LIPIcs.ICDT.2025.3.pdf
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Evaluating First-Order Formulas in Structured Graphs (Invited Talk)
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Szymon Toruńczyk 
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28th International Conference on Database Theory (ICDT 2025)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Database Theory (ICDT) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2025-03-21
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Szymon Toruńczyk. Evaluating First-Order Formulas in Structured Graphs (Invited Talk). In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 3:1-3:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
https://doi.org/10.4230/LIPIcs.ICDT.2025.3
Abstract
A central problem in database theory concerns the complexity of the query evaluation problem, also called the model-checking problem in finite model theory: the problem of evaluating a given formula in a given structure. Here, I will focus on formulas of first-order logic, and the data complexity (or parameterized complexity) of their evaluation. Leveraging tools from structural graph theory, I will assume that the input structure is a graph which comes from a fixed class of well-structured graphs, such as the class of planar graphs, classes of bounded treewidth or clique-width, or much more general "tame" graph classes, such as the nowhere dense graph classes introduced by Ossona de Mendez and Nešetřil, or classes of bounded twin-width studied by Bonnet, Thomassé, and coauthors. I will survey the recent progress in this area, which connects tools from structural graph theory, from model theory - such as stability and dependence - and from statistical learning theory and computational geometry - such as VC-dimension and ε-nets.
Subject Classification
ACM Subject Classification
- Theory of computation → Finite Model Theory
- Mathematics of computing → Graph theory
Keywords
- Finite model theory
- first-order model checking
- graph parameters
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References
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- Jan Dreier, Ioannis Eleftheriadis, Nikolas Mählmann, Rose McCarty, Michał Pilipczuk, and Szymon Toruńczyk. First-order model checking on monadically stable graph classes. In 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024, Chicago, IL, USA, October 27-30, 2024. IEEE, 2024. URL: https://doi.org/10.1109/FOCS61266.2024.00012.
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