eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-03-11
12:1
12:18
10.4230/LIPIcs.ICDT.2020.12
article
When Can Matrix Query Languages Discern Matrices?
Geerts, Floris
1
University of Antwerp, Belgium
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol155-icdt2020/LIPIcs.ICDT.2020.12/LIPIcs.ICDT.2020.12.pdf
matrix query languages
linear algebra
expressive power