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Mar 21, 2021 at 12:29 comment added Hendrik Jan The special symbols like $a \choose 0$ code both the presence of symbol $a$ at any position in the string, but also the boolean value indication either the position of a certain variable $i$, or the positions of the elements a set $X$.
Mar 20, 2021 at 17:04 comment added Algebruh Great answer! This helped me a lot to understand more on this topic, thank you! I'm having some trouble understanding the automata added by @HendrikJan. What exactly is the meaning of $\binom{a}{0}$? I've intrepreted it as $a$ in position $i$, since I thought that the first trace describes $i$ and the second one $j$. I'm generally having some issue to comprehend how these automata work, but am I right with my assumption on $i,j$?
Jan 2, 2021 at 11:11 vote accept Walter Schulze
Feb 26, 2020 at 19:26 comment added Klas. S Thank you for the excellent answer!
Oct 28, 2017 at 10:14 comment added Walter Schulze Thank you for a great response. I am still processing all of this and working through it, looking up terms, thinking how I would implement this, etc. In the mean time I think number 3 was the wrong question. Maybe it should rather have been why is the relation between automata and logic so important, that it is mentioned in so many articles?
Oct 25, 2017 at 19:11 comment added Hendrik Jan Added my suggestion for the converse. Pending approval by @DavidRicherby
Oct 25, 2017 at 19:10 history edited Hendrik Jan CC BY-SA 3.0
added MSO to FSA construction
Oct 25, 2017 at 11:32 history answered David Richerby CC BY-SA 3.0