基于Fourier分析的随机约束条件问题可满足性估计的一般界
General Bounds on Satisfiability Thresholds for Random CSPs via Fourier Analysis
摘要：
随机约束满足问题在人工智能和复杂性理论中得到了广泛的研究。经验和理论上，许多随机CSP已被证明表现出相变。当约束与变量的比率超过一定的阈值时，它们从几乎肯定可满足转变为不可满足。这个阈值的确切位置已经被彻底研究过了，但只针对某些常见的约束类别。在本文中，我们提出了新的界限，这些阈值在布尔CSP的位置。我们的主要贡献是，我们的边界是完全通用的，并适用于任何固定的约束函数，可以用来生成一个合奏的随机CSP。这些界限依赖于一种新的傅立叶分析，可以很容易地计算出从傅立叶频谱的约束函数。我们的界限是在一个恒定的因素的确切阈值位置，许多研究的随机CSP。我们证明，我们的界限可以很容易地实例化，以获得许多约束函数，以前没有研究的阈值，并评估他们的实验。
英文摘要：
Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to variables passes certain thresholds, they transition from being almost certainly satisfiable to unsatisfiable. The exact location of this threshold has been thoroughly investigated, but only for certain common classes of constraints. In this paper, we present new bounds for the location of these thresholds in boolean CSPs. Our main contribution is that our bounds are fully general, and apply to any fixed constraint function that could be used to generate an ensemble of random CSPs. These bounds rely on a novel Fourier analysis and can be easily computed from the Fourier spectrum of a constraint function. Our bounds are within a constant factor of the exact threshold location for many well-studied random CSPs. We demonstrate that our bounds can be easily instantiated to obtain thresholds for many constraint functions that had not been previously studied, and evaluate them experimentally.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
