在有界度模型的一个变体中的更快的属性测试器
Faster Property Testers in a Variation of the Bounded Degree Model
摘要：
属性测试算法是具有概率精度保证的高效算法。对于属性P，目标是通过仅查询输入的少量局部部分来区分具有P的输入与那些远离具有P的输入。在图的属性测试中，距离是通过边修改（添加或删除）的数量来测量的，这是将图转换为具有属性P的图所必需的。e.算法对输入进行查询的次数，但考虑到应用程序，算法的运行时间同样相关。在（Adler，Harwath STACS 2018）中，引入了属性测试的有界度图模型到有界度的关系数据库的自然扩展，并表明在有界度和有界树宽度的数据库上，可以在一元二阶计数逻辑（CMSO）中表达的每个属性都是可测试的，查询复杂度和次线性运行时间不变。它仍然开放是否可以改善到恒定的运行时间。在本文中，我们介绍了一种新的模型，它是基于有界度模型，但距离测量允许边（元组）的修改和顶点（元素）的修改。我们的主要定理表明，在有界度和有界树宽的数据库中，CMSO中可表达的每个属性在新模型中具有恒定的查询复杂度和恒定的运行时间是可测试的。我们还表明，在经典模型中可测试的每个属性在我们的模型中也是可测试的，具有相同的查询复杂度和运行时间，但反之则不然。我们认为，我们的模型是自然的，我们的元定理显示恒定时间CMSO可测试性支持这一点。
英文摘要：
Property testing algorithms are highly efficient algorithms, that come with probabilistic accuracy guarantees. For a property P, the goal is to distinguish inputs that have P from those that are far from having P with high probability correctly, by querying only a small number of local parts of the input. In property testing on graphs, the distance is measured by the number of edge modifications (additions or deletions), that are necessary to transform a graph into one with property P. Much research has focussed on the query complexity of such algorithms, i. e. the number of queries the algorithm makes to the input, but in view of applications, the running time of the algorithm is equally relevant. In (Adler, Harwath STACS 2018), a natural extension of the bounded degree graph model of property testing to relational databases of bounded degree was introduced, and it was shown that on databases of bounded degree and bounded tree-width, every property that is expressible in monadic second-order logic with counting (CMSO) is testable with constant query complexity and sublinear running time. It remains open whether this can be improved to constant running time. In this paper we introduce a new model, which is based on the bounded degree model, but the distance measure allows both edge (tuple) modifications and vertex (element) modifications. Our main theorem shows that on databases of bounded degree and bounded tree-width, every property that is expressible in CMSO is testable with constant query complexity and constant running time in the new model. We also show that every property that is testable in the classical model is testable in our model with the same query complexity and running time, but the converse is not true. We argue that our model is natural and our meta-theorem showing constant-time CMSO testability supports this.
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。
