Extend nominal-automata learning to ordered domains

Develop an extension of the active-learning framework for nominal automata with equality tests to ordered data domains, thereby resolving the problem of accommodating ordered comparisons within that framework.

Background

The paper discusses prior work on learning nominal automata, which are equivalent in expressive power to register automata over infinite domains with equality tests. That prior framework was noted as potentially accommodating ordered domains, but the required extension had not been worked out. The passage explicitly identifies this extension as unresolved.

References

The authors of briefly note that their framework is intended to accommodate both equality and ordered domains, although working out the extension to ordered domains is left open.

— Learning Canonical Register Automata over Ordered Data Domains  (2608.18765 - Li et al., 19 Aug 2026) in Section 1, Related Work

We leave a full learning algorithm using only membership and equivalence queries as future work. Unsurprisingly, this approach requires an exponential number of membership queries, as also in, to fill the observation table since all concrete suffixes $z$ over $D_{u, v}$ must be enumerated and added to the suffix set for $u$.

— Learning Canonical Register Automata over Ordered Data Domains  (2608.18765 - Li et al., 19 Aug 2026) in Section 5, Conclusion and Discussion