Circuits for Datalog Provenance.

The annotation of the results of database queries with provenance information has many applications. This paper studies provenance for datalog queries. We start by considering provenance representation by (positive) Boolean expressions, as pioneered in the theories of incomplete and probabilistic databases. We show that even for linear datalog programs the representation of provenance using Boolean expressions incurs a super-polynomial size blowup in data complexity. We address this with an approach that is novel in provenance studies, showing that we can construct in PTIME poly-size (data complexity) provenance representations as Boolean circuits. Then we present optimization techniques that embed the construction of circuits into seminaive datalog evaluation, and further reduce the size of the circuits. We also illustrate the usefulness of our approach in multiple application domains such as query evaluation in probabilistic databases, and in deletion propagation. Next, we study the possibility of extending the circuit approach to the more general framework of semiring annotations introduced in earlier work. We show that for a large and useful class of provenance semirings, we can construct in PTIME poly-size circuits that capture the provenance.