IterLara：面向大数据、AI、科学计算与数据库的图灵完备代数
IterLara: A Turing Complete Algebra for Big Data, AI, Scientific Computing, and Database
AI总结：
本文提出扩展迭代算子的 IterLara 代数，以统一大数据、AI、科学计算与数据库操作，并证明其可表达矩阵求逆、行列式且图灵完备，同时提出 OP 计算量度量。
摘要：
Lara 是一种键值代数，旨在通过三类操作抽象统一线性代数与关系代数。关于 Lara 表达能力的研究表明，它能够表示关系代数以及大多数线性代数操作。然而，若干基本计算（例如矩阵求逆和行列式）无法在 Lara 中表达。Lara 也无法表示全局计算和迭代计算。本文提出 IterLara，通过为 Lara 扩展迭代算子，提供一种统一大数据、AI、科学计算和数据库等通用计算中各类操作的代数模型。我们研究了 Lara 与 IterLara 的表达能力，并证明带聚合函数的 IterLara 能够表示矩阵求逆和行列式。此外，我们证明在函数效用不受限制的情况下，IterLara 是图灵完备的。我们还提出 Operation Count（OP）作为 IterLara 计算量的度量，并确保 OP 度量与现有计算度量保持一致。
英文摘要：
\textsc{Lara} is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of \textsc{Lara}'s expressive ability reports that it can represent relational algebra and most linear algebra operations. However, several essential computations, such as matrix inversion and determinant, cannot be expressed in \textsc{Lara}. \textsc{Lara} cannot represent global and iterative computation, either. This article proposes \textsc{IterLara}, extending \textsc{Lara} with iterative operators, to provide an algebraic model that unifies operations in general-purpose computing, like big data, AI, scientific computing, and database. We study the expressive ability of \textsc{Lara} and \textsc{IterLara} and prove that \textsc{IterLara} with aggregation functions can represent matrix inversion, determinant. Besides, we demonstrate that \textsc{IterLara} with no limitation of function utility is Turing complete. We also propose the Operation Count (OP) as a metric of computation amount for \textsc{IterLara} and ensure that the OP metric is in accordance with the existing computation metrics.
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。
