An algebraic generalization of the well-known binary q-function array to a multivalued q-function array is presented. It is possible to associate tree-structure realizations for binary q-functions and multivalued q-functions. Synthesis of multivalued functions using this array is very simple.

A nonexhaustive procedure for obtaining minimal Reed-Muller canonical (RMC) forms of switching functions is presented. This procedure is a modification of a procedure presented earlier in the literature and enables derivation of an upper bound on the number of RMC forms to be derived to choose a minimal one. It is shown that the task of obtaining minimal RMC forms is simplified in the case of symmetric functions and self-dual functions.

Canonical forms for m-valued functions referred to as m-Reed–Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ⊕m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

If a set of connectives is not functionally complete, then there is no simple way of deciding whether or not an arbitrary truth-function is expressible by a proposition-letter formula which has only the connectives in this set. In order to assert that a set of connectives is not complete with respect to a particular truth-function, it is often necessary to give a formal proof by some inductive argument. To come up with such an inductive argument is not always easy. An algorithm by which the expressive power of a set of connectives may be determined is described.