随机k-SAT和两个选择的力量
Random k-SAT and the Power of Two Choices
摘要：
我们研究了Achlioptas过程版本的随机k-SAT过程：一个有限数量的k-子句均匀随机地绘制在每一步，并根据特定的规则添加到增长公式。我们证明了一个规则的存在，移动的可满足性阈值。这将概率组合学（Achlioptas过程）的一个很好的研究领域扩展到随机CSP。特别地，虽然先前已知延迟2-SAT阈值的规则，但这是对于k >= 3移动k-SAT阈值的规则的第一个证明。然后，我们提出了一个间隙判定问题的基础上，这个半随机模型。问题的目的是调查的硬度随机k-SAT判定问题，而不是找到一个分配或证书的不满足的问题。最后，我们讨论了连接到Achlioptas随机图过程的研究。
英文摘要：
We study an Achlioptas-process version of the random k-SAT process: a bounded number of k-clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule. We prove the existence of a rule that shifts the satisfiability threshold. This extends a well-studied area of probabilistic combinatorics (Achlioptas processes) to random CSP's. In particular, while a rule to delay the 2-SAT threshold was known previously, this is the first proof of a rule to shift the threshold of k-SAT for k >= 3. We then propose a gap decision problem based upon this semi-random model. The aim of the problem is to investigate the hardness of the random k-SAT decision problem, as opposed to the problem of finding an assignment or certificate of unsatisfiability. Finally, we discuss connections to the study of Achlioptas random graph processes.
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