A compositional algebra for multi-valued switching systems is presented. The algebra is based on a basic set consisting of the sum, product, cycling and inverter operations.

It is shown that simple canonical forms are obtainable, which serve as the starting point of a minimization process for general switching functions.

An algorithmic procedure is developed to allow straightforward optimization of the functions into near-minimal "sum of products of sums" forms. Starting with an initial set of covers that describe the given function, the algorithm generates a set of covers of "cover implicants" and merges them into a transfer cover. The optimized form of the transfer cover allows direct implementation of the function into a near-minimal form.

Possibilities of further reduction in cost when multi-stage implementation is feasible, are discussed.