NPN-representatives of a set of optimal boolean formulas

For an arbitrary set B of Boolean functions satisfying a certain condition, we give a general method of constructing a class C_B of read-once Boolean formulas over the basis B that has the following property: For any F in CB, F can be transformed to an optimal formula (i.e., a simplest formula over the standard basis {AND,OR,NOT}) by replacing each occurrence of a basis function h ∈ B in F with an optimal formula for h. For a particular set of basis functions B^* = {AND,OR,NOT,XOR,MUX}, we give a canonical form representation for C_B ^* so that the set of canonical form formulas consists of only NPNr epresentatives in C _B ^*.