Article collection "Mathematical Problems of Cybernetics" №18, Moscow, 2013

Authors:Mikhailets E.V.

On the rank of implicit representations of k-valued logic functions over the class of monotone functions

Abstract:

The article considers implicit representations of k-valued logic functions: a function is represented as the unique solution of a system of equations over a closed function class. The rank of a function is the smallest number of equations sufficient for its representation. The maximum of n-variable functions' ranks is called the rank function. For functions implicitly representable over the class of monotone kvalued logic functions with a linear order, an exact expression for the rank function is obtained.

Keywords:

k-valued logic, implicit representation, monotone functions, linear order, rank function