  Sentential decision diagrams (SDDs) introduced by Darwiche in 2011 are a
promising representation type used in knowledge compilation. The relative
succinctness of representation types is an important subject in this area. The
aim of the paper is to identify which kind of Boolean functions can be
represented by SDDs of small size with respect to the number of variables the
functions are defined on. For this reason the sets of Boolean functions
representable by different representation types in polynomial size are
investigated and SDDs are compared with representation types from the classical
knowledge compilation map of Darwiche and Marquis. Ordered binary decision
diagrams (OBDDs) which are a popular data structure for Boolean functions are
one of these representation types. SDDs are more general than OBDDs by
definition but only recently, a Boolean function was presented with polynomial
SDD size but exponential OBDD size. This result is strengthened in several
ways. The main result is a quasipolynomial simulation of SDDs by equivalent
unambiguous nondeterministic OBDDs, a nondeterministic variant where there
exists exactly one accepting computation for each satisfying input. As a side
effect an open problem about the relative succinctness between SDDs and free
binary decision diagrams (FBDDs) which are more general than OBDDs is answered.
