Active Learning for Deterministic Bottom-up Nominal Tree Automata

TL;DR

This paper introduces deterministic bottom-up nominal tree automata (DBNTA), proves a Myhill-Nerode theorem for them, and presents an active learning algorithm that handles various data symmetries with guaranteed termination.

Contribution

It extends active learning to a new class of automata operating on trees with nominal data, generalizing previous work to broader symmetries and establishing foundational theorems.

Findings

Proved a Myhill-Nerode theorem for DBNTA

Developed an active learning algorithm for DBNTA

Established termination guarantees for the learning process

Abstract

Nominal set plays a central role in a group-theoretic extension of finite automata to those over an infinite set of data values. Moerman et al. proposed an active learning algorithm for nominal word automata with the equality symmetry. In this paper, we introduce deterministic bottom-up nominal tree automata (DBNTA), which operate on trees whose nodes are labelled with elements of an orbit finite nominal set. We then prove a Myhill-Nerode theorem for the class of languages recognized by DBNTA and propose an active learning algorithm for DBNTA. The algorithm can deal with any data symmetry that admits least support, not restricted to the equality symmetry and/or the total order symmetry. To prove the termination of the algorithm, we define a partial order on nominal sets and show that there is no infinite chain of orbit finite nominal sets with respect to this partial order between any two orbit finite sets.