3- SAT的一个新的上界

Non Uniform Selection of Solutions for Upper Bounding the 3-SAT Threshold

We give a new insight into the upper bounding of the 3-SAT threshold by the first moment method. The best criteria developed so far to select the solutions to be counted discriminate among neighboring solutions on the basis of uniform information about each individual free variable. What we mean by uniform information, is information which does not depend on the solution: e.g. the number of positive/negative occurrences of the considered variable. What is new in our approach is that we use non uniform information about variables. Thus we are able to make a more precise tuning, resulting in a s…

随机3-SAT可满足性阈值的一个上界：4.268

An upper bound of 4.268 for the random 3-SAT satisfiability threshold

该研究证明随机3-SAT公式的可满足性阈值上界为4.268，基于插值与能量方法，通过与简单约束系统比较简化为有限计算，在Lean 4中形式化，使严格上界接近腔方法预测值。

一个新的Max-2-Sat上界：图论方法

A New Upper Bound for Max-2-Sat: A Graph-Theoretic Approach

在{ \sc MaxSat}中，我们要求一个赋值满足CNF中布尔公式的最大子句数。我们提出了一个算法，产生运行时间上界的$O^*(2^{\frac{1}{6.2158}})$为{ \sc Max-2-Sat}（每个子句包含最多2个文字），其中$K$是子句的数量。运行时间已经通过使用启发式优先级的选择上的变量，我们的分支。这些启发式优先级的实现相当简单，尽管它们对运行时间有显著的影响。该分析是使用定制的非标准措施。

Automated Proofs in Geometry : Computing Upper Bounds for the Heilbronn Problem for Triangles

We propose a method for computing upper bounds for the Heilbronn problem for triangles.

$k\geq 3$的随机$d$-正则$k$-均匀超图$2$-着色阈值的上界

Upper bounds on the $2$-colorability threshold of random $d$-regular $k$-uniform hypergraphs for $k\geq 3$

本文研究了随机$d$-正则$k$-均匀超图$2$-着色与随机$d$-正则$k$-NAE-SAT模型，针对所有$k\geq 3$证明了显式可满足性上界$d_{\ast}(k)$，该上界与统计物理学预测吻合且在$k$足够大时与已知阈值一致。