Learning automata and transducers: a categorical approach

TL;DR

This paper introduces a categorical framework for learning automata and transducers, resulting in a versatile, generic $L^*$-like algorithm applicable to various automata types, with proven correctness and minimality conditions.

Contribution

It develops a new categorical approach to automata learning, creating a generic algorithm that unifies different automata types under a common framework.

Findings

A new generic $L^*$-like algorithm for automata learning.

Proof of correctness and minimality under certain categorical conditions.

Applicability to deterministic automata, weighted automata, and transducers.

Abstract

In this paper, we present a categorical approach to learning automata over words, in the sense of the $L^*$-algorithm of Angluin. This yields a new generic $L^*$-like algorithm which can be instantiated for learning deterministic automata, automata weighted over fields, as well as subsequential transducers. The generic nature of our algorithm is obtained by adopting an approach in which automata are simply functors from a particular category representing words to a "computation category". We establish that the sufficient properties for yielding the existence of minimal automata (that were disclosed in a previous paper), in combination with some additional hypotheses relative to termination, ensure the correctness of our generic algorithm.