空腔法中随机K-SAT的阈值
Threshold values of Random K-SAT from the cavity method
摘要：
利用\cite{mezard:parisi:zecchina:02,mezard:zecchina:02}的腔方程，我们导出了随机$K$ -可满足性问题中每个变量子句数目的各种阈值，将以前的结果推广到$K \ge 4$ .我们还给出了一个解析解的方程，和一些封闭的表达式，这些阈值，在大$K$周围的扩展。还计算了解的稳定性。对于任何$K$，可满足性阈值被发现是在稳定区域的解决方案，这增加了进一步的信用的猜想，这种计算给出了确切的可满足性阈值。
英文摘要：
Using the cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to $K \ge 4$. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large $K$. The stability of the solution is also computed. For any $K$, the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
