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Impact of relaxing variable-count and constant-right-hand-side constraints on tractability and decidability

Investigate how far the constraints requiring a single variable and a constant right-hand side in FDDS equations can be relaxed while preserving tractability and decidability, and characterize the boundary beyond which the problems become intractable or undecidable.

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Background

General polynomial equations over FDDS with variables on both sides are known to be undecidable, whereas the paper’s focus on constant right-hand sides yields decidable and often efficiently solvable cases.

The authors explicitly ask how much these constraints can be loosened—e.g., more variables or non-constant right-hand sides—before crossing into intractability or undecidability, aiming to delineate the precise frontier of solvable subclasses.

References

Furthermore, how much can we relax the constraints on the number of variables and the fact that the right-hand side of equations must be constant without them becoming intractable or even undecidable?

— Solving "pseudo-injective" polynomial equations over finite dynamical systems (2504.06986 - Porreca et al., 9 Apr 2025) in Section “Conclusions”