One approach to decoding monotone logical function

We consider the problem of decoding a two-valued monotone function $f$ defined on a $k $-valued $n $-dimensional cube. The traditional approach to solving this problem is to construct a Shannon-optimal algorithm. The Shannon-optimal decoding algorithm has minimal “worst-case” complexity (efficient for the most difficult case). The authors propose and study an approach to the decoding problem based on the application of an asymptotically optimal dualization algorithm over the product of $k $-valued chains. The asymptotically optimal decoding of the function $f$ is aimed at the “typical case” (typical version of the problem). The conditions for the applicability of the traditional and new approaches are experimentally revealed.