Expressive power of linear algebra query languages

by   Floris Geerts, et al.

Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that they allow looping for a number of steps that is bounded by the matrix dimension. In this paper we extend the matrix query language MATLANG with this type of recursion, and show that this suffices to express classical linear algebra algorithms. We study the expressive power of this language and show that it naturally corresponds to arithmetic circuit families, which are often said to capture linear algebra. Furthermore, we analyze several sub-fragments of our language, and show that their expressive power is closely tied to logical formalisms on semiring-annotated relations.


page 1

page 2

page 3

page 4


On the expressive power of query languages for matrices

We investigate the expressive power of MATLANG, a formal language for ma...

On the expressive power of linear algebra on graphs

Most graph query languages are rooted in logic. By contrast, in this pap...

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

We study the expressive power of the LARA language – a recently proposed...

On matrices and K-relations

We show that the matrix query language MATLANG corresponds to a natural ...

Comparing Downward Fragments of the Relational Calculus with Transitive Closure on Trees

Motivated by the continuing interest in the tree data model, we study th...

Graphical Piecewise-Linear Algebra

Graphical (Linear) Algebra is a family of diagrammatic languages allowin...

On the Relationship between Shy and Warded Datalog+/-

Datalog^E is the extension of Datalog with existential quantification. W...