Query Containment of Tier-2 Queries over a Probabilistic Database

We study the containment problem for a query language over probabilistic relational databases that allows queries like "is the probabil- ity that q1 holds greater than 0.2 and the probability that q2 holds greater than 0.6?" where q1 and q2 are Boolean conjunctive queries. In addition to being a fundamental problem in its own right, the containment prob- lem is the key problem that an optimizer must solve for many standard optimizations (such as picking up an index or using a materialized view). Our main technical result is that the containment problem is decidable, and we give an EXPSPACE-algorithm based on linear programming for it. We believe that we are the first to study the containment problem for any such probabilistic languages.