对随机排序约束满足问题的强反驳
Strong Refutation of Random Ordering CSPs
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中文总结 AI 辅助
研究随机排序约束满足问题可满足性的强反驳，给出子句数超阈值时的多项式时间\(\varepsilon\)-反驳算法，用菊池方法得到运行时间、子句密度和反驳强度间的三方权衡，并通过计算下限证明该权衡接近最优。
中文摘要 AI 辅助
在本研究中，我们开启了对随机排序约束满足问题可满足性的强反驳研究。我们证明，当子句数量高于阈值\(\tilde{\Omega}(n^{d/2}/\varepsilon^2)\)时，对于带有谓词\(P\)的随机排序约束满足问题存在多项式时间\(\varepsilon\)-反驳算法，其中\(d\)是谓词\(P\)的坐标度。我们还使用菊池方法给出了运行时间、子句密度和反驳强度\(\varepsilon\)之间平滑的三方权衡。最后，基于低坐标度算法类别给出计算下限，证明所建立的三方权衡接近最优。
英文摘要
In this work, we initiate the study of strongly refuting the satisfiability of random ordering constraint satisfaction problems. We show that there is a polynomial-time $\varepsilon$-refutation algorithm for random ordering CSP with predicate $P$ when the number of clauses is above the threshold $\tildeΩ\left(n^{d/2}/\varepsilon^2\right)$, where $d$ is the coordinate degree of the predicate $P$. We further give a smooth three-way tradeoff between the running time, the clause density, and the refutation strength $\varepsilon$ using the Kikuchi method. Finally, we complement our algorithmic results with a computational lower bound based on the class of low coordinate degree algorithms, providing evidence that the established three-way tradeoff is near optimal.
