Establish the action-extended correspondence for register automata

Establish a formal correspondence between the action-extended deterministic register automata over $A \times D$ and the corresponding action-labelled register automata, and determine whether the learning and complexity bounds developed for direct data-word deterministic register automata carry over to this extension.

Background

The paper’s model processes words directly over an infinite data domain, whereas RaLib and related action-labelled models process data words over a finite action alphabet paired with an infinite data domain. The authors propose extending their model to A×DA \times D, preserving finite action sequences while applying comparisons and renamings only to data components. They explicitly conjecture equal expressive power and leave both the formal correspondence and transfer of learning and complexity bounds unresolved.

References

We conjecture that this action-extended variant has the same expressive power as the corresponding action-labelled register automata. Establishing a formal correspondence between the two models, and determining whether our learning and complexity bounds carry over to this extension, are interesting directions for future work.

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