Abstract:
For the multivalued logic $P_k$, where $k=p^r$, $p$ is a prime number and $r\ge2$, we describe some families of closed classes which
contain the class $\operatorname{Pol}_k$ of polynomials and are contained in
the class $\mathfrak M_k$ of the functions preserving
congruence modulo $d=p^j$, $j=1,\dots,r-1$.
These classes are closely related to subsets of the special complete system
of the class $\mathfrak M_k$. We reveal a significant difference between the
cases where $p=2$ and $p=3$.
This research was supported by the Russian Foundation for Basic Research,
grant 94–01–01206.