Representation of geometric types of Boolean functions in three variables by algebraic threshold functions

Algebraic threshold functions are defined in the article. It is shown that the class $AT_n^k$ of all $k$-valued algebraic threshold functions in $n$ variables includes the class of $k$-valued ordinary threshold functions in $n$ variables and is much greater than it. It is proved that, for $k=2$ and $n=3$, the only geometric type is determined by a function which is not an algebraic threshold one, but others belong to the class $AT_3^2$. Algebraic threshold functions are simply realized in different computing areas, including the perspective optical ones, what makes important researching them for the synthesis of highspeed information processing systems.