# Query Learning Algorithm for Residual Symbolic Finite Automata

## TL;DR

This paper introduces a new query learning algorithm for residual symbolic finite automata (RSFAs), which combine properties of SFAs and RFAs to efficiently learn automata over large alphabets, outperforming existing methods.

## Contribution

The paper presents the first efficient query learning algorithm for RSFAs, enabling more succinct automata representations and improved learning efficiency over large alphabets.

## Key findings

- The algorithm efficiently learns RSFAs over huge alphabets.
- RSFAs can be exponentially smaller than deterministic finite automata.
- Learning RSFAs outperforms existing algorithms for deterministic SFAs.

## Abstract

We propose a query learning algorithm for residual symbolic finite automata (RSFAs). Symbolic finite automata (SFAs) are finite automata whose transitions are labeled by predicates over a Boolean algebra, in which a big collection of characters leading the same transition may be represented by a single predicate. Residual finite automata (RFAs) are a special type of non-deterministic finite automata which can be exponentially smaller than the minimum deterministic finite automata and have a favorable property for learning algorithms. RSFAs have both properties of SFAs and RFAs and can have more succinct representation of transitions and fewer states than RFAs and deterministic SFAs accepting the same language. The implementation of our algorithm efficiently learns RSFAs over a huge alphabet and outperforms an existing learning algorithm for deterministic SFAs. The result also shows that the benefit of non-determinism in efficiency is even larger in learning SFAs than non-symbolic automata.