论文标题
超越真实的存在理论
Beyond the Existential Theory of the Reals
论文作者
论文摘要
我们表明，在较高级别的真实理论上的完整性是一个强大的概念（在改变量化词的签名和界限下）。这修补了层次结构中认可的差距，并为各种计算问题带来了更强的完整性结果。我们展示了几个完全问题的家庭，可用于将来的完整性结果。作为应用程序，我们对Bürgisser和Cucker的一些结果提高了半ge式集合的性能的复杂性，包括Jungeblut，Kleist和Miltzow也研究了Hausdorff距离问题。
We show that completeness at higher levels of the theory of the reals is a robust notion (under changing the signature and bounding the domain of the quantifiers). This mends recognized gaps in the hierarchy, and leads to stronger completeness results for various computational problems. We exhibit several families of complete problems which can be used for future completeness results in the real hierarchy. As an application we sharpen some results by Bürgisser and Cucker on the complexity of properties of semialgebraic sets, including the Hausdorff distance problem also studied by Jungeblut, Kleist, and Miltzow.
