Generalization of single-variable complexity results to a constant number of variables

Ascertain whether any complexity classification established for solving single-variable FDDS equations (such as AX = B or P(X) = B) extends to equations with any constant number of variables.

Background

The authors raise a follow-on question about the robustness of any eventual complexity classification for single-variable FDDS equation solving: whether such results generalize when the number of variables is any fixed constant.

This concerns the scalability of algorithmic or hardness insights from the single-variable setting to small multivariate settings in the FDDS semiring.