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Effect on finite transformation semigroup under a particular modification of the generators
The following question arises in connection with problems in automata theory related to the road problem. Let $f_1, f_2: [N] \to [N]$ be maps such that the transformation semigroup $S = \langle f_1, f …
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Given an automatic set $S$ coming from a DFA $M$ when read little-endian, is $\overline{d}(S...
I believe the answer to Question 1 is positive, though maybe I've misunderstood something and the following sketch misses something important.
For $n \in [1,N]$, the DFA halts and decides whether $n \ …
1
vote
Given an automatic set $S$ coming from a DFA $M$ when read little-endian, is $\overline{d}(S...
I'm posting a new answer because I think the discussion on my previous answer is helpful for understanding the edits to the question, and what I'm adding here is a complete rewrite and is much too lon …