Branching programs are a well established computation model for Boolean functions, especially read-once branching programs have been studied intensively. In this paper the expressive power of nondeterministic read-once branching programs, i.e., the class of functions representable in polynomial size, is investigated. For that reason two restricted models of nondeterministic read-once branching programs are defined and a lower bound method is presented. Furthermore, the first exponential lower bound for integer multiplication on the size of a nondeterministic nonoblivious read-once branching program model is proven.
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