Structure and Function in Polyfunctional Nets

Abstract—This paper investigates various aspects of functional and structural complexity in Boolean polyfunctional nets. These are nets each of whose constituent elements are capable of performing any single function from a prescribed set of functions assigned to the element. Such nets are characterized in the paper as functionally redundant, universal, ultrastable, perfect, imperfect, etc. These descriptors are measures of net function complexity and describe, in general, the range over which net function varies as the function of each element varies over its assigned set of functions. For example, in a net which is functionally ultrastable, any allowable variation in element function produces no variation in net function. In a net which is functionally perfect, every variation in element function produces a corresponding variation in net function; furthermore, every possible net function is obtained. All nets which are not perfect are called imperfect.