Decidability of WRP equivalence and presentability

Determine whether equivalence of two weighted-rank polyregular presentations is decidable, and more generally determine, for a fixed finitely presented ambient transducer model, whether a presented map admits a weighted-rank polyregular presentation.

Background

The WRP model is defined syntactically through polyregular atom selection and labeling together with prefix-additive rank functions and a global rank sort. The paper establishes several expressiveness and separation results but does not provide decision procedures for comparing presentations or recognizing WRP-presentability.

The unresolved question concerns both equivalence of two given WRP descriptions and the broader membership problem relative to a finitely presented ambient model.

References

Is equivalence of two $WRP$ presentations decidable? More generally, after fixing a finitely presented ambient transducer model, is it decidable whether a presented map admits a $WRP$ presentation?

— A Computational Obstruction to Swapping Area and Dinv: An Automata-Theoretic View of the $q,t$-Catalan Symmetry  (2609.05005 - Baek et al., 4 Sep 2026) in Section “Related work and open problems”, item 2