MongoDB（扩展版）的表达性和复杂性
Expressivity and Complexity of MongoDB (Extended Version)
摘要：
在过去的十年中，已经提出了大量新颖的数据库体系结构和数据模型。虽然这些新系统中的一些已经流行起来，但它们缺乏适当的形式化，以及对相关查询语言的表达性和计算特性的精确理解。在本文中，我们的目标是填补这一空白，我们这样做，考虑MongoDB，一个广泛采用的文档数据库管理复杂的（树结构）值表示在基于JSON的数据模型，配备了强大的查询机制。我们提供了MongoDB数据模型的形式化，以及MongoDB查询语言的核心片段MQuery。我们研究了MQuery的表达能力，证明了它与嵌套关系代数的等价性。我们进一步研究了它的重要片段的计算复杂性，获得了几个（紧）结合复杂性的界限，其范围从LOGSPACE交替指数时间与多项式数量的交替。因此，我们也得到了嵌套关系代数查询评价的组合复杂性的表征。
英文摘要：
A significant number of novel database architectures and data models have been proposed during the last decade. While some of these new systems have gained in popularity, they lack a proper formalization, and a precise understanding of the expressivity and the computational properties of the associated query languages. In this paper, we aim at filling this gap, and we do so by considering MongoDB, a widely adopted document database managing complex (tree structured) values represented in a JSON-based data model, equipped with a powerful query mechanism. We provide a formalization of the MongoDB data model, and of a core fragment, called MQuery, of the MongoDB query language. We study the expressivity of MQuery, showing its equivalence with nested relational algebra. We further investigate the computational complexity of significant fragments of it, obtaining several (tight) bounds in combined complexity, which range from LOGSPACE to alternating exponential-time with a polynomial number of alternations. As a consequence, we obtain also a characterization of the combined complexity of nested relational algebra query evaluation.
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。
