We develop a generic reduction procedure for active learning problems. Our
approach is inspired by a recent polynomial-time reduction of the exact
learning problem for weighted automata over integers to that for weighted
automata over rationals (Buna-Marginean et al. 2024). Our procedure improves
the efficiency of a category-theoretic automata learning algorithm, and poses
new questions about the complexity of its implementation when instantiated to
concrete categories. As our second main contribution, we address these
complexity aspects in the concrete setting of learning weighted automata over
number rings, that is, rings of integers in an algebraic number field. Assuming
a full representation of a number ring OK, we obtain an exact learning
algorithm of OK-weighted automata that runs in polynomial time in the size of
the target automaton, the logarithm of the length of the longest
counterexample, the degree of the number field, and the logarithm of its
discriminant. Our algorithm produces an automaton that has at most one more
state than the minimal one, and we prove that doing better requires solving the
principal ideal problem, for which the best currently known algorithm is in
quantum polynomial time.

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