Orders of discriminator classes in multivalued logic
Sergey Seraphimovich Marchenkov · Mathematical Notes · 2009
For k ≥ 2, discriminator classes, that is, closed classes of functions of k -valued logic containing the ternary discriminator p , are considered. It is proved that any discriminator class has order at most max(3, k ); moreover, the order of any discriminator class containing all homogeneous functions does not exceed max(3, k − 1), and the order of a discriminator class containing all even functions does not exceed max(3, k − 2). All of these three bounds are attainable.