Complexity of sequential implementation of partial Boolean functions

The sequential implementation of systems of Boolean functions by Boolean circuits over an arbitrary finite basis are studied. A circuit implements a system of partial functions if it implements some completely defined system that is a specification (extension) of the initial system. In the sequential implementation of a system, its functions are implemented in turn and every function can use the outputs of the gates of the circuit constructed for the previous functions. The theorem proved that in the case D(f) ⊇ D(g), the sequential implementation of pairs (f', g') from ℜ in the order f', g' gives asymptotically the same complexity as simultaneous implementation.