A dichotomy in the complexity of counting database repairs

An uncertain database db is defined as a database in which distinct tuples of the same relation can agree on their primary key. A repair is obtained by selecting a maximal number of tuples without ever selecting two distinct tuples of the same relation that agree on their primary key. Obviously, the number of possible repairs can be exponential in the size of the database. Given a Boolean query q, certain (or consistent) query answering concerns the problem to decide whether q evaluates to true on every repair. In this article, we study a counting variant of consistent query answering. For a fixed Boolean query q, we define ♮CERTAINTY(q) as the following counting problem: Given an uncertain database db, how many repairs of db satisfy q? Our main result is that conjunctive queries q without self-join exhibit a complexity dichotomy: ♮CERTAINTY(q) is in FP or ♮P-complete. ► Studies consistent query answering for CQs over inconsistent databases under keys. ► Studies a counting version of the problem: How many repairs satisfy the query? ► Proves a dichotomy for CQs without self-join: They are either tractable or ♮P-complete.