Boolean Curve Fitting With The Aid Of Variable-Entered Karnaugh Maps

The Variable-Entered Karnaugh Map is utilized to grant a simpler view and a visual perspective to Boolean curve fitting (Boolean interpolation); a topic whose inherent complexity hinders its potential applications. We derive the function(s) through m points in the Boolean space Bn+1 together with consistency and uniqueness conditions, where B is a general `big' Boolean algebra of l >= 1 generators, L atoms (2(l-1) < L <= 2(l)) and 2(L) elements. We highlight prominent cases in which the consistency condition reduces to the identity (0 = 0) with a unique solution or with multiple solutions. We conjecture that consistent (albeit not necessarily unique) curve fitting is possible if, and only if, m = 2(n). This conjecture is a generalization of the fact that a Boolean function of n variables is fully and uniquely determined by its values in the {0,1}(n) subdomain of its B-n domain. A few illustrative examples are used to clarify the pertinent concepts and techniques.