Fast analysis of the minimal decision algorithm from non-unate loops of the Karnaugh map

Abstract

Extending to multiple-output logic functions, the similarity between the two-input MUX network and the binary decision tree and progressively analysing the pairs of loops created by splitting the Karnaugh map, leads to a simple expression for the number of tests at any level. This number is related to the number of non-unate loops, i.e. the loops receiving different states, that appear at any step of the splitting procedure; duplicates are also identified on the Karnaugh map and a graphical criterion for the minimal number of tests is found. Examples are presented.