Residuality and Learning for Nondeterministic Nominal Automata

TL;DR

This paper introduces residual nominal automata, a subclass of nondeterministic automata, with canonical forms enabling active learning algorithms despite residuality being undecidable in general.

Contribution

It develops the theory of residual nominal automata, providing canonical representatives and a machine-independent characterization of residual languages.

Findings

Residual automata have canonical forms constructible from finite observations.

Residuality is undecidable for nominal automata.

The work advances understanding of learnability of nondeterministic automata.

Abstract

We are motivated by the following question: which data languages admit an active learning algorithm? This question was left open in previous work by the authors, and is particularly challenging for languages recognised by nondeterministic automata. To answer it, we develop the theory of residual nominal automata, a subclass of nondeterministic nominal automata. We prove that this class has canonical representatives, which can always be constructed via a finite number of observations. This property enables active learning algorithms, and makes up for the fact that residuality -- a semantic property -- is undecidable for nominal automata. Our construction for canonical residual automata is based on a machine-independent characterisation of residual languages, for which we develop new results in nominal lattice theory. Studying residuality in the context of nominal languages is a step towards a better understanding of learnability of automata with some sort of nondeterminism.