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A relational database is said to be uncertain if primary key constraints canpossibly be violated. A repair (or possible world) of an uncertain database isobtained by selecting a maximal number of tuples without ever selecting twodistinct tuples with the same primary key value. For any Boolean query q,CERTAINTY(q) is the problem that takes an uncertain database db on input, andasks whether q is true in every repair of db. The complexity of this problemhas been particularly studied for q ranging over the class of self-join-freeBoolean conjunctive queries. A research challenge is to determine, given q,whether CERTAINTY(q) belongs to complexity classes FO, P, or coNP-complete. Inthis paper, we combine existing techniques for studying the above complexityclassification task. We show that for any self-join-free Boolean conjunctivequery q, it can be decided whether or not CERTAINTY(q) is in FO. Further, forany self-join-free Boolean conjunctive query q, CERTAINTY(q) is either in P orcoNP-complete, and the complexity dichotomy is effective. This settles aresearch question that has been open for ten years, since [9].

A Trichotomy in the Data Complexity of Certain Query Answering for Conjunctive Queries