Relationships between Post and Boolean Algebras with Application to Multi-Valued Switching Theory.

The fundamentals of Post algebras are presented along with extensions that will be useful in a proposed multi-valued switching theory. A detailed examination of Post and Boolean functions is presented along with a functional representation that facilitates the comparison of Post and Boolean algebras. It is shown that Boolean functions of one variable can be represented as Post functions. The general relationships between Post and Boolean algebras are examined. The structure of Boolean subalgebras of Post algebras is discussed, with particular emphasis placed on algebras which are composed of Boolean and Post functions. A transformation between sets of Boolean functions and Boolean algebras of vectors is presented along with a further transformation from the Boolean algebras of vectors to sets of Post functions. The structure of equivalence classes of Post functions and their relationship to Boolean functions is examined. (Author)