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引用次数: 108
摘要
Paturi, Pudl\ ak, Saks, and Zane[1998]提出的PPSZ算法是目前已知的最快的Unique k-SAT算法，该算法的输入公式不会有多于一个满意的赋值。对于k>=5，一般k- sat也有相同的界。我们使用稍微修改的PPSZ算法证明，对于k=3,4也是如此。我们通过定义一个可满足CNF公式的成本来进行分析，我们证明了每个PPSZ步骤都会减少一定数量的成本。这改进了我们之前使用Moser和Scheder[2011]对3-SAT到O(1.308^n)和4-SAT到O(1.469^n)的最佳界限。
3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General
The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane [1998] is the fastest known algorithm for Unique k-SAT, where the input formula does not have more than one satisfying assignment. For k>=5 the same bounds hold for general k-SAT. We show that this is also the case for k=3,4, using a slightly modified PPSZ algorithm. We do the analysis by defining a cost for satisfiable CNF formulas, which we prove to decrease in each PPSZ step by a certain amount. This improves our previous best bounds with Moser and Scheder [2011] for 3-SAT to O(1.308^n) and for 4-SAT to O(1.469^n).
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