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Understand the relationship between chain length and non-redundancy for CSPs

Determine the relationship between chain length CL(R,n) and non-redundancy NRD(R,n) for CSP predicates R ⊆ D^r; in particular, ascertain whether general bounds relate CL(R,n) and NRD(R,n) across all CSPs.

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Background

The paper shows that unweighted sparsification is governed by non-redundancy, whereas weighted sparsification is governed by chain length. For non-linear codes, these parameters can differ dramatically, but their relationship for CSP predicates is not understood.

Clarifying how CL and NRD relate for CSPs would unify the theory of unweighted and weighted sparsification and could impact query-complexity models studied in prior work.

References

For non-linear codes, $NRD$ and $CL$ can be very different (e.g., Example~\ref{example:chain}), but the relationship for CSPs is unknown.

— Redundancy Is All You Need (2411.03451 - Brakensiek et al., 5 Nov 2024) in Subsection “Open Questions” (Introduction)