Consistent Query Answering for Self-Join-Free Conjunctive Queries Under Primary Key Constraints

A relational database is said to be uncertain if primary key constraints can possibly be violated. A repair (or possible world) of an uncertain database is obtained by selecting a maximal number of tuples without ever selecting two distinct tuples with the same primary key value. For any Boolean query q, CERTAINTY(q) is the problem that takes an uncertain database db as input and asks whether q is true in every repair of db. The complexity of this problem has been particularly studied for q ranging over the class of self-join-free Boolean conjunctive queries. A research challenge is to determine, given q, whether CERTAINTY(q) belongs to complexity classes FO, P, or coNP-complete. In this article, we combine existing techniques for studying this complexity classification task. We show that, for any self-join-free Boolean conjunctive query q, it can be decided whether or not CERTAINTY(q) is in FO. We additionally show how to construct a single SQL query for solving CERTAINTY(q) if it is in FO. Further, for any self-join-free Boolean conjunctive query q, CERTAINTY(q) is either in P or coNP-complete and the complexity dichotomy is effective. This settles a research question that has been open for 10 years.