Separating Non-redundancy and Chain Length

2026-09-15

AI Summary

研究通过构造一个四元关系，证明了约束满足问题中链长度与非冗余度之间的渐近分离。

Abstract

For a constraint satisfaction problem defined by a relation $R$, its non-redundancy $\text{NRD}(R,n)$ is the size of largest instance (as a function of the number $n$ of variables) for which no constraint is implied by the rest. Its chain length $\text{CL}(R,n)$ is the largest such instance where the constraints can be ordered so that no constraint is implied by the preceding ones. Clearly $\text{CL}(R,n) \ge \text{NRD}(R,n)$ but so far no asymptotic separation was known between these quantities. We exhibit an explicit arity $4$ relation for which $\text{CL}(R,n) \ge ω(\text{NRD}(R,n))$.

Problem

• constraint satisfaction problem
• non-redundancy
• chain length
• asymptotic separation

Innovation

• constraint satisfaction problem
• non-redundancy
• chain length
• asymptotic separation