Classification of Ternary Logic Functions by Self-Dual Equivalence Classes

Remarks on Applications of Shapes of Decision Diagrams in Classification of Multiple-Valued Logic Functions

“…A brute force search shows that there can be MDDs with 29 different shapes [12]. For n = 3 and n = 4, there are 982205208 and 2376042139520266057185384126838871 ∼ 2 · 10 33 classes out of approximately 7.6·10 12 and 4.4·10 38 functions [8]. We conjecture that the number of different shapes of MDDs will be considerably smaller, since an MDD of the given shape can represent many functions as can be seen from the following example.…”

“…In [8], proposed are three classifications of ternary functions. The strongest among them in terms of the number of different classes, the NP S-classification, is defined by the analogy to the NP N-classification of binary functions.…”

“…In classification by the shape of MDDs, for n = 1, there are also three classes, since we can distinguish three MDDs consisting of a non-terminal node and at most three constant nodes. If the function is a constant For n = 2, in NP S-classification of ternary functions, there are 84 different classes [8]. A brute force search shows that there can be MDDs with 29 different shapes [12].…”

Discrete and Continuous Systems of Logic in Nuclear Magnetic Resonance

“…An extension of the NPN classification of binary logic functions places the 19,683 different two-input, one-output ternary logic functions into 84 different equivalence classes [13,14] by still allowing the order of the inputs to be The 84 canonical logic functions with two inputs and one output which represent each of the 84 equivalence classes in this type of logic function. These functions can be transformed under the equivalences described in Appendix A to produce all 19,683 functions of this type.…”

“…These functions can be transformed under the equivalences described in Appendix A to produce all 19,683 functions of this type. Each class is numbered based on the order found in previous classifications [13,14]. The number of functions present in each class is given following the class number.…”