集函数增广的嵌套关系演算的内蕴表达能力的二分法和幂集算子

L. Wong
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引用次数: 3

摘要

表现力的外延方面——即。查询可以或不可以表达什么——一直是许多查询语言研究的主题。矛盾的是,尽管效率是计算机科学主要关注的问题,但表达能力的内涵方面——即:什么查询可以有效地实现,什么查询不能有效地实现——在很大程度上被忽视了。本文讨论了NRC(Q, +,·,@,÷, Σ, powerset)的内涵表达能力,NRC(Q, +,·,@,÷, Σ, powerset)是一个嵌套关系演算,它具有聚集函数和幂集运算。我们证明了对长链、深树等结构的查询具有二分类行为:要么它们在微积分中已经可以不使用幂集运算表示,要么它们至少需要指数空间。这一结果以三种重要的方式推广了几个古老的类二分类结果,如Suciu和Paredaens关于Abiteboul和Beeri的复对象代数需要指数空间来实现长链的传递闭包的结论。首先,这里考虑一种更具表现力的查询语言——特别是捕获SQL的语言。其次,这里考虑的是对比长链更一般的结构类的查询。最后,我们的证明是更一般的,适用于所有的查询语言表现出一定的范式和具有局部性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A dichotomy in the intensional expressive power of nested relational calculi augmented with aggregate functions and a powerset operator
The extensional aspect of expressive power---i.e., what queries can or cannot be expressed---has been the subject of many studies of query languages. Paradoxically, although efficiency is of primary concern in computer science, the intensional aspect of expressive power---i.e., what queries can or cannot be implemented efficiently---has been much neglected. Here, we discuss the intensional expressive power of NRC(Q, +, ·, ‏, ÷, Σ, powerset), a nested relational calculus augmented with aggregate functions and a powerset operation. We show that queries on structures such as long chains, deep trees, etc. have a dichotomous behaviour: Either they are already expressible in the calculus without using the powerset operation or they require at least exponential space. This result generalizes in three significant ways several old dichotomy-like results, such as that of Suciu and Paredaens that the complex object algebra of Abiteboul and Beeri needs exponential space to implement the transitive closure of a long chain. Firstly, a more expressive query language---in particular, one that captures SQL---is considered here. Secondly, queries on a more general class of structures than a long chain are considered here. Lastly, our proof is more general and holds for all query languages exhibiting a certain normal form and possessing a locality property.
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CiteScore
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