存在与剥削：弱假设下的主干和后门的不透明性
Existence versus Exploitation: The Opacity of Backbones and Backdoors Under a Weak Assumption
摘要：
布尔公式的后门和主干是隐藏的结构属性。一个自然的目标，已经部分实现，是求解器算法寻求通过利用这些结构获得更好的性能。然而，本文并不打算提高SAT求解器的性能，而是一个警示文件。特别是，本文的主题是，在布尔公式中存在这样的结构和能够有效地利用它们之间存在着潜在的鸿沟。这并不意味着这些结构对求解器没有用。它确实意味着人们必须非常小心，不要假设从结构的存在到能够得到它和/或能够利用结构在计算上是容易的。例如，在本文中，我们表明，在假设P $\neq$ NP，有很容易识别的家庭布尔公式强后门，很容易找到，但它是很难（事实上，NP-完全），以确定是否满足的公式。我们还表明，也在假设P $\neq$ NP，有很容易识别的布尔公式集，它是很难（事实上，NP-完全），以确定他们是否有一个大的骨干。
英文摘要：
Backdoors and backbones of Boolean formulas are hidden structural properties. A natural goal, already in part realized, is that solver algorithms seek to obtain substantially better performance by exploiting these structures. However, the present paper is not intended to improve the performance of SAT solvers, but rather is a cautionary paper. In particular, the theme of this paper is that there is a potential chasm between the existence of such structures in the Boolean formula and being able to effectively exploit them. This does not mean that these structures are not useful to solvers. It does mean that one must be very careful not to assume that it is computationally easy to go from the existence of a structure to being able to get one's hands on it and/or being able to exploit the structure. For example, in this paper we show that, under the assumption that P $\neq$ NP, there are easily recognizable families of Boolean formulas with strong backdoors that are easy to find, yet for which it is hard (in fact, NP-complete) to determine whether the formulas are satisfiable. We also show that, also under the assumption P $\neq$ NP, there are easily recognizable sets of Boolean formulas for which it is hard (in fact, NP-complete) to determine whether they have a large backbone.
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。
