Moore's seminal paper can be taken as the starting point
of Algorithmic Learning Theory. Moore studied the problem of unraveling
the inner structure of a (minimum state) deterministic finite automaton
(DFA) from its input-output behaviour.
In this note we pursue Moore's line of research, studying conditions
under which it is possible to compute a grammar and/or
an automaton for a given language L from a language class C.
It doesn't come as a surprise that such conditions must be quite strong.
We improve on the algorithms in some cases where computing the
grammar/automaton is possible.
We correct some mistakes in the literature and come up with some
new results, positive and negative,
for (subclasses of) context-free languages.