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

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) ${\mathbf{L}}^{\ast }$ 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 ${\mathbf{L}}^{\ast }$ directly learns a minimal automaton for the target language.