Classification under permutations of the ternary functions of two variables

The paper presents a classification of the ternary functions of two variables by application of the permutation group either to the input variables or to the output, and by the interchange of the input variables. A set of invariants for the characterisation of the equivalence classes resulting from this classification is introduced, and also an algorithm for their calculation. As an alternative characterisation, the canonical function for each equivalence class is defined. The algorithm for the calculation of the invariants allows us to obtain the transformations that lead from a given function to any other function in its equivalence class. The classification procedure allocates each of the 19683 ternary functions of two variables to one of 84 equivalence classes; these are given, indicating the invariants and the canonical function corresponding to each.