IterLara: A Concise General-Purpose Algebraic Model

Hongxiao Li, Wanling Gao, Lei Wang, Jianfeng Zhan

Abstract: In the realm of theoretical computer science, establishing a general-purpose model capable of representing various computations in fields such as big data, AI, scientific computing, and databases is of utmost importance. However, there is a need to balance this with the requirement for a concise model that utilizes minimal operators and simple combinations for each computation. To address these concerns, researchers introduced Lara, a key-value algebra that serves as a computational abstraction for both linear and relational algebras. However, previous studies have revealed limitations in Lara’s expressive capability, particularly in essential computations like matrix inversion and determinant. To overcome these limitations, we propose IterLara, an extension of Lara that incorporates iterative operators. We aim to provide a concise algebraic model that unifies operations in general-purpose computing. Through our research on the expressive ability of both Lara and IterLara, we demonstrate that IterLara, equipped with aggregation functions, not only enables the representation of matrix inversion and determinant but also encompasses significant computations in the fields of big data, artificial intelligence, scientific computing, and databases. Furthermore, we showcase the conciseness of IterLara in representing major big data and AI operations. Additionally, we prove that IterLara, without any limitations on function utility, possesses Turing completeness.