发表机构
University of Southampton（南安普顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本工作为合取查询的包包含问题提出统一框架，涵盖并扩展了已知可判定情形，通过将包含归约为受控丢番图问题，证明连接一致查询类的包包含可判定。
AI 中文摘要
查询包含是数据库理论中的一个基本决策问题：给定两个查询，确定在所有数据库实例上，第一个查询产生的每个答案是否也由第二个查询产生。对于集合语义下的合取查询，该问题通过经典的基于同态的刻画来理解。在包语义下（即真实关系数据库所依据的解释），包含变成了答案多重性的定量比较。尽管经过数十年的研究，合取查询的包包含的可判定性仍然悬而未决。这一前沿是脆弱的：对于稍微更具表达力的类，包包含是不可判定的，负面结果依赖于希尔伯特第十问题变体的归约。本工作为合取查询的包包含开发了一个统一框架，该框架涵盖了先前研究的两个可判定情形：包含查询无投影和无连接。该框架为更广泛的类（称为连接一致查询）带来了可判定性，同时允许包含查询是任意的。这与对包含查询施加限制的技术形成对比。该方法基于其多重性必须受限的查询的内部统一结构来识别可处理类。具体来说，它将包含归约到一个受控的丢番图问题。从被包含查询出发，构建一个由其所有可能的统一生成的规范模型，在该模型上多重性具有有限的算术刻画。包含被证明等价于相应的丢番图不等式系统无解。尽管这些问题一般不可判定，但我们表明由连接一致包含产生的系统构成一个可判定的子类。因此，包包含不可判定性的标准来源成为决策过程的核心。
英文摘要
Query containment is a fundamental decision problem in database theory: given two queries, determine whether, over all database instances, every answer produced by the first is also produced by the second. For conjunctive queries under set semantics, the problem is understood through the classical homomorphism-based characterisation. Under bag semantics, the interpretation underlying real relational databases, containment becomes a quantitative comparison of answer multiplicities. Despite decades of work, the decidability of bag containment for conjunctive queries remains open. This frontier is fragile: for slightly more expressive classes, bag containment is undecidable, with negative results relying on reductions from variants of Hilbert's 10th problem. This work develops a unified framework for bag containment of conjunctive queries that subsumes two previously studied decidable cases: projection-free and join-on-free containee queries. The framework yields decidability for a broader class, called join-uniform queries, while leaving the containing query arbitrary. This contrasts with techniques that impose restrictions on the containing query. The approach identifies tractable classes based on the internal unification structure of the query whose multiplicities must be bounded. Specifically, it reduces containment to a controlled Diophantine problem. Starting from the containee query, one builds a canonical model generated by all its possible unifications, over which multiplicities admit a finite arithmetic characterisation. Containment is proved equivalent to the non-existence of solutions of a corresponding Diophantine inequality system. Although these problems are undecidable in general, we show that the systems arising from join-uniform containment form a decidable subclass. Thus, the standard source of undecidability for bag containment becomes the core of the decision procedure.
