IterLara: A Turing Complete Algebra for Big Data, AI, Scientific Computing, and Database
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Abstract (arXiv)
textscLara is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of textscLara'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 textscLara. textscLara cannot represent global and iterative computation, either. This article proposes textscIterLara, extending textscLara 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 textscLara and textscIterLara and prove that textscIterLara with aggregation functions can represent matrix inversion, determinant. Besides, we demonstrate that textscIterLara with no limitation of function utility is Turing complete. We also propose the Operation Count (OP) as a metric of computation amount for textscIterLara and ensure that the OP metric is in accordance with the existing computation metrics.
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References · 6
- 2020Pooling Methods in Deep Neural Networks, a Reviewcited by 52
- 2017LaraDB: A Minimalist Kernel for Linear and Relational Algebra Computationcited by 5
- 2020Expressive power of linear algebra query languagescited by 4
- 2016Lara: A Key-Value Algebra underlying Arrays and Relationscited by 1
- 2016Associative Array Model of SQL, NoSQL, and NewSQL Databasescited by 1
- 2019On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebracited by 1
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