发表机构
University of Bamberg; Leipzig University; ScaDS.AI Center Dresden/Leipzig; LIRMM; Inria; University of Montpellier; CNRS; University of Warsaw（班贝格大学; 莱比锡大学; 德累斯顿/莱比锡可扩展数据分析与人工智能中心; 法国朗格多克信息、机器人与微电子实验室; 法国国家信息与自动化研究所; 蒙彼利埃大学; 法国国家科学研究中心; 华沙大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文首次研究递归查询语言的属性测试，证明2RPQ及一类线性递归、α-无环规则体的单元Datalog的非答案可常数查询单侧错误测试，同时给出无自连接规则体下非α-无环单元Datalog的不可测性结果。
AI 中文摘要
在数据库查询的语境下，属性测试提供了一个框架，可通过完成查询和大小查询，在仅检查数据库的亚线性部分的情况下高置信度地测试查询结果。Chen和Yoshida（2019）的一项基础结果表明：布尔合取查询$q$的不满足性可通过常数数量的此类查询以单侧错误进行测试，当且仅当$q$等价于一个$α$-无环查询。本文中，我们首次开展递归查询语言的属性测试研究，聚焦于双向正则路径查询（2RPQ）和单元Datalog。我们的主要结果之一是正向的：任意2RPQ的非答案都可通过常数次查询以单侧错误测试。我们将这一结果略微扩展到一类单元Datalog程序，这类程序的递归被限制为线性的，且规则体必须是$α$-无环的。转向无限制的单元Datalog，我们接下来证明：若一个单元Datalog程序$Π$不等价于$α$-无环程序，则$Π$的假性无法通过常数次查询以单侧错误测试，该结论基于所有规则体均无自连接的假设。我们暂未解决具有$α$-无环规则体且不受线性递归限制的单元Datalog程序的情况，但作为第一步观察到：存在轻度非线性的$α$-无环程序，可通过常数次查询以单侧错误测试。
英文摘要
In the context of database querying, property testing provides a framework for testing query answers with high confidence while inspecting only a sublinear part of the database, through completion queries and size queries. A fundamental result of Chen and Yoshida (2019) states that non-satisfaction of a Boolean conjunctive query $q$ is testable with a constant number of such queries and one-sided error if and only if $q$ is equivalent to an $α$-acyclic query. In this article, we initiate the study of property testing for recursive query languages, focusing on two-way regular path queries (2RPQs) and monadic Datalog. One of our main results is positive: non-answers to any 2RPQ are constant query testable with one-sided error. We extend this slightly to a certain class of monadic Datalog programs in which recursion is restricted to be linear and rule bodies must be $α$-acyclic. Turning towards unrestricted monadic Datalog, we next show that if a monadic Datalog program $Π$ is not equivalent to an $α$-acyclic program, then falsity of $Π$ is not constant query testable with one-sided error. This is under the assumption that all rule-bodies are self-join free. We leave open the case of monadic Datalog programs with $α$-acyclic rule bodies that are not restricted to linear recursion, but observe as a first step that there exist $α$-acyclic programs that are mildly non-linear and constant query testable with one-sided error.
DOI：10.1145/3850131
