平面可满足性问题的种植解的检测
Detection of Planted Solutions for Flat Satisfiability Problems
摘要：
我们研究了在随机情况下的平面可满足性问题，布尔可满足性公式的推广寻找种植解决方案的检测问题。我们描述的属性的随机情况下，平坦的可满足性，以及相关的假设检验问题的最佳检测率。我们还研究了算法有效的测试过程的性能。我们介绍了我们的模型的修改，光种植的解决方案，并表明，这是很难的学习奇偶噪声的问题。这强烈暗示了检测种植平坦可满足性对于广泛的测试类的困难。
英文摘要：
We study the detection problem of finding planted solutions in random instances of flat satisfiability problems, a generalization of boolean satisfiability formulas. We describe the properties of random instances of flat satisfiability, as well of the optimal rates of detection of the associated hypothesis testing problem. We also study the performance of an algorithmically efficient testing procedure. We introduce a modification of our model, the light planting of solutions, and show that it is as hard as the problem of learning parity with noise. This hints strongly at the difficulty of detecting planted flat satisfiability for a wide class of tests.
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