Geodesic
Representation of geometric types of Boolean functions in three variables by algebraic threshold functions
Prikladnaâ diskretnaâ matematika, no. 1 (2016), pp. 32-45

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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.
Keywords: threshold functions, multiple-valued logic, algebraical threshold functions, geometric types. 
@article{PDM_2016_1_a2,
     author = {D. A. Soshin},
     title = {Representation of geometric types of {Boolean} functions in three variables by algebraic threshold functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {32--45},
     publisher = {mathdoc},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2016_1_a2/}
}
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D. A. Soshin. Representation of geometric types of Boolean functions in three variables by algebraic threshold functions. Prikladnaâ diskretnaâ matematika, no. 1 (2016), pp. 32-45. http://geodesic.mathdoc.fr/item/PDM_2016_1_a2/