The Complexity of Evaluation Relational Queries

Abstract

We show that, given a relation R, a relational query ? Involving only projection and join, and a conjectured result r, resting with ?(R)=r is D^p complete. Bounding the size of ?(R) from below (above) is NP-hard (co-NP-hard), and bounding it both ways is D^p hard. Computing the size of ?(R) is #P-hard. We also show that, given two relations R1 and R2 and two queries ?1 and ?2 as above, testing whether ?1)R1)⊆?2(R2) and testing whether ?1(R1)=?2(R2) and both ∏p2-complete, even when R1-R2 or when ?1=?2.