License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICDT.2020.6
URN: urn:nbn:de:0030-drops-119305
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11930/
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Barceló, Pablo ; Higuera, Nelson ; Pérez, Jorge ; Subercaseaux, Bernardo

On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra

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Abstract

We study the expressive power of the Lara language - a recently proposed unified model for expressing relational and linear algebra operations - both in terms of traditional database query languages and some analytic tasks often performed in machine learning pipelines. We start by showing Lara to be expressive complete with respect to first-order logic with aggregation. Since Lara is parameterized by a set of user-defined functions which allow to transform values in tables, the exact expressive power of the language depends on how these functions are defined. We distinguish two main cases depending on the level of genericity queries are enforced to satisfy. Under strong genericity assumptions the language cannot express matrix convolution, a very important operation in current machine learning operations. This language is also local, and thus cannot express operations such as matrix inverse that exhibit a recursive behavior. For expressing convolution, one can relax the genericity requirement by adding an underlying linear order on the domain. This, however, destroys locality and turns the expressive power of the language much more difficult to understand. In particular, although under complexity assumptions the resulting language can still not express matrix inverse, a proof of this fact without such assumptions seems challenging to obtain.

BibTeX - Entry

@InProceedings{barcel_et_al:LIPIcs:2020:11930,
  author =	{Pablo Barcel{\'o} and Nelson Higuera and Jorge P{\'e}rez and Bernardo Subercaseaux},
  title =	{{On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Carsten Lutz and Jean Christoph Jung},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11930},
  URN =		{urn:nbn:de:0030-drops-119305},
  doi =		{10.4230/LIPIcs.ICDT.2020.6},
  annote =	{Keywords: languages for linear and relational algebra, expressive power, first order logic with aggregation, matrix convolution, matrix inverse, query genericity, locality of queries, safety}
}

Keywords: languages for linear and relational algebra, expressive power, first order logic with aggregation, matrix convolution, matrix inverse, query genericity, locality of queries, safety
Collection: 23rd International Conference on Database Theory (ICDT 2020)
Issue Date: 2020
Date of publication: 11.03.2020
Supplementary Material: Video of the Presentation: https://doi.org/10.5446/46829

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