A Categorical Framework for Learning Generalised Tree Automata

TL;DR

This paper extends a category-theoretic framework to unify automata learning algorithms, including tree automata, providing a foundation for new algorithms and simplifying correctness proofs.

Contribution

It generalizes the CALF framework to include algebraic structures beyond coalgebras and introduces an abstract L* algorithm for learning such structures.

Findings

Unified framework for automata learning using category theory

Recovery of practical tree automata learning algorithms

Development of new algorithms for quotiented polynomial functors

Abstract

Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify these using category theory in order to ease correctness proofs and guide the design of new algorithms. In this paper, we extend CALF to cover learning of algebraic structures that may not have a coalgebraic presentation. Furthermore, we provide a detailed algorithmic account of an abstract version of the popular L* algorithm, which was missing from CALF. We instantiate the abstract theory to a large class of Set functors, by which we recover for the first time practical tree automata learning algorithms from an abstract framework and at the same time obtain new algorithms to learn algebras of quotiented polynomial functors.