正则随机序列$k$ - SAT的阈值界
Bounds on Threshold of Regular Random $k$-SAT
摘要：
我们考虑了Boufkhad等人提出的合取范式公式生成的正则模型。我们推导出一个上界的可满足性阈值和NAE可满足性阈值的定期随机$k$-SAT的任何$k \geq 3$。我们表明，这些边界匹配的公式生成的统一模型与相应的边界。通过对满足赋值的个数应用二阶矩方法，我们得到了阈值的下界。对于大的$k$，我们注意到，所获得的下限阈值的一个定期随机公式收敛到下界的均匀模型。因此，我们回答了在\cite{AcM06}中提出的关于二阶矩法对规则随机公式的性能的问题。
英文摘要：
We consider the regular model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad et. al. We derive an upper bound on the satisfiability threshold and NAE-satisfiability threshold for regular random $k$-SAT for any $k \geq 3$. We show that these bounds matches with the corresponding bound for the uniform model of formula generation. We derive lower bound on the threshold by applying the second moment method to the number of satisfying assignments. For large $k$, we note that the obtained lower bounds on the threshold of a regular random formula converges to the lower bound obtained for the uniform model. Thus, we answer the question posed in \cite{AcM06} regarding the performance of the second moment method for regular random formulas.
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