A Novel Learning Algorithm for B\"uchi Automata based on Family of DFAs and Classification Trees

TL;DR

This paper introduces a new algorithm for learning B"uchi automata from an $$-regular language, utilizing classification trees and family of DFAs, resulting in improved storage efficiency and performance.

Contribution

It presents a novel tree-based learning algorithm for B"uchi automata using FDFAs, with better storage efficiency and competitive performance.

Findings

Quadratic reduction in worst-case storage space compared to table-based methods.

The new algorithm outperforms existing methods in solving learning tasks.

The ROLL library implements all $$-regular learning algorithms, including the new one.

Abstract

In this paper, we propose a novel algorithm to learn a B\"uchi automaton from a teacher who knows an $\omega$-regular language. The algorithm is based on learning a formalism named family of DFAs (FDFAs) recently proposed by Angluin and Fisman[10]. The main catch is that we use a classification tree structure instead of the standard observation table structure. The worst case storage space required by our algorithm is quadratically better than the table-based algorithm proposed in [10]. We implement the first publicly available library ROLL (Regular Omega Language Learning ), which consists of all $\omega$-regular learning algorithms available in the literature and the new algorithms proposed in this paper. Experimental results show that our tree-based algorithms have the best performance among others regarding the number of solved learning tasks.