Almost the same types of restricted branching programs (or binary decision diagrams BDDs) are considered in complexity theory and in applications like hardware verification. These models are read-once branching programs (free BDDs) and certain types of oblivious branching programs (ordered and indexed BDDs with k layers). The complexity of the satisfiability problem for these restricted branching programs is investigated and tight hierarchy results are proved for the classes of functions representable by k layers of ordered or indexed BDDs of polynomial size.
