一类看似难处理的随机约束满足问题的可满足性阈值
The Satisfiability Threshold for a Seemingly Intractable Random Constraint Satisfaction Problem
摘要：
我们确定一个特定的NP完全约束满足问题（CSP）的随机实例的可满足性的确切阈值。这是第一个随机CSP模型，我们已经确定了一个精确的线性可满足性阈值，密度接近该阈值的随机实例似乎是计算困难的。更正式地说，它是第一个已知可满足性阈值的随机CSP模型，并且与随机k-SAT（k >= 3）共享以下特征。该问题是NP-完全的，满足性阈值出现在子句数为线性时，并且具有线性子句数的一致随机实例渐近几乎必然具有指数分解复杂度。
英文摘要：
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability threshold, and for which random instances with density near that threshold appear to be computationally difficult. More formally, it is the first random CSP model for which the satisfiability threshold is known and which shares the following characteristics with random k-SAT for k >= 3. The problem is NP-complete, the satisfiability threshold occurs when there is a linear number of clauses, and a uniformly random instance with a linear number of clauses asymptotically almost surely has exponential resolution complexity.
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