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

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 on 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 paper, we combine existing techniques for studying the above 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. 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 ten years, since [9]

Consistent Answers of Conjunctive Queries on Graphs

During the past decade, there has been an extensive investigation of the computational complexity of the consistent answers of Boolean conjunctive queries under primary key constraints. Much of this investigation has focused on self-join-free Boolean conjunctive queries. In this paper, we study the consistent answers of Boolean conjunctive queries involving a single binary relation, i.e., we consider arbitrary Boolean conjunctive queries on directed graphs. In the presence of a single key constraint, we show that for each such Boolean conjunctive query, either the problem of computing its consistent answers is expressible in first-order logic, or it is polynomial-time solvable, but not expressible in first-order logic