  The evaluation of a query over a probabilistic database boils down to
computing the probability of a suitable Boolean function, the lineage of the
query over the database. The method of query compilation approaches the task in
two stages: first, the query lineage is implemented (compiled) in a circuit
form where probability computation is tractable; and second, the desired
probability is computed over the compiled circuit. A basic theoretical quest in
query compilation is that of identifying pertinent classes of queries whose
lineages admit compact representations over increasingly succinct, tractable
circuit classes. Fostering previous work by Jha and Suciu (2012) and Petke and
Razgon (2013), we focus on queries whose lineages admit circuit implementations
with small treewidth, and investigate their compilability within tame classes
of decision diagrams. In perfect analogy with the characterization of bounded
circuit pathwidth by bounded OBDD width, we show that a class of Boolean
functions has bounded circuit treewidth if and only if it has bounded SDD
width. Sentential decision diagrams (SDDs) are central in knowledge
compilation, being essentially as tractable as OBDDs but exponentially more
succinct. By incorporating constant width SDDs and polynomial size SDDs, we
refine the panorama of query compilation for unions of conjunctive queries with
and without inequalities.
