Active Learning of Deterministic Transducers with Outputs in Arbitrary Monoids

We study monoidal transducers, transition systems arising as
deterministic automata whose transitions also produce outputs in an
arbitrary monoid, for instance allowing outputs to commute or to cancel out.
In a first part I'll explain how Vilar's algorithm for the active
learning à la Angluin of (classical) transducers generalize to monoidal
transducers. In a second part I'll then discuss how this is an instance
of the categorical framework for minimization and learning of Colcombet,
Petrişan and Stabile: the active learning algorithm was obtained by
instantiating monoidal transducers in this framework.