Weighted automata are compact and actively learnable

TL;DR

This paper demonstrates that weighted automata over fields can be exponentially more compact than traditional automata and are efficiently learnable using a linear algebraic extension of existing algorithms.

Contribution

It introduces a linear algebraic algorithm for learning weighted automata over any field, showing their compactness and learnability.

Findings

Weighted automata can be exponentially more compact than non-deterministic finite automata.

Weighted automata are efficiently learnable with a polynomial number of queries.

The paper provides a general algorithm for learning weighted automata over any field.

Abstract

We show that weighted automata over the field of two elements can be exponentially more compact than non-deterministic finite state automata. To show this, we combine ideas from automata theory and communication complexity. However, weighted automata are also efficiently learnable in Angluin's minimal adequate teacher model in a number of queries that is polynomial in the size of the minimal weighted automaton.. We include an algorithm for learning WAs over any field based on a linear algebraic generalization of the Angluin-Schapire algorithm. Together, this produces a surprising result: weighted automata over fields are structured enough that even though they can be very compact, they are still efficiently learnable.