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

Abstract

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.