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Given an automatic set $S$ coming from a DFA $M$ when read little-endian, is $\overline{d}(S)$ at most the Büchi acceptance probability of $M$?
Note: I've entirely rewritten this question! Originally it was just the third formulation, take note of that when reading answers.
Let's say $S$ is a $b$-automatic set, and let's say $M$ is a DFA ...
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