We present the current fastest deterministic algorithm for $k$-SAT, improving the upper bound $(2-2/k)^{n + o(n)}$ dues to Moser and Scheder [STOC'11]. The algorithm combines a branching algorithm with the derandomized local search, whose analysis relies on a special sequence of clauses called chain, and a generalization of covering code based on linear programming. We also provide a more ingenious branching algorithm for $3$-SAT to establish the upper bound $1.32793^n$, improved from $1.3303^n$.

中文翻译：

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k-SAT 的链、覆盖代码的泛化和确定性算法

我们提出了当前最快的 $k$-SAT 确定性算法，提高了由于 Moser 和 Scheder [STOC'11] 的上限 $(2-2/k)^{n + o(n)}$。该算法结合了分支算法和去随机化局部搜索，其分析依赖于称为链的特殊子句序列，以及基于线性规划的覆盖代码的泛化。我们还为 $3$-SAT 提供了一个更巧妙的分支算法，以建立从 $1.3303^n$ 改进的上限 $1.32793^n$。