A polynomial algorithm for recognizing the membership of a function of $k$-valued logic realized by a polynomial in precomplete classes of self-dual functions

Properties of polynomials modulo $k$ for self-dual functions of $k$-valued logic are investigated (if $k$ is a prime number). It is proved that there exists an algorithm which with polynomial time complexity determines whether a function of $k$-valued logic, realized by a polynomial modulo $k$, belongs to a precomplete class of self-dual functions.