Minimal synthesis of multivalued functions with new operators

The operators pi and sigma for multivalued logic are examined. While pi has been originally proposed in the literature, in connection with fuzzy logic, sigma is introduced here. Simple implementations of these operators in the form of I²L circuits are also proposed, with examples for four-valued logic. A simple algebraic treatment leads to the definition of a minimal form for any given function, that is, a form which includes the minimum number of operators. A procedure to derive a minimal form is also outlined, based on concepts which are extensions of those of binary logic. The minimisation process leads to simple circuits for arbitrary functions.