Several models of restricted branching programs or binary decision diagrams have a lot of applications in hardware verification. These models are investigated here from a complexity theoretical viewpoint. Because of depth restrictions projections are not suitable as reduction type and have to be restricted to read-once projections. Several types of polynomial-size binary decision diagrams have complete problems with respect to polynomial read-once projections. On the contrary it can be proved that the classes of polynomial-size decision trees and polynomial-size read-once branching programs or free binary decision diagrams do not have such complete problems.