Learning Automata with Name Allocation

TL;DR

This paper introduces active learning algorithms for bar automata, enabling the processing of data words with name binding over infinite alphabets, and extends these methods to infinite words and trees.

Contribution

It develops a generic framework that adapts existing finite automata learning algorithms to bar automata, handling data with name binding over infinite alphabets.

Findings

First active learning methods for data languages of infinite words.

Extension of learning algorithms to bar tree automata.

Framework bridges finite and infinite alphabet automata.

Abstract

Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for bar automata, a species of automata that process finite data words represented as bar strings, which are words with explicit name binding letters. Bar automata have pleasant algorithmic properties. We develop a framework in which every learning algorithm for standard deterministic or nondeterministic finite automata over finite alphabets can be used to learn bar automata, with a query complexity determined by that of the chosen learner. The technical key to our approach is the algorithmic handling of $\alpha$-equivalence of bar strings, which allows bridging the gap between finite and infinite alphabets. The principles underlying our framework are generic and also apply to bar B\"uchi automata and bar tree automata, leading to the first active learning methods for data languages of infinite words and finite trees.