The combinational complexity of equivalence

Consider the Boolean functions and$\text{(n)=}\text{?}\text{i=1}\text{n}\text{x}{}_{\mathrm{i}}\text{nor}\text{(n)=}\text{?}\text{i=1}\text{n}\text{¬ x}{}_{\mathrm{i}}$ and the equivalence Eq(n)=and (n)∨nor(n). Let L (F) be the smallest number of arbitrary binary Boolean operations that are used in any Boolean computation for F. We prove L(Eq(n))=2n ?3, L (and(n), nor(n))=2n?2. There exist many structurally different optimal computations for Eq (n).