几何查询的评价：约束数据库和量词消去
The evaluation of geometric queries: constraint databases and quantifier elimination
摘要：
我们对几何消除的算法任务进行建模（例如，实数和复数的基本场论中的量词消去）。作为一个特殊的情况下，这样的几何消除任务，我们认为样本点查询。我们展示了指数较低的复杂性边界，以评估几何查询在一般情况下，在特定情况下的样本点查询。虽然本文是理论性的，但其目的是探索计算机实现的约束数据库查询评估算法的可能性和（复杂性）限制，基于最先进的几何消除过程及其实现的原理，例如，“Kronecker”软件包。
英文摘要：
We model the algorithmic task of geometric elimination (e.g., quantifier elimination in the elementary field theories of real and complex numbers) by means of certain constraint database queries, called geometric queries. As a particular case of such a geometric elimination task, we consider sample point queries. We show exponential lower complexity bounds for evaluating geometric queries in the general and in the particular case of sample point queries. Although this paper is of theoretical nature, its aim is to explore the possibilities and (complexity-)limits of computer implemented query evaluation algorithms for Constraint Databases, based on the principles of the most advanced geometric elimination procedures and their implementations, like, e.g., the software package "Kronecker".
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