Bounds of non-monotone complexity for the multi-valued logic functions

The non-monotone complexity of realization of $k$-valued logic functions by circuits in a special basis was investigated. The basis consists of elements of two types: the first type comprises all monotone functions (with respect to the order $0<1<2<\cdots <k-1$) with zero weight; the second type includes non-monotone elements with unit weight, the non-empty set of which is finite. The upper and lower bounds of non-monotone complexity (the minimum number of non-monotone elements) for an arbitrary $k$-valued logic function were established. The difference between the upper and lower bounds does not exceed a universal constant. The difference between the best upper and lower bounds known before is a constant that depends on the basis. The range of values for these constants is infinite.