We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In Koutris and Wijsen (ACM Trans. Database Syst. 42(2), 9:1–9:45, 2017), the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this article, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog (with some aggregation operator) or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition.

我们研究了可能违反主键约束的数据库上一致查询应答的复杂性。这种数据库的修复是可以通过删除最小的元组来获得的任何一致的数据库。对于每一个布尔查询q，Ç È ř Ť甲我Ñ Ť ý（q）是采用一个数据库作为输入，并询问是否该问题q在每次维修评估为真。在Koutris和Wijsen（ACM跨数据库SYST。42（2），9：1-9：45，2017年）中，作者表明，对于每一个自联接-自由布尔联合查询q，问题Ç È ř Ť甲我Ñ Ť ý（ q）是无论是在P或Ç ö Ñ P -complete，并且它是可判定的，其中这两种情况下适用。在本文中，我们通过显示对于每个无自连接布尔布尔联合查询q来精化此结果，问题C E R T A I N T Y（ q）可以在对称分层数据日志中表达（带有一些聚合运算符）或C o N P-完成。由于对称分层数据记录在L中我们因此得到之间的复杂性理论二分法大号和Ç ö Ñ P -complete。另一个具有实际意义的新发现是C E R T A I N T Y（q）位于查询q二分法的对数空间一侧，其中所有联接条件都表示外键与主键匹配，这无疑是最常见的连接条件的类型。