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When Can Matrix Query Languages Discern Matrices?

Author Floris Geerts



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Floris Geerts
  • University of Antwerp, Belgium

Acknowledgements

I want to thank Lieven Le Bruyn for inspiring discussions and for pointing me to the connections to linear control theory.

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Floris Geerts. When Can Matrix Query Languages Discern Matrices?. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 12:1-12:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ICDT.2020.12

Abstract

We investigate when two graphs, represented by their adjacency matrices, can be distinguished by means of sentences formed in MATLANG, a matrix query language which supports a number of elementary linear algebra operators. When undirected graphs are concerned, and hence the adjacency matrices are real and symmetric, precise characterisations are in place when two graphs (i.e., their adjacency matrices) can be distinguished. Turning to directed graphs, one has to deal with asymmetric adjacency matrices. This complicates matters. Indeed, it requires to understand the more general problem of when two arbitrary matrices can be distinguished in MATLANG. We provide characterisations of the distinguishing power of MATLANG on real and complex matrices, and on adjacency matrices of directed graphs in particular. The proof techniques are a combination of insights from the symmetric matrix case and results from linear algebra and linear control theory.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database query languages (principles)
  • Mathematics of computing → Graph theory
Keywords
  • matrix query languages
  • linear algebra
  • expressive power

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