On the Relation between Boolean Curve Fitting and the Inverse Problem of Boolean Equations

This paper explores the similarities and differences between two prominent problems in the mathematics of Boolean functions. The first of these problems is that of Boolean curve fitting (BCF), also known as Boolean interpolation, which deals with constructing a curve 𝑧=𝑓(𝐗) through a number of points z𝑘=𝑓(𝐗𝑘) where 𝑘=1,2,…,𝑚. The second problem is the Inverse Problem of Boolean equations (IPBE), which constructs a Boolean function whose zeroes are all known. While the problem of Boolean curve fitting might require a consistency condition for its solution, the Inverse Problem of Boolean equations might use a consistency condition as an input. Without a consistency condition, the Inverse Problem of Boolean equations can be viewed as a special case of the problem of Boolean curve fitting, provided the specified points z𝑘 are the only zeros of 𝑓(𝐗). Our findings are illustrated via a detailed typical example.