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.2018.10
URN: urn:nbn:de:0030-drops-86007
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8600/
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Brijder, Robert ; Geerts, Floris ; Van den Bussche, Jan ; Weerwag, Timmy

On the Expressive Power of Query Languages for Matrices

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Abstract

We investigate the expressive power of MATLANG, a formal language for matrix manipulation based on common matrix operations and linear algebra. The language can be extended with the operation inv of inverting a matrix. In MATLANG + inv we can compute the transitive closure of directed graphs, whereas we show that this is not possible without inversion. Indeed we show that the basic language can be simulated in the relational algebra with arithmetic operations, grouping, and summation. We also consider an operation eigen for diagonalizing a matrix, which is defined so that different eigenvectors returned for a same eigenvalue are orthogonal. We show that inv can be expressed in MATLANG + eigen. We put forward the open question whether there are boolean queries about matrices, or generic queries about graphs, expressible in MATLANG + eigen but not in MATLANG + inv. The evaluation problem for MATLANG + eigen is shown to be complete for the complexity class Exists R.

BibTeX - Entry

@InProceedings{brijder_et_al:LIPIcs:2018:8600,
  author =	{Robert Brijder and Floris Geerts and Jan Van den Bussche and Timmy Weerwag},
  title =	{{On the Expressive Power of Query Languages for Matrices}},
  booktitle =	{21st International Conference on Database Theory (ICDT 2018)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-063-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{98},
  editor =	{Benny Kimelfeld and Yael Amsterdamer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8600},
  URN =		{urn:nbn:de:0030-drops-86007},
  doi =		{10.4230/LIPIcs.ICDT.2018.10},
  annote =	{Keywords: matrix query languages, relational algebra with aggregates, query evaluation problem, graph queries}
}

Keywords: matrix query languages, relational algebra with aggregates, query evaluation problem, graph queries
Collection: 21st International Conference on Database Theory (ICDT 2018)
Issue Date: 2018
Date of publication: 05.03.2018

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