The query containment problem is a fundamental algorithmic problem in data management. While this problem is well understood under set semantics, it is by far less understood under bag semantics. In particular, it is a long-standing open question whether or not the conjunctive query containment problem under bag semantics is decidable. We unveil tight connections between information theory and the conjunctive query containment under bag semantics. These connections are established using information inequalities, which are considered to be the laws of information theory. Our first main result asserts that deciding the validity of maxima of information inequalities is many-one equivalent to the restricted case of conjunctive query containment in which the containing query is acyclic; thus, either both these problems are decidable or both are undecidable. Our second main result identifies a new decidable case of the conjunctive query containment problem under bag semantics. Specifically, we give an exponential time algorithm for conjunctive query containment under bag semantics, provided the containing query is chordal and admits a simple junction tree.

中文翻译：

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Bag Query Containment与信息论

查询包含问题是数据管理中的一个基本算法问题。虽然这个问题在集合语义下很好理解，但在包语义下却鲜为人知。特别是，袋语义下的联合查询包含问题是否可判定是一个长期悬而未决的问题。我们揭示了信息理论与包语义下的联合查询包含之间的紧密联系。这些联系是使用信息不等式建立的，这被认为是信息论的定律。我们的第一个主要结果断言，决定信息不等式最大值的有效性是多对等的，相当于连接查询包含的受限情况，其中包含查询是非循环的；因此，这两个问题要么都是可判定的，要么都是不可判定的。我们的第二个主要结果确定了袋语义下连接查询包含问题的一个新的可判定案例。具体来说，我们给出了袋语义下的联合查询包含的指数时间算法，前提是包含查询是和弦的并且允许一个简单的连接树。