Restricted branching programs are considered in complexity theory in order to study the space complexity of sequential computations and in applications as a data structure for Boolean functions. In this paper (direct +, k)-branching programs and (V, k)-branching programs are considered, i.e., branching programs starting with a direct +-(or V-)node with a fan-out of k whose successors are k read-once branching programs. This model is motivated by the investigation of the power of nondeterminism in branching programs and of similar variants that have been considered as a data structure. Lower bound methods for these variants of branching programs are presented, which allow to prove even hierarchy results for polynomial size (direct +, k)- and (V, k)-branching programs with respect to k.
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