Simulation of chiIMP algorithms by Polynomial Calculus

Determine whether an efficient algorithm for the truncated membership problem chiIMP_d can be simulated by Polynomial Calculus while preserving bounded degree and the requisite certificate-size bounds.

Background

The paper contrasts its syntactic Polynomial Calculus reductions with the interpolation-based reductions developed for the related problem chiIMP_d. Efficient chiIMP algorithms can construct truncated Gröbner bases semantically, but it is unresolved whether those computations can be converted into bounded-degree Polynomial Calculus derivations. Resolving this issue would clarify whether the related framework can yield the certificate-level consequences needed for Sum-of-Squares automatability.

References

It remains however unclear whether such an algorithm can be simulated by $PC$.

— Ideal Membership in Polynomial Calculus: Complexity and Reductions  (2609.28243 - Bortolotti et al., 23 Sep 2026) in Introduction, subsection “Related work”