Minimal synthesis of multivalued functions with new operators

The operators ? and ? for multivalued logic are examined. While ? has been originally proposed the literature, in connection with fuzzy logic, a is introduced here. Simple implementations of these operators in the form of I?2 L 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 the ones of binary logic. The minimization process leads to simple circuits for arbitrary functions.