In giving a formal definition of Boolean circuits, Vollmer starts by defining a basis as set "B" of Boolean functions, corresponding to the gates allowable in the circuit model. A Boolean circuit over a basis "B", with "n" inputs and "m" outputs, is then defined as a finite directed acyclic graph. Each vertex corresponds to either a basis function or one of the inputs, and there is a set of exactly "m" nodes which are labeled as the outputs. The edges must also have some ordering, to distinguish between different arguments to the same Boolean function.