Functions on finite sets of cardinality k and their values at points of a mesh with width d, d|k, are considered. In the previous paper of the author (MPC, iss. 7, 1998) property of preserving the first-order d-differences by classes of such functions preserving d-differences defined in terms of these values. Functions preserving d-differences and their classes closed with respect to the superposition operations were introduced. In the present paper study of these classes is continued. Formulae for their elements, generating sets of the classes are being found, the lattice of the classes with respect to inclusion is being constructed.

k-valued logics, finite differences, functions superposition, closed classes, generating set, lattice with respect to inclusion

Mathematical problems and theory of numerical methods