 implemented via an equipment built out of a few building blocks (let us indicate them as b1, b2, by), all operating on a subset of the elements constituting a. A layered representation of the function F(x) can be achieved as follows. Let us imagine to identify a first set of functions 81182 simpler than F(x), but still complex than b1, b2, bn. Let us also assume that F(x) can be implemented by a finite num- ber of applications of the functions 81, 82 to the input . In the language of the layering model, it is said that there is a client server relationship between F(x) and 81, 82, or that the functions are at the lower layer with respect to F(x). This relationship can also graphically represented with a graph like those in Figure 3.17. Since there is no physical device implementing directly the functions g1, 82 each of them has to be further decomposed into simpler elements and this procedure has to be repeated as shown in Figure 3.10 up to a layer in which the considered functions are directly performed by the available physical building blocks. At that point, the layered decomposition is terminated and every function in a layer can be built by using the functions of the bottom layer, up to achieving the target function F(x). Networks Fundamentals and Present Architectures Complex Functions of layer 3 function Functions of layer 2 Functions of layer 1 Physical elements realizing simple functions FIGURE 3.17 Graphical scheme of the layered model of a complex system. Thus, F(x) can be synthesized by traveling the layered model bottom up and at the end it will result in its implementation by the available simple physical elements. Up to now no news, the technique of dividing a complex problem into simpler elements is diffused in all the engineering fields. The strength of the layering technique is that it gives a structured procedure to carry the synthesis of complex functions through its for- malism, which has to be somehow adapted to the particular field of application. Here we will not introduce in a completely