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I found a seminal paper of renowned authors (Inference of Finite Automata Using Homing Sequences (1993) by Ron Rivest and Robert Schapire) in which the authors define the very same set-theoretic ...

(I'm not entirely sure what to tag this; feel free to retag.) While thinking about automata (specifics below), I ran into the following phenomenon: A cofunction system is a pair of sets $X, A$, ...