Congruence-based Learning of Probabilistic Deterministic Finite Automata

TL;DR

This paper introduces a congruence-based framework for learning probabilistic deterministic finite automata, extending classical concepts to probabilistic models and providing an active learning algorithm for regular language models.

Contribution

It defines a new congruence extending Myhill-Nerode for probabilistic automata and presents an active learning algorithm based on this congruence.

Findings

The new congruence characterizes regularity in probabilistic language models.

An active learning algorithm computes automata using this congruence.

Recognizability coincides with regularity for congruences in probabilistic models.

Abstract

This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on probability distributions. We introduce a congruence that extends the classical Myhill-Nerode congruence for formal languages. This new congruence is the basis for defining regularity over language models. We present an active learning algorithm that computes the quotient with respect to this congruence whenever the language model is regular. The paper also defines the notion of recognizability for language models and shows that it coincides with regularity for congruences. For relations which are not congruences, it shows that this is not the case. Finally, it discusses the impact of this result on learning in the context of language models.