Active Learning of Deterministic Transducers with Outputs in Arbitrary Monoids

2024-10-02

Annual Conference for Computer Science Logic

AI Summary

This paper investigates the minimization problem for deterministic transducers with outputs in an arbitrary monoid, establishing for the first time necessary and sufficient conditions for the existence and uniqueness (up to isomorphism) of minimal realizations. Methodologically, it develops a unified categorical framework that tightly integrates automata minimization with active learning—specifically membership and equivalence queries—and generalizes classical categorical learning models to accommodate monoidal output structures, including commutative and cancellative monoids. The main contributions are: (1) an algebraic characterization of minimizability for deterministic monoid-output transducers; (2) an abstract learning algorithm that identifies learnability conditions for structured-output models; and (3) a general theoretical foundation and constructive methodology for sequence modeling and learning with algebraically structured outputs.

Technology Category

• Machine Learning: Active Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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, Petric{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.

Problem

• Study monoidal transducers with outputs in arbitrary monoids
• Determine conditions for minimal transducer existence and uniqueness
• Develop learning algorithm using membership and equivalence queries

Innovation

• Active learning of monoidal transducers
• Categorical framework for minimization
• Membership and equivalence queries