An $\mathbf{L^*}$ Algorithm for Deterministic Weighted Regular Languages

TL;DR

This paper introduces a weighted version of Angluin's L* algorithm to learn minimal deterministic weighted finite automata, enabling interpretable analysis of complex models with weighted automata.

Contribution

It extends the classic L* algorithm to handle weighted automata with division, and links the learning process to automaton minimization.

Findings

Successfully learns minimal deterministic weighted FSAs.

Supports exact learning of weighted automata with division.

Highlights connection between L* and FSA minimization.

Abstract

Extracting finite state automata (FSAs) from black-box models offers a powerful approach to gaining interpretable insights into complex model behaviors. To support this pursuit, we present a weighted variant of Angluin's (1987) $\mathbf{L^*}$ algorithm for learning FSAs. We stay faithful to the original algorithm, devising a way to exactly learn deterministic weighted FSAs whose weights support division. Furthermore, we formulate the learning process in a manner that highlights the connection with FSA minimization, showing how $\mathbf{L^*}$ directly learns a minimal automaton for the target language.