In the final form of the Hanson method for the synthesis of ternary threshold functions on r-basis, a weighting vector appears whose coordinates were calculated by a tabular procedure. This must follow a definite ordered sequence since the value of each coordinate depends on the values of some of the previously calculated coordinates.

The original multivalued algebra defined by Post in 1921 [1] included the cyclization operation in its generating set. Up to now the algebra has not been used for the synthesis of ternary digital systems because of two shortcomings: no simple canonical forms are possible, and the cyclization is difficult to implement.

Abstract—This note discusses a particular kind of ternary functional decomposition based on a ternary function ↑ to be performed on the set of composite functions. Such function is closely related to the cycling concept of Postian algebras. A systematic method is given to determine the set of all decompositions of that kind admitted by the function. Such set is called the cyclo-set and it is proved that it is a filter in the partitions lattice. Since any partition of the lattice can be expressed as an intersection of cardinality-2 partitions, it follows that the method consists merely in finding the infimum of the cardinality-2 partitions belonging to the cyclo-set and then determining the filter having this infimum as vertex. The existence of proper subsets of the cardinality-2 partitions set leading to the determination of the ifiter-vertex is discussed, and results obtained for functions of domain-order up to seven are stated. Finally, the total number of cyclo-decompositions for a given partitional structure is calculated.

This paper presents a synthesis method of ternary digital systems by means of a threshold algebra. The method is based on the fact that the K operations of any ternary function can be expressed as threshold operations on a set of functions called midterms. Such midterms can be easily generated from the outputs of the ternary multivibrators described by the authors in a previous paper [4]. The Quine method is extended to the minimization of ternary threshold normal forms. RTL circuits implementing the operations are described, and the threshold design of a fast carry propagation ternary adder is outlined in order to illustrate the method.

A new group of time-delay polynomial approximations are obtained by trial and error methods. The results of the trial and error procedure suggest an analytic method for finding the new approximations. The new approximations and their usable bandwidths are tabulated for second-through sixth-order polynomials. Delay vs. frequency graphs of the fourth-and fifth-order polynomials are compared with several previously published approximations.