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Bag Containment of Join-On-Free Queries

Authors George Konstantinidis , Fabio Mogavero

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Author Details

George Konstantinidis
  • University of Southampton, UK
Fabio Mogavero
  • Università degli Studi di Napoli Federico II, Italy

Funding

G. Konstantinidis was partially funded by the Horizon Europe projects DATAPACT (No. 101189771), RAISE (No. 101058479) and UPCAST (No. 101093216). F. Mogavero is member of the Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica (GNCS-INdAM) and acknowledges a partial support by GNCS 2024 project "Certificazione, Monitoraggio, ed Interpretabilità in Sistemi di Intelligenza Artificiale".

Acknowledgements

We would like to thank the anonymous reviewers for their insightful comments (e.g., regarding the connection with the Möbius inversion formula) that considerably improved the paper.

Cite As Get BibTex

George Konstantinidis and Fabio Mogavero. Bag Containment of Join-On-Free Queries. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICDT.2025.5

Abstract

Bag-semantics allows for atomic relations and query answers to contain multiple copies of the same data tuple, reflecting real-world database systems more accurately. Deciding containment under bag-semantics (or simply, bag-containment) for two conjunctive queries (CQs) requires determining whether the answer of the first query, taking multiplicities into account, is contained within the answer of the second query, across all databases. Despite numerous attempts in the last thirty years, this problem of determining decidability and complexity of this task remains open as one of the prominent challenges in database theory, given its relevance in important applications.
Previous works have established the decidability of the problem for specific classes of queries, among which is the the bag-containment of projection-free queries (PFQs), i.e., queries without existentially quantified variables, into general CQs. In this work, we push the boundaries further by addressing a broader, yet natural, fragment of CQs, called join-on-free queries (JoFQ), which allows existential variables, while prohibiting joins involving them. We prove decidability of bag-containment of a JoFQ within a general CQ, placing the complexity of the problem in the first non-deterministic layer of the exponential hierarchy. The approach involves a homomorphism-counting reduction to the solution of a system of Diophantine inequalities with a specific structure (an undecidable problem in its general form) and an algorithm designed to address this category of inequalities.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database query languages (principles)
  • Theory of computation → Database query processing and optimization (theory)
  • Theory of computation → Logic and databases
  • Mathematics of computing → Combinatorics
Keywords
  • Query Containment
  • Bag Semantics
  • Bag Containment
  • Diophantine Problems

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