05 comment added Ville Salo We once also proved with Thibault Godin that splic epicness is decidable for certain automata semigroups, if you like I can send you that too. (Like one-sided automorphisms of full shifts, automata groups act on trees, so a priori seems relevant.) Though that also seems quite different from your case. But maybe check 1001's first.
Aug 14, 2023 at 15:45 comment added no_hurry Thanks again for the references and pointing out the connection to your papers! We might have to look whether we can adapt these results to the "one-sided" case, in case the other approach does not work out.
Aug 14, 2023 at 10:30 comment added Ville Salo It precisely seemed to me that the one-sided version doesn't allow a simple periodic point condition, since you cannot look both ways and thus it's hard to know where you should go at each moment... I only believed that the "recursive bound on radius from simplifying an existing section by imagining repeated cycles to the right" type argument (which is what we use in the general sofic case also in the two-sided setting) might adapt. Anyway hopefully 1001's answer is correct, and this doesn't matter.
S Aug 14, 2023 at 9:59 history suggested Sam van G CC BY-SA 4.0
add one-sided and correct typo
Aug 14, 2023 at 9:59 review Suggested edits
S Aug 14, 2023 at 9:59
Aug 14, 2023 at 9:51 history edited no_hurry CC BY-SA 4.0
deleted 1 character in body
Aug 14, 2023 at 9:50 history edited no_hurry CC BY-SA 4.0
typo
Aug 14, 2023 at 9:49 history edited no_hurry CC BY-SA 4.0
shortened awkard sentence
S Aug 14, 2023 at 9:44 review First answers
Aug 14, 2023 at 11:14
S Aug 14, 2023 at 9:44 history answered no_hurry CC BY-SA 4.0