简洁数据表示的统一视角
A Unifying Perspective on Succinct Data Representations
AI总结：
本文从未命名数据库视角定义因子分解表示，揭示其与命名表示、等长语言上下文无关文法及路径多重集表示的联系，统一了多种简洁数据表示。
摘要：
因子分解表示（FRs）是一种用于简洁表示连接查询结果的著名工具，最初是使用命名数据库视角定义的。我们在未命名数据库视角下定义 FRs，并用它们建立若干新联系。首先，未命名 FRs 可能比命名 FRs 简洁指数倍，但通过对列施加不相交条件，可以缓解这种差异。反过来，命名 FRs 也可能比未命名 FRs 简洁指数倍。其次，对于每个单词都具有相同长度的语言，未命名 FRs 与其上下文无关文法相同（即同构）。这种紧密联系使我们能够将关于上下文无关文法的大量结论迁移到数据库因子分解；我们在论文中给出了其中一部分。第三，当我们将未命名 FRs 推广到任意元组集合时，它们成为 path multiset representations（路径多重集表示）的推广；后者是最近引入的一种形式体系，用于在图数据库查询评估场景中简洁表示路径集合。
英文摘要：
Factorized representations (FRs) are a well-known tool to succinctly represent results of join queries and have been originally defined using the named database perspective. We define FRs in the unnamed database perspective and use them to establish several new connections. First, unnamed FRs can be exponentially more succinct than named FRs, but this difference can be alleviated by imposing a disjointness condition on columns. Conversely, named FRs can also be exponentially more succinct than unnamed FRs. Second, unnamed FRs are the same as (i.e., isomorphic to) context-free grammars for languages in which each word has the same length. This tight connection allows us to transfer a wide range of results on context-free grammars to database factorization; of which we offer a selection in the paper. Third, when we generalize unnamed FRs to arbitrary sets of tuples, they become a generalization of \emph{path multiset representations}, a formalism that was recently introduced to succinctly represent sets of paths in the context of graph database 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。
