Several remarks on the complexity of set-valued switching functions

We explore the complexity of circuits that implement set-valued logic functions on a complete basis that we propose in this paper. This basis is related to the bases used in the main sources on this subject, as we show in Section 2. After discussing properties of the constituents of this basis (which consist of both Boolean and non-Boolean components) we prove that almost all set-valued functions require a large number of Boolean components.