Binary periodic signals and flows: Chapters 1-9

The concept of boolean autonomous deterministic regular asynchronous system has its origin in switching theory, the theory of modeling the switching circuits from the digital electrical engineering. The attribute boolean vaguely refers to the Boole algebra with two elements; autonomous means thatthere is no input; determinism means the existence of a unique (state) function; and regular indicates the existence of a function that ’generates’ the system. Time is discrete:or continuous.The system, which is analogue to the (real, usual) dynamical systems, iterates (asynchronously) its coordinates independently on the others. The fl‡ows are these that result by analogy with the dynamical systems.The ’nice ’discrete time and real time functions that the (boolean) asynchronous systems work with are called signals and periodicity is a very important feature in Nature.In the first two Chapters we give the most important concepts concerning the signals and periodicity. The periodicity properties are used to characterize the eventually constant signals in Chapter 3 and the constant signals in Chapter 4. Chapters 5,...,8 are dedicated to the eventually periodic points, eventually periodic signals, periodic points and periodic signals. Chapter 9 shows constructions that, given an (eventually) periodic point, by changing some values of the signal, change the periodicity properties of the point