Bag Semantics Query Containment: The CQ vs. UCQ Case and Other Stories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910979394109440 |
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| author | Marcinkowski, Jerzy Ostropolski-Nalewaja, Piotr |
| author_facet | Marcinkowski, Jerzy Ostropolski-Nalewaja, Piotr |
| contents | Query Containment Problem (QCP) is a fundamental decision problem in query processing and optimization. While QCP has for a long time been completely understood for the case of set semantics, decidability of QCP for conjunctive queries under multi-set semantics ($QCP_{\text{CQ}}^{\text{bag}}$) remains one of the most intriguing open problems in database theory. Certain effort has been put, in last 30 years, to solve this problem and some decidable special cases of $QCP_{\text{CQ}}^{\text{bag}}$ were identified, as well as some undecidable extensions, including $QCP_{\text{UCQ}}^{\text{bag}}$. In this paper we introduce a new technique which produces, for a given UCQ $Φ$, a CQ $ϕ$ such that the application of $ϕ$ to a database $D$ is, in some sense, an approximation of the application of $Φ$ to $D$. Using this technique we could analyze the status of $QCP^{\text{bag}}$ when one of the queries in question is a CQ and the other is a UCQ, and we reached conclusions which surprised us a little bit. We also tried to use this technique to translate the known undecidability proof for $QCP_{\text{UCQ}}^{\text{bag}}$ into a proof of undecidability of $QCP_{\text{CQ}}^{\text{bag}}$. And, as you are going to see, we got stopped just one infinitely small $\varepsilon$ before reaching this ultimate goal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07219 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bag Semantics Query Containment: The CQ vs. UCQ Case and Other Stories Marcinkowski, Jerzy Ostropolski-Nalewaja, Piotr Databases Query Containment Problem (QCP) is a fundamental decision problem in query processing and optimization. While QCP has for a long time been completely understood for the case of set semantics, decidability of QCP for conjunctive queries under multi-set semantics ($QCP_{\text{CQ}}^{\text{bag}}$) remains one of the most intriguing open problems in database theory. Certain effort has been put, in last 30 years, to solve this problem and some decidable special cases of $QCP_{\text{CQ}}^{\text{bag}}$ were identified, as well as some undecidable extensions, including $QCP_{\text{UCQ}}^{\text{bag}}$. In this paper we introduce a new technique which produces, for a given UCQ $Φ$, a CQ $ϕ$ such that the application of $ϕ$ to a database $D$ is, in some sense, an approximation of the application of $Φ$ to $D$. Using this technique we could analyze the status of $QCP^{\text{bag}}$ when one of the queries in question is a CQ and the other is a UCQ, and we reached conclusions which surprised us a little bit. We also tried to use this technique to translate the known undecidability proof for $QCP_{\text{UCQ}}^{\text{bag}}$ into a proof of undecidability of $QCP_{\text{CQ}}^{\text{bag}}$. And, as you are going to see, we got stopped just one infinitely small $\varepsilon$ before reaching this ultimate goal. |
| title | Bag Semantics Query Containment: The CQ vs. UCQ Case and Other Stories |
| topic | Databases |
| url | https://arxiv.org/abs/2503.07219 |