  In this paper, we consider situations in which a given logical function is
realized by a multithreshold threshold function. In such situations, constant
functions can be easily obtained from multithreshold threshold functions, and
therefore, we can show that it becomes possible to optimize a class of
high-order neural networks. We begin by proposing a generating method for
threshold functions in which we use a vector that determines the boundary
between the linearly separable function and the high-order threshold function.
By applying this method to high-order threshold functions, we show that
functions with the same weight as, but a different threshold than, a threshold
function generated by the generation process can be easily obtained. We also
show that the order of the entire network can be extended while maintaining the
structure of given functions.
