Active Learning of Deterministic Transducers with Outputs in Arbitrary Monoids

TL;DR

This paper introduces a categorical framework for learning minimal deterministic monoidal transducers, providing conditions for their uniqueness and an abstract algorithm for their inference from queries.

Contribution

It extends the theory of automata learning to transducers with outputs in arbitrary monoids, including conditions for minimality and a new learning algorithm.

Findings

Established necessary and sufficient conditions for minimal transducers to exist and be unique.

Developed an abstract learning algorithm based on membership and equivalence queries.

Discussed practical implementation aspects of the proposed algorithm.

Abstract

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. We use the categorical framework for minimization and learning of Colcombet, Petri\c{s}an and Stabile to recover the notion of minimal transducer recognizing a language, and give necessary and sufficient conditions on the output monoid for this minimal transducer to exist and be unique (up to isomorphism). The categorical framework then provides an abstract algorithm for learning it using membership and equivalence queries, and we discuss practical aspects of this algorithm's implementation.