The generalized orthonormal expansion of functions with multiple-valued inputs and some of its applications

The fundamental concept of generalized orthonormal expansion, which generalizes the ring forms of the Shannon expansion to logic with multivalued (MV) inputs and standard trivial functions of an arbitrary number of variables, is introduced. Some applications of the generalized orthonormal expansion are presented, including several generalizations of canonical forms both known from the literature and new. These include a family of canonical tree circuits, which are considered for binary and multivalued input cases. They can be multilevel or flattened to two-level AND-EXOR circuits.<>