Improving the characterization of p-valued threshold functions

Renewed interest in multiple-valued threshold logic in recent years, from the point of view of neural networks, motivates the return to deepen research on multiple-valued threshold logic. Realizations of threshold logic are based on a partition of the set of multiple-valued functions of a given arity and tables of characterizing parameters of each block of the equivalence relation. Any improvement on the equivalence relation contributes to reduce the size of the table. The paper strengthens the idea of semidual functions introduced in the early seventies for symmetric ternary threshold logic, extends it to p-valued logic and shows that realization tables would be reduced by ca. 50%