Super-linear Lower Bounds for CSP Non-Redundancy via Shrinking Instances

2026-05-18

AI Summary

This work investigates near-linear non-redundancy degree (NRD) bounds for predicates in constraint satisfaction problems (CSPs), with the goal of identifying predicates that admit super-linear NRD lower bounds. To this end, the authors introduce a hypergraph projection framework together with the notion of minimization factors, enabling a more precise analysis of gadget reduction efficacy. By integrating SAT solvers, they automate the discovery of such reductions, thereby overcoming limitations of existing techniques. This approach yields the first super-linear NRD lower bounds for several pivotal CSP predicates—bounds previously unattainable by manual or conventional methods—and demonstrates the feasibility of automated reduction construction in this context.

Abstract

The non-redundancy (NRD) of a constraint satisfaction problem (CSP) is a combinatorial quantity closely tied to the behavior of CSPs in various computational models including their sparsification, kernelization, and streaming complexity. A primary open question in the study of non-redundancy is the identification of which CSP predicates have near-linear NRD. Recent works by Carbonnel [CP 2022], Khanna, Putterman and Sudan [STOC 2025], Brakensiek and Guruswami [STOC 2025] and Brakensiek, Guruswami, Jansen, Lagerkvist, and Wahlström [2025] have introduced various forms of gadget reductions between CSPs to relate their non-redundancy. The primary contribution of this work is to recontextualize many of these gadget reductions in a framework which we call hypergraph projections. By studying a quantity we call the shrinking factor of these hypergraph projections, we can more precisely predict when a gadget reduction between predicates can yield a super-linear NRD lower bound, greatly improving on the analysis of previous works. To illustrate the power of our framework, we identify some concrete CSP predicates whose non-redundancy is at the cusp of our understanding and show how our methods give lower bounds that could not have been achieved with these previous methods. We also demonstrate how these gadget reductions can be automatically deduced using SAT solvers, thereby opening up novel computational avenues for discovering further relationships between the non-redundancy of various CSPs.

Problem

• constraint satisfaction problem
• non-redundancy
• super-linear lower bound
• CSP predicates
• sparsification

Innovation

• hypergraph projections
• shrinking factor
• non-redundancy
• gadget reductions
• CSP