有序结构中的推土机回弹与试验
Earthmover Resilience and Testing in Ordered Structures
摘要：
属性测试中的主要挑战之一是表征那些可以用恒定数量的查询来测试的属性。对于无序结构，如图和超图，这个任务已经基本解决。然而，对于有序结构，如字符串，图像和有序图，一般的特征化问题似乎非常困难。在本文中，我们确定了一个广泛的有序结构的属性-推土机弹性（ER）的属性-并表明，“良好的行为”，这样的属性，使我们能够获得一般的可测性结果是类似的（和更一般的）无序图。如果粗略地说，满足P的对象中元素顺序的微小变化不能使该对象远离P，则属性P是ER。ER属性的类别包括，例如，所有无序图的性质，图像的许多自然视觉性质，如凸性，以及有序图和图像的所有遗传性质。一个特殊的情况下，我们的结果意味着，建立在最近的结果阿隆和作者，一个给定的图像或有序图的距离从任何遗传属性可以估计（具有良好的概率），以一个常数的附加误差，使用一个常数的查询。
英文摘要：
One of the main challenges in property testing is to characterize those properties that are testable with a constant number of queries. For unordered structures such as graphs and hypergraphs this task has been mostly settled. However, for ordered structures such as strings, images, and ordered graphs, the characterization problem seems very difficult in general. In this paper, we identify a wide class of properties of ordered structures - the earthmover resilient (ER) properties - and show that the "good behavior" of such properties allows us to obtain general testability results that are similar to (and more general than) those of unordered graphs. A property P is ER if, roughly speaking, slight changes in the order of the elements in an object satisfying P cannot make this object far from P. The class of ER properties includes, e.g., all unordered graph properties, many natural visual properties of images, such as convexity, and all hereditary properties of ordered graphs and images. A special case of our results implies, building on a recent result of Alon and the authors, that the distance of a given image or ordered graph from any hereditary property can be estimated (with good probability) up to a constant additive error, using a constant number of queries.
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