# On the Expressive Power of Query Languages for Matrices

@article{Brijder2018OnTE, title={On the Expressive Power of Query Languages for Matrices}, author={Robert Brijder and Floris Geerts and Jan Van den Bussche and Timmy Weerwag}, journal={ACM Transactions on Database Systems (TODS)}, year={2018}, volume={44}, pages={1 - 31} }

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 for 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…

## 27 Citations

### MATLANG: Matrix operations and their expressive power

- Computer Science, MathematicsSGMD
- 2019

The expressive power of MATLANG, a formal language for matrix manipulation based on common matrix operations and linear algebra, is investigated and it is shown that the basic language can be simulated in the relational algebra with arithmetic operations, grouping, and summation.

### On the Expressive Power of Linear Algebra on Graphs

- Mathematics, Computer ScienceTheory of Computing Systems
- 2020

This paper considers MATLANG, a matrix query language recently introduced, in which some basic linear algebra functionality is supported, and investigates the problem of characterising the equivalence of graphs, represented by their adjacency matrices, for various fragments ofMATLANG.

### On the Expressive Power of Linear Algebra on Graphs

- Mathematics, Computer ScienceICDT
- 2019

This paper considers M A T L A N G, a matrix query language recently introduced, in which some basic linear algebra functionality is supported, and investigates the problem of characterising the equivalence of graphs, represented by their adjacency matrices, for various fragments of M AT L AN G.

### When Can Matrix Query Languages Discern Matrices?

- Computer Science, MathematicsICDT
- 2020

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…

### Expressive Power of Linear Algebra Query Languages

- Computer SciencePODS
- 2021

The matrix query language MATLANG is extended with this type of recursion, and it is shown that this suffices to express classical linear algebra algorithms.

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

- Computer ScienceICDT
- 2020

This work shows LARA to be expressive complete with respect to first-order logic with aggregation, and distinguishes two main cases depending on the level of genericity queries are enforced to satisfy.

### On matrices and K-relations

- MathematicsFoIKS
- 2020

The matrix query language can express all matrix queries expressible in the positive relational algebra on $K-relations, when intermediate arities are restricted to three, and is offered an analogue to the situation in classical logic, where the algebra of binary relations is equivalent to first-order logic with three variables.

### Functional collection programming with semi-ring dictionaries

- Computer ScienceProc. ACM Program. Lang.
- 2022

SDQL is developed, a statically typed language that can express relational algebra with aggregations, linear algebra, and functional collections over data such as relations and matrices using semi-ring dictionaries, and unifies a wide range of optimizations commonly used in databases (DB) and linear algebra (LA).

### Expressiveness of Matrix and Tensor Query Languages in terms of ML Operators

- Computer ScienceDEEM@SIGMOD
- 2019

This short paper studies a matrix and a tensor query language that have been recently proposed in the database literature and shows, by using examples, how these proposals are in line with the practical interest in rethinking tensor abstractions.

### Recursive SPARQL for Graph Analytics

- Computer ScienceArXiv
- 2020

A minimalistic extension of SPARQL to allow for expressing analytical tasks is proposed, and it is shown that this language can express key analytical tasks on graphs, offering a more declarative alternative to existing frameworks and languages.

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