Expressive Power of Linear Algebra Query Languages
Summary: Extend MATLANG with dimension-bounded recursion (loops up to matrix size) to express classical linear-algebra algorithms such as Gaussian elimination and matrix inversion. Characterize expressiveness as arithmetic-circuit families; subfragments correspond to logics on semiring-annotated relations. (summarized by gpt-5-mini on Feb 09 2026)
Incoming Non-self Citations Over Time
Authors
- 1. Floris Geerts (University of Antwerp)
- 2. Thomas Muñoz (Millennium Institute for Foundational Research on Data (Chile); Pontifical Catholic University of Chile)
- 3. Cristian Riveros (Millennium Institute for Foundational Research on Data (Chile); Pontifical Catholic University of Chile)
- 4. Domagoj Vrgoč (Millennium Institute for Foundational Research on Data (Chile); Pontifical Catholic University of Chile)
BibTeX Citation
@inproceedings{geerts_pods21,
address = {New York, NY, USA},
series = {{PODS} '21},
title = {{Expressive Power of Linear Algebra Query Languages}},
url = {https://dl.acm.org/doi/10.1145/3452021.3458314},
doi = {10.1145/3452021.3458314},
booktitle = {Proceedings of the {ACM} {SIGMOD} Symposium on {Principles} of {Database} {Systems}},
publisher = {Association for Computing Machinery},
author = {Geerts, Floris and Muñoz, Thomas and Riveros, Cristian and Vrgoč, Domagoj},
year = {2021}
}Incoming Citations (Sorted by Pagerank)
Showing 4 of 4 citing papers.
| Rank | Citing Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 5,893 | A Query Language Perspective on Graph Learning | 2023 | PODS | 6.0486927e-05 |
| 10,166 | Recursive Querying of Neural Networks via Weighted Structures | 2026 | PODS | 5.093636e-05 |
| 11,208 | Automating Vectorized Distributed Graph Computation | 2024 | SIGMOD | 5.093636e-05 |
| 11,561 | Givens QR Decomposition over Relational Databases | 2022 | SIGMOD | 5.093636e-05 |
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Outgoing Citations (Sorted by Pagerank)
Showing 1 of 1 cited papers.
Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.
| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 17 | Provenance Semirings | 2007 | PODS | 0.00059843817 |
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Semantically Similar Papers
| # | Overall Rank | Paper | Year | Venue |
|---|---|---|---|---|
| 1 | 13,040 | Investigation of Algebraic Query Optimisation for Database Programming Languages | 1994 | VLDB |
| 2 | 4,467 | A Query Language for List-Based Complex Objects | 1994 | PODS |
| 3 | 7,849 | New Techniques for Studying Set Languages, Bag Languages and Aggregate Functions | 1994 | PODS |
| 4 | 1,890 | Relational Expressive Power of Constraint Query Languages | 1996 | PODS |
| 5 | 1,864 | The Expressiveness of a Family of Finite Set Languages | 1991 | PODS |
| 6 | 2,076 | A Study of Transitive Closure As a Recursion Mechanism | 1987 | SIGMOD |
| 7 | 6,563 | Functional Database Query Languages as Typed Lambda Calculi of Fixed Order (Extended Abstract) | 1994 | PODS |
| 8 | 312 | A Graphical Query Language Supporting Recursion | 1987 | SIGMOD |
| 9 | 2,111 | Querying Constraints | 1990 | PODS |
| 10 | 7,260 | On the Power of Algebras with Recursion | 1993 | SIGMOD |